Exercises-HYP-1824805.ipynb

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   "source": [
    "# Programming Lesson and Exercises - HYP\n",
    "\n",
    "The goal of these programming lesson and exercises is to teach you how to do hypothesis testing with *Python* and the `StatsModels` library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "This notebook has the following structure:\n",
    "\n",
    "- The first part introduces the concepts for this week. The theory is interleaved with small exercises, which have the goal of letting you practice the concepts that were just intruduced.\n",
    "- At the end there are one or more larger exercises, which have the goal to test what you have learned earlier. These will be more difficult and will require more independent work than the exercises in the first part.\n",
    "\n",
    "All exercises can be solved with the concepts that were introduced earlier. Since there are often more than one correct way to solve a programming problem, we try to accept various correct anwers. However, many of the automatic tests in Momotor (see _How to submit your work_ below) assume that your answers are constructed using the concepts introduced in these notebooks. If you look for answers on the Internet (e.g. if you import other libraries) you run the risk that your answers will be rejected.\n",
    "\n",
    "Some of the small exercises can be solved by copy-pasting code from the examples. However, it is up to you to try to solve the exercises yourself, which will help you learn, before copy-pasting the answers. The ease of looking up answers is meant to provide guidance when you get stuck, especially for those of you who are new to programming.\n",
    "\n",
    "For your convenience, in the `support` directory you will find a summary of the Python methods introduced in this notebook.\n"
   ]
  },
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   "source": [
    "\n",
    "# Introduction to This Template Notebook\n",
    "\n",
    "* This is a **personal** notebook.\n",
    "* Make sure you work in a **copy** of `...-template.ipynb`,\n",
    "**renamed** to `...-yourIDnr.ipynb`,\n",
    "where `yourIDnr` is your TU/e identification number.\n",
    "\n",
    "<div class=\"alert alert-danger\" role=\"danger\">\n",
    "<h3>Integrity</h3>\n",
    "<ul>\n",
    "    <li>In this course you must act according to the rules of the TU/e code of scientific conduct.</li>\n",
    "    <li>All the exercises and the graded assignments are to be executed individually and independently.</li>\n",
    "    <li>You must not copy from the Internet, your friends, books... If you represent other people's work as your own, then that constitutes fraud and will be reported to the Examination Committee.</li>\n",
    "    <li>Making your work available to others (complicity) also constitutes fraud.</li>\n",
    "</ul>\n",
    "</div>\n",
    "\n",
    "You are expected to work with Python code in this notebook.\n",
    "\n",
    "The locations where you should write your solutions can be recognized by\n",
    "**marker lines**,\n",
    "which look like this:\n",
    "\n",
    ">`#//`\n",
    ">    `BEGIN_TODO [Label]` `Description` `(n points)`\n",
    ">\n",
    ">`#//`\n",
    ">    `END_TODO [Label]`\n",
    "\n",
    "<div class=\"alert alert-warning\" role=\"alert\">Do NOT modify or delete these marker lines.  Keep them as they are.<br/>\n",
    "NEVER write code <i>outside</i> the marked blocks.\n",
    "Such code cannot be evaluated.\n",
    "</div>\n",
    "\n",
    "Proceed in this notebook as follows:\n",
    "* **Read** the text.\n",
    "* **Fill in** your solutions between `BEGIN_TODO` and `END_TODO` marker lines.\n",
    "* **Run** _all_ code cells (also the ones _without_ your code),\n",
    "    _in linear order_ from the first code cell.\n",
    "\n",
    "**Personalize your notebook**:\n",
    "1. Copy the following three lines of code:\n",
    "\n",
    "  ```python\n",
    "  AUTHOR_NAME = 'Your Full Name'\n",
    "  AUTHOR_ID_NR = '1234567'\n",
    "  AUTHOR_DATE = 'YYYY-MM-DD'\n",
    "  ```\n",
    "1. Paste them between the marker lines in the next code cell.\n",
    "1. Fill in your _full name_, _identification number_, and the current _date_ (i.e. when you first modified this notebook, e.g. '2022-02-06') as strings between the `Author` markers.\n",
    "1. Run the code cell by putting the cursor there and typing **Control-Enter**.\n"
   ]
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       "('Ben Lentschig', '1824805', '2024-12-10')"
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   "source": [
    "#// BEGIN_TODO [Author] Name, Id.nr., Date, as strings (1 point)\n",
    "\n",
    "AUTHOR_NAME = 'Ben Lentschig'\n",
    "AUTHOR_ID_NR = '1824805'\n",
    "AUTHOR_DATE = '2024-12-10'\n",
    "\n",
    "#// END_TODO [Author]\n",
    "\n",
    "AUTHOR_NAME, AUTHOR_ID_NR, AUTHOR_DATE"
   ]
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   "source": [
    "## Table of Contents\n",
    "\n",
    "- [Introduction](#Introduction)\n",
    "    - [Concepts and Terminology](#Concepts-and-Terminology)\n",
    "    - [Steps to Address the Problem](#Steps-to-Address-the-Problem)\n",
    "- [Loading the Libraries](#Loading-the-Libraries)\n",
    "- [1. Hypothesis Testing for Equality of Means](#1.-Hypothesis-Testing-for-Equality-of-Means)\n",
    "    - [Learning Objectives of This Section](#Learning-Objectives-of-This-Section)\n",
    "    - [Example: Speed of Light](#Example:-Speed-of-Light)\n",
    "    - [Step 1 (Speed of Light): Define Quantitative Question](#Step-1-(Speed-of-Light):-Define-Quantitative-Question)\n",
    "    - [Step 2 (Speed of Light): Formulate Hypothesis](#Step-2-(Speed-of-Light):-Formulate-Hypothesis)\n",
    "    - [Step 3 (Speed of Light): Check Assumptions](#Step-3-(Speed-of-Light):-Check-Assumptions)\n",
    "        - [Kernel Density Plot](#Kernel-Density-Plot)\n",
    "        - [Q-Q Plot](#Q-Q-Plot)\n",
    "        - [Anderson-Darling Normality Test](#Anderson-Darling-Normality-Test)\n",
    "    - [Step 4 (Speed of Light): Apply Appropriate Test](#Step-4-(Speed-of-Light):-Apply-Appropriate-Test)\n",
    "        - [t-test for Equality of Means (One-sample)](#t-test-for-Equality-of-Means-(One-sample))\n",
    "        - [t-test for Equality of Means (Two-sample)](#t-test-for-Equality-of-Means-(Two-sample))\n",
    "    - [Step 5 (Speed of Light): Decision](#Step-5-(Speed-of-Light):-Decision)\n",
    "        - [Confidence Interval](#Confidence-Interval)\n",
    "- [Exercise: Cloud Seeding](#Exercise:-Cloud-Seeding)\n",
    "    - [Step 1 (Cloud Seeding): Define Quantitative Question](#Step-1-(Cloud-Seeding):-Define-Quantitative-Question)\n",
    "        - [Exercise 1.a](#Exercise-1.a)\n",
    "    - [Step 2 (Cloud Seeding): Formulate Hypothesis](#Step-2-(Cloud-Seeding):-Formulate-Hypothesis)\n",
    "        - [Exercise 1.b](#Exercise-1.b)\n",
    "    - [Step 3 (Cloud Seeding): Check Assumptions](#Step-3-(Cloud-Seeding):-Check-Assumptions)\n",
    "        - [Exercise 1.c](#Exercise-1.c)\n",
    "        - [Exercise 1.d](#Exercise-1.d)\n",
    "        - [Exercise 1.e](#Exercise-1.e)\n",
    "        - [Exercise 1.f](#Exercise-1.f)\n",
    "        - [Exercise 1.g](#Exercise-1.g)\n",
    "        - [Exercise 1.h](#Exercise-1.h)\n",
    "        - [Exercise 1.i](#Exercise-1.i)\n",
    "    - [Step 4 (Cloud Seeding): Apply Appropriate Test](#Step-4-(Cloud-Seeding):-Apply-Appropriate-Test)\n",
    "        - [Exercise 1.j](#Exercise-1.j)\n",
    "        - [Exercise 1.k](#Exercise-1.k)\n",
    "        - [Exercise 1.l](#Exercise-1.l)\n",
    "    - [Step 5 (Cloud Seeding): Decision](#Step-5-(Cloud-Seeding):-Decision)\n",
    "        - [Exercise 1.m](#Exercise-1.m)\n",
    "- [2. Hypothesis Testing on Proportions](#2.-Hypothesis-Testing-on-Proportions)\n",
    "    - [Learning Objectives of This Section](#Learning-Objectives-of-This-Section)\n",
    "    - [Example: Exams](#Example:-Exams)\n",
    "    - [Step 1 (Exams): Define Quantitative Question](#Step-1-(Exams):-Define-Quantitative-Question)\n",
    "    - [Step 2 (Exams): Formulate Hypothesis](#Step-2-(Exams):-Formulate-Hypothesis)\n",
    "    - [Step 3 (Exams): Check Assumptions](#Step-3-(Exams):-Check-Assumptions)\n",
    "    - [Step 4 (Exams): Apply Appropriate Test](#Step-4-(Exams):-Apply-Appropriate-Test)\n",
    "        - [z-test for Equality of Proportions (One-sample)](#z-test-for-Equality-of-Proportions-(One-sample))\n",
    "        - [z-test for Equality of Proportions (Two-sample)](#z-test-for-Equality-of-Proportions-(Two-sample))\n",
    "        - [Extract the p-value](#Extract-the-p-value)\n",
    "        - [Extract the Confidence Interval (One-sample)](#Extract-the-Confidence-Interval-(One-sample))\n",
    "        - [Extract the Confidence Interval (Two-sample)](#Extract-the-Confidence-Interval-(Two-sample))\n",
    "    - [Step 5 (Exams): Decision](#Step-5-(Exams):-Decision)\n",
    "        - [p-value](#p-value)\n",
    "        - [Confidence Interval](#Confidence-Interval)\n",
    "- [Exercise: Silicon Wafers](#Exercise:-Silicon-Wafers)\n",
    "    - [Exercise 2.a](#Exercise-2.a)\n",
    "    - [Step 1 (Silicon Wafers): Define a Quantitative Question](#Step-1-(Silicon-Wafers):-Define-a-Quantitative-Question)\n",
    "        - [Exercise 2.b](#Exercise-2.b)\n",
    "    - [Step 2 (Silicon Wafers): Formulate Hypothesis](#Step-2-(Silicon-Wafers):-Formulate-Hypothesis)\n",
    "        - [Exercise 2.c](#Exercise-2.c)\n",
    "    - [Step 3 (Silicon Wafers): Check Assumptions](#Step-3-(Silicon-Wafers):-Check-Assumptions)\n",
    "        - [Exercise 2.d](#Exercise-2.d)\n",
    "    - [Step 4 (Silicon Wafers): Apply Correct Test](#Step-4-(Silicon-Wafers):-Apply-Correct-Test)\n",
    "        - [Exercise 2.e](#Exercise-2.e)\n",
    "        - [Exercise 2.f](#Exercise-2.f)\n",
    "- [3. Performing Diagnostics on Regression Results](#3.-Performing-Diagnostics-on-Regression-Results)\n",
    "    - [Learning Objectives of This Section](#Learning-Objectives-of-This-Section)\n",
    "    - [Example: Boiling Point of Water](#Example:-Boiling-Point-of-Water)\n",
    "        - [Model Evaluation](#Model-Evaluation)\n",
    "    - [Exercise: Timber](#Exercise:-Timber)\n",
    "        - [Exercise 3.a](#Exercise-3.a)\n",
    "        - [Exercise 3.b](#Exercise-3.b)\n",
    "        - [Exercise 3.c](#Exercise-3.c)\n",
    "    - [First Order Polynomial Model](#First-Order-Polynomial-Model)\n",
    "        - [Exercise 3.d](#Exercise-3.d)\n",
    "        - [Exercise 3.e](#Exercise-3.e)\n",
    "        - [Exercise 3.f](#Exercise-3.f)\n",
    "        - [Exercise 3.g](#Exercise-3.g)\n",
    "        - [Exercise 3.h](#Exercise-3.h)\n",
    "    - [Better Model](#Better-Model)\n",
    "        - [Exercise 3.i](#Exercise-3.i)\n",
    "        - [Exercise 3.j](#Exercise-3.j)\n",
    "        - [Exercise 3.k](#Exercise-3.k)\n",
    "        - [Exercise 3.l](#Exercise-3.l)\n",
    "        - [Exercise 3.m](#Exercise-3.m)\n",
    "- [4. Exercise: Hypothesis Testing](#4.-Exercise:-Hypothesis-Testing)\n",
    "    - [Exercise 4.a](#Exercise-4.a)\n",
    "    - [Exercise 4.b](#Exercise-4.b)\n",
    "    - [Exercise 4.c](#Exercise-4.c)\n",
    "    - [Exercise 4.d](#Exercise-4.d)\n",
    "    - [Exercise 4.e](#Exercise-4.e)\n",
    "    - [Exercise 4.f](#Exercise-4.f)\n",
    "- [5. Exercise: Regression Analysis](#5.-Exercise:-Regression-Analysis)\n",
    "    - [Exercise 5.a](#Exercise-5.a)\n",
    "    - [Exercise 5.b](#Exercise-5.b)\n",
    "    - [Exercise 5.c](#Exercise-5.c)\n",
    "    - [Exercise 5.d](#Exercise-5.d)\n",
    "    - [Exercise 5.e](#Exercise-5.e)\n",
    "    - [Exercise 5.f](#Exercise-5.f)\n",
    "    - [Exercise 5.g](#Exercise-5.g)"
   ]
  },
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   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "In this lesson,\n",
    "we explain how to do\n",
    "hypothesis testing with Python and _StatsModels_ for (all combinations of)\n",
    "\n",
    "* _one-sided_ and _two-sided_ tests,\n",
    "* with _one-sample_ and _two-sample_ data,\n",
    "* for _equality of means_ and for _equality of proportions_.\n",
    "\n",
    "We explain how to check the underlying normality assumption on the data.\n",
    "\n",
    "In addition we explain how to perform diagnostics on a regression model.\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concepts and Terminology\n",
    "\n",
    "The following items are needed for statistical hypothesis testing.\n",
    "Sometimes, items are just given, but in other cases, you will have to do some work to obtain them.\n",
    "    \n",
    "1. **Null hypothesis $H_0$**\n",
    "    (the \"there-is-nothing-special-to-this-and-it-is-all-just-coincidence\" assumption) and\n",
    "    **alternative hypothesis $H_a$** (the \"there-is-something-special-to-this\" assumption).\n",
    "\n",
    "2. **Level of significance**, also known as $\\alpha$-value.\n",
    "    Typically, $\\alpha = 0.05$.  \n",
    "    It is the probability of a _Type-I error_ that one is willing to accept,\n",
    "    that is, the probability that the null hypothesis will be rejected while it is actually true.\n",
    "\n",
    "3. **Test statistic**,\n",
    "    a value calculated from the observed data according to a standardized formula,\n",
    "    that depends on the type of test being applied.\n",
    "\n",
    "4. **p-value** (probability of the observed data under the assumption of the null hypothesis)\n",
    "    and/or **confidence interval**\n",
    "    (an interval estimated from the observed data that contains the actual value with a given\n",
    "    probability, the level of confidence, which is typically $1 - \\alpha$).\n",
    "    \n",
    "The decision rule is this.\n",
    "If, under the assumption that the null hypothesis holds, the probability of the observed data\n",
    "is less than $\\alpha$,\n",
    "then the null hypothesis is _rejected_;\n",
    "that is, the observed data is considered statistically significant ('special')\n",
    "under the null hypothesis;\n",
    "that is, the observed data is not likely to be explained by coincidence under the null hypothesis.\n",
    "\n",
    "Equivalently, this is the case if and only if\n",
    "\n",
    "* the computed p-value is less than the significance level\n",
    "\n",
    "and also if and only if\n",
    "\n",
    "* the computed test statistic lies within the confidence interval."
   ]
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   "source": [
    "### Steps to Address the Problem\n",
    "\n",
    "In the lecture you were shown how to address scientific problems. We will now formalize 5 steps to address these problems.\n",
    "1. Define quantitative question\n",
    "2. Formulate Hypothesis\n",
    "3. Pick correct test and test if its assumptions are met\n",
    "4. Apply correct test\n",
    "5. Decision on hypothesis\n",
    "\n",
    "These steps will be further explained in the rest of this exercise set."
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Loading the Libraries\n",
    "\n",
    "To show examples, we load some Data Analytics libraries first:"
   ]
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    "import numpy as np  # import auxiliary library, typical idiom\n",
    "import pandas as pd  # import the Pandas library, typical idiom\n",
    "\n",
    "# next command ensures that plots appear inside the notebook\n",
    "%matplotlib inline\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = 10, 5  # default hor./vert. size of plots, in inches\n",
    "plt.rcParams['lines.markeredgewidth'] = 1  # to fix issue with seaborn box plots; needed after import seaborn\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set()  # set Seaborn defaults\n",
    "\n",
    "from sklearn.linear_model import LinearRegression  # for linear regression\n",
    "\n",
    "# reveal a hint only while holding the mouse down\n",
    "from IPython.display import HTML\n",
    "HTML(\"<style>.h,.c{display:none}.t{color:#296eaa}.t:active+.h{display:block;}</style>\")"
   ]
  },
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   "source": [
    "Next we load the _StatsModels_ library for doing statistics in Python (ignore the `FutureWarning`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 1. Hypothesis Testing for Equality of Means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning Objectives of This Section\n",
    "\n",
    "After this section, you should\n",
    "\n",
    "* know how to do _one-sided_ and _two-sided_ tests for **equality of the means**\n",
    "    of _one-sample_ and _two-sample_ data\n",
    "* know how to test whether data follows a normal distribution using\n",
    "\n",
    "  * a density plot\n",
    "  * a Q-Q plot\n",
    "  * the Anderson-Darling test statistic\n",
    "* know how to draw conclusions about acceptance or rejection of the null hypothesis based on:\n",
    "  * p-value resulting from the t-test\n",
    "  * Confidence intervals\n",
    "    "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Speed of Light\n",
    "\n",
    "In the 19th century,\n",
    "French physicists Fizeau and Foucault independently invented ways to measure the speed of light in vacuum.\n",
    "Foucault's method turned out to be the most accurate one.\n",
    "The Foucault method is based on fast rotation mirrors.\n",
    "The American physicists Michelson and Newcomb improved Foucault's method. \n",
    "The data set `datasets/light_michelson.csv` contains measurements by Michelson from 1880 and `datasets/light_newcomb.csv` contains measurements by Newcomb from 1882."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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   "source": [
    "df_michelson = pd.read_csv(\"datasets/light_michelson.csv\")\n",
    "df_michelson.head()"
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    }
   ],
   "source": [
    "df_newcomb = pd.read_csv(\"datasets/light_newcomb.csv\")\n",
    "df_newcomb.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 (Speed of Light): Define Quantitative Question\n",
    "\n",
    "We wish to test whether Newcombs measurements where accurate. The speed of light in vacuum is defined to be 299 792.458 km/s. We can define a quantitative question as follows:\n",
    "\n",
    "> Is Newcomb's estimate of the speed of light significantly different from 299 792.458 km/s?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 (Speed of Light): Formulate Hypothesis\n",
    "\n",
    "As we have seen in the lectures, there are two different types of hypotheses which then define which hypothesis test to choose. We are either interested in the equality of means or in the equality of proportions. It is important to consciously choose between the two.\n",
    "\n",
    "In our case we are interested in the speed of light measured by Newcomb. We want to compare the experimental data mean with the currently known value. Hence we are interested in the **equality of means** on **one-sample** data.\n",
    "\n",
    "As defined in step 1, we are interested in equality. We do not hypothesize Newcombs measurement to be greater or smaller. Therefore we should formulate a **two-sided** alternative hypothesis. \n",
    "\n",
    "In short, we will define a **two-sided** hypothesis for **equality of means** on **one-sample** data.\n",
    "\n",
    "The corresponding hypotheses are\n",
    "\n",
    "$$H_0:\\mu_{newcomb}=299792.458$$\n",
    "\n",
    "$$H_a:\\mu_{newcomb}\\neq299792.458$$ \n",
    "\n",
    "The appropriate test you were taught for this situation is:\n",
    "* **t-test for equality of means**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 (Speed of Light): Check Assumptions\n",
    "\n",
    "As explained in the lecture a **t-test for equality of means** is appropriate under the assumption that the data comes from a normal distribution *or* the dataset is large. If the dataset is small *and* not normally distributed, the test would not be valid. Therefore, before doing the test we should verify that this assumption holds.\n",
    "\n",
    "As a rule of thumb in these exercises, a dataset is considered small if it contains fewer than 50 samples. In general, deciding if a dataset should be considered small is complicated and outside the scope of this course.\n",
    "\n",
    "We present three techniques to test for normality:\n",
    "\n",
    "* A **kernel density plot** (which we already encountered in the EDA exercises)\n",
    "* A **Q-Q plot** (which was mentioned in the EDA Lecture, but not yet practiced)\n",
    "* The **Anderson-Darling normality test**\n",
    "\n",
    "Note that when the dataset is large, normality is not needed for the t-test for equality of means to be valid.\n",
    "\n",
    "In the examples below we will test the `df_newcomb` data for normality. Let's see how large it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_newcomb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since it contains more than 50 samples, strictly speaking we would not need to test for normality before performing the t-test for equality of means. However, we will use it to illustrate the methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Kernel Density Plot\n",
    "\n",
    "This is a visual check, where you compare the kernel density plot of the actual data to the\n",
    "'ideal' bell curve of the normal (or Gaussian) distribution.\n",
    "\n",
    "Let's first set the default figure size to a square aspect ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = 8, 8  # square plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the kernel density plot for Newcomb's measurements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vLSmazNQYPtW4v8g5U/iLSI/UNrZS7Krvk4V9TmX04FS+KDpCq075EzknCn8R6ZFdh44AMGKAeeF/4ZAU2txedh6tRUTOjsJfRHrki6IjRIRbGZQRb1oNw/snYQuz8vkBjfuLnAuFv4j0yK6iIwzLSsQWZt7XRkR4GMOyEth5qNq0GkSCgcJfRLrV0NxGcXk9w02Y5X+8kQOSKXLW6yp/IudA4S8i3dpVdAQDTDnF73gjBiRh0F6TiJwdhb+IdOuLQ0ewhVkZ0i/B7FIY0i+RcJuVnQd16F/kbCn8RaRbXxQdYWi/BMJtfX9+//HCbVaGZSVq3F/kHCj8ReS0GpvdHHLWMWJAktmldBo5MJliVwO1ja1mlyISkHwa/qtWrSI/P58pU6bw4osvnrB9x44dzJo1i7y8PBYsWIDb7QagtLSU2bNnM3XqVO68804aGhoAqK+v595772XmzJnMnDmTzz77zJfliwiwp6QGw8AvJvt1OP/oWgO7dL6/yFnxWfg7nU6WLVvG8uXLKSgo4KWXXmLPnj1dHjN//nwWLlzImjVrMAyDFStWALB48WJuueUWCgsLGT16NE8//TQAS5YsITMzk4KCAv77v/+bhx56yFfli8hRu4uPYLVYGNov0exSOg3KjCcyPIwdOvQvclZ8Fv7r169n4sSJJCUlERMTQ15eHoWFhZ3bS0pKaG5uZty4cQDMmjWLwsJC2tra2LhxI3l5eV3uNwyDtWvXcvvttwOQm5vLY4895qvyReSovSU19HfEmbKe/6nYwqycl53IF9rzFzkrNl+9cHl5OXa7vfO2w+Fg27Ztp9xut9txOp1UV1cTFxeHzWbrcn9lZSUREREsX76cf//730RGRvLAAw+cUU2pqXHn+K76ht1u3gpqgUI96l5v9MjjNThwuI5rLh7gdz0fPzKdv7y+g6jYSOJjIs7qNfztPfkj9ah7gdgjn4W/1+vFYrF03jYMo8vtU20//nEAFosFj8dDRUUF8fHxvPTSS7z//vvcddddvPnmmz2uqbKyHq/XOId35Xt2ezwuV53ZZfg19ah7vdWjQ846mls99EuJ9rue90uOAuCDrSWMG5Z2xs/X56h76lH3/LlHVqvllDu9Pjvsn5GRgcvl6rztcrlwOByn3F5RUYHD4SAlJYW6ujo8Hk+X5yUnJ2Oz2Zg+fToAl19+OY2NjVRW6vKeIr6yt7QWgKFZ/jPe32FQZgJhVgu7i4+YXYpIwPFZ+E+aNIkNGzZQVVVFU1MTa9euJTc3t3N7VlYWkZGRbN68GYCVK1eSm5tLeHg4OTk5rF69GoCCggJyc3OJiIhg0qRJ/POf/wRgy5YtREdHk5xs3hXGRILd3pIa4mPCsSdGmV3KCSLDwxiYEc+e4hqzSxEJOD4L//T0dObNm8ecOXOYOXMm06dPZ8yYMcydO5ft27cDsHTpUpYsWcLUqVNpbGxkzpw5ACxatIgVK1aQn5/Ppk2buOeeewB49NFHWbduHdOnT+ehhx5i2bJlWK1aqkDEV/aW1jK0X+IJQ3H+YlhWIvvL6mhze80uRSSgWAzD8O9B8F6kMf/goB51rzd6VN/Uxt1PvMvXJw9h2mWDeqewXrb5i3KeevVTHvjORQw7w6EJfY66px51z597ZMqYv4gEtr0l7YfTzzRU+9Kw7CQAHfoXOUMKfxE5qb2lNVgtFgZlmH8xn1NJjI3AkRytSX8iZ0jhLyIntbeklmxHrF8t7nMy52UnHl2C2L+H9ET8icJfRE7g9RrsK6v1y1P8jndedhJ1jW04q5vMLkUkYCj8ReQEJRUNtLR6GNrPfw/5d+j4A0Xj/iI9p/AXkRPsL2tf3GeIH13M51QyU2OIjgzrrFlEuqfwF5ETHDhcR3SkDUdytNmldKtjUuK+UoW/SE8p/EXkBAfKahmUEY/VTxf3Od6QfgkUu+ppbfOYXYpIQFD4i0gXbW4vReX1DMwInCuVDclMwOM1OOSsN7sUkYCg8BeRLkoq6vF4DQYFUvgfnZi4r1ST/kR6QuEvIl0cKGtfqnRQpv/P9O+QGBdJakIk+zTpT6RHFP4i0sWBw7XERtn88kp+pzM4U5P+RHpK4S8iXRwoq2NQRrzfXsnvVIb0S6SippnaxlazSxHxewp/EenU5vZQUtEQUIf8OwzObJ+jsF97/yLdUviLSKei8oaAm+zXYVBGAlaLRYf+RXpA4S8inQ4cbg9Of76S36lERoSRZY/VpD+RHlD4i0inA2V1xMeEk5IQaXYpZ2VwZgL7S2t1hT+Rbij8RaTTgcO1DMpICLjJfh2G9EugscWtK/yJdEPhLyIAtLQdnewXgOP9HTpqP3i4zuRKRPybwl9EAChy1mMYMCgzcMO/X1ostjCrwl+kGwp/EQFgfwBP9utgC7PS3xHbOXFRRE5O4S8iABw6XEdCbATJ8YE52a/DwPR4DjrrNelP5DQU/iICwKHyegakx5ldxjkbmBFPU4sb1xFN+hM5FYW/iOD2eCmtaGCAI3DH+zt0DFsc0Li/yCkp/EWE0or2lf2CYc+/X1osYVYLB50Kf5FTUfiLSGdQ9ncEfviH26xk2+M041/kNBT+IkKRs57I8DDSk2PMLqVXDMyI5+DhOk36EzkFhb+IcKi8nmxHLFZrYK7sd7yBGfE0NLuprGk2uxQRv6TwFwlxhmFQVF4XFJP9OnSs9KdJfyInp/AXCXEVNc00tXjoHwST/Tpk2zXpT+R0FP4iIe7Q0YAMpj3/cFsY/dJiNelP5BQU/iIh7pCzHoulfW85mAzMiOeAJv2JnJTCXyTEFZXXk5kaS0R4mNml9KqB6fHUN7VRXddidikifkfhLxLiDpXXMSAIzu8/nib9iZyawl8khNU3tVFV2xJUk/06ZDvisFi+nNMgIl9S+IuEsM7JfunBM9mvQ2R4GBkpMRSV15tdiojfUfiLhLBDzvZgDIZlfU+mvyOu8z2KyJcU/iIhrKi8juT4SBJiIswuxSf6O+KorG2msbnN7FJE/IrCXySEHXLWB+1eP3w5nKFD/yJdKfxFQlRrm4eyysagHO/v0PGHzSGFv0gXCn+REFVS0YDXMILyNL8OibERJMSEU6Rxf5EuFP4iIarjUPiAIDzNr4PFYqG/I06H/UWOo/AXCVGHnHVERYSRlhRtdik+1T89npKKetwer9mliPgNhb9IiCouryfbHofVYjG7FJ8a4IjD7TE4XNVodikifkPhLxKCDMOg2NVAdhCP93fomPSncX+RLyn8RUJQdV0LjS3uoLuS38lkpMZgC7NyqFzL/Ip0UPiLhKCOCXDZ9uDf8w+zWsmyx2rSn8gxFP4iIajYFTrhD+3j/oec9RiGYXYpIn5B4S8SgopdDaQmRBITZTO7lD7R3xFHfVMbR+pbzS5FxC/4NPxXrVpFfn4+U6ZM4cUXXzxh+44dO5g1axZ5eXksWLAAt9sNQGlpKbNnz2bq1KnceeedNDQ0APDRRx9x6aWXMmPGDGbMmMFPfvITX5YvErQ6ZvqHii+X+dW4vwj4MPydTifLli1j+fLlFBQU8NJLL7Fnz54uj5k/fz4LFy5kzZo1GIbBihUrAFi8eDG33HILhYWFjB49mqeffhqATz/9lNtuu42VK1eycuVKlixZ4qvyRYJWm9vL4arGkJjp36HjDx2N+4u081n4r1+/nokTJ5KUlERMTAx5eXkUFhZ2bi8pKaG5uZlx48YBMGvWLAoLC2lra2Pjxo3k5eV1uR9g+/btvPfee1x//fX813/9F2VlZb4qXyRolVU24PEaIbXnHxNlIy0xSpf3FTnKZ+FfXl6O3W7vvO1wOHA6nafcbrfbcTqdVFdXExcXh81m63I/QHx8PN/5zndYtWoVkydPZt68eb4qXyRolbjah9FCac8f0DK/Isfw2Wwfr9eL5ZiVwwzD6HL7VNuPfxzQefvhhx/uvO9b3/oWv/rVr6irqyM+vmdXJUtNDYwvO7s9eK+y1lvUo+6dqkeV9YewhVkZPdyBLSx05vyePziVLXsqiE+IJiqyY+dCn6PuqEfdC8Qe+Sz8MzIy2LRpU+dtl8uFw+Host3lcnXerqiowOFwkJKSQl1dHR6Ph7CwsM7neb1ennnmGW6//XbCwsI6n3fsf3ensrIer9e/T/Wx2+NxuTQp6XTUo+6drke7DlbRLzWG6qqGPq7KXMmxERgGbPvCyeDMBH2OekA96p4/98hqtZxyp9dnf/ZPmjSJDRs2UFVVRVNTE2vXriU3N7dze1ZWFpGRkWzevBmAlStXkpubS3h4ODk5OaxevRqAgoICcnNzsVqtvPHGG6xZs6bz/rFjxxITE+OrtyASlIpd9SF3yB8g29G+mmGxDv2L+C7809PTmTdvHnPmzGHmzJlMnz6dMWPGMHfuXLZv3w7A0qVLWbJkCVOnTqWxsZE5c+YAsGjRIlasWEF+fj6bNm3innvuAeAXv/gFL7zwAtOmTePll1/mkUce8VX5IkGp41z3UJrs18GeFE1EuJUil8JfxGKE0JJXOuwfHNSj7p2qRzsPVvP43z7hv28ay+jBqSZUZq6f/XkjURE25n9rvD5HPaAedc+fe2TKYX8R8T8de739Q3DPHyDLHte5tLFIKFP4i4SQ4vJ64qLDSYiNMLsUU2Tb46hrbKOmQcv8SmhT+IuEkGJXA/0dcSecThsqOi5hrL1/CXUKf5EQ4fUalFTUk3U0AENRx0THEs34lxCn8BcJEa4jTbS2eUN2vB8gITaChJhwil2htcaByPEU/iIhouNQdyie438sTfoTUfiLhIyi8nosQL+00D3sD+1r/JdWtF/cSCRUKfxFQkSJqwFHSgyR4T1fEjsYZdljaXV7cVbq0L+ELoW/SIgoctXTP4Qn+3XomPS3v6zW5EpEzKPwFwkBLa0eXNVNIbms7/H6pcViAQ4q/CWEKfxFQkBJRQMGmuwHEBkehiM5mgMKfwlhCn+RENA501+H/YH2Q//a85dQpvAXCQHF5fVEhoeRlhRtdil+IcseS1llAy1tHrNLETGFwl8kBBS76sm2x2IN0WV9j5dtj8MwoLRCM/4lNCn8RYKcYRgUldeTpcl+nTrmPmixHwlVCn+RIHekvpWGZjf9NdmvkyMpmojwMEq0zK+EKIW/SJDTZL8TWa0WBmTEa89fQpbCXyTIFZdrTf+TGZSRoAv8SMhS+IsEuWJXPcnxkcRGhZtdil8ZmJlAbUMrtQ2tZpci0ucU/iJBrqi8QSv7ncSgzHhAk/4kNCn8RYKY2+OlrLJB4/0nMTAzAUCH/iUkKfxFgpizqhGP19Ce/0kkx0cRHxOuPX8JSQp/kSDWsVebpT3/k8q2x1Gi8JcQpPAXCWLFrnqsFguZqQr/k8myx1JS0YDXMMwuRaRPKfxFgliJq4GM1BjCbfpVP5lsexytbV4qjjSZXYpIn9I3gkgQ61jTX06uYy6EVvqTUKPwFwlSTS1uKmqaNdnvNPqlxQA63U9Cj8JfJEiVHL1incL/1KIibNiTojp7JRIqFP4iQUpr+vdMVlqczvWXkKPwFwlSxeX1REWEkZoYZXYpfi3LHouzqpE2t9fsUkT6jMJfJEgVuxrIssdisVjMLsWvZdvj8HgNDlc1ml2KSJ9R+IsEIcMwKHHVa7y/BzoWQNJiPxJKFP4iQaiqtpmGZrfCvwcyUmIIs1o07i8hReEvEoQOlNUCmuzXE7YwKxmpMdrzl5Ci8BcJQgePhn+W9vx7JNuuGf8SWhT+IkHoQFktSXERxEWHm11KQMhKi6WytpmmFrfZpYj0CYW/SBA6WFan8f4z0LnMrxb7kRCh8BcJMh6vl6LyOrIdCv+e0ox/CTUKf5Eg46xqos3t1WS/M5CaGEVkRJjG/SVkKPxFgsyXy/pqz7+nrBYLWWmx2vOXkKHwFwkyxa56rFYLmana8z8T2fZYil0NGIZhdikiPqfwFwkyxeXty/qG2/TrfSay0uKob2qjtrHN7FJEfE7fDiJBpthVz8CMBLPLCDgdcySKdehfQoDCXySINLW4qahpZlCmwv9MdSyIVKJJfxICFP4iQaT06HnqAxX+ZywhNoKEmHBN+pOQoPAXCSIdh6y15392srTMr4QIhb9IECl2NRAZHoYjOcbsUgJSlj2W0ooGvJrxL0FO4S8SREpc9WTbY7FaLWaXEpCy7XG0tHmoqGk2uxQRn1L4iwQJwzAoKq/XlfzOgZb5lVCh8BcJEkfqW2lodmtZ33PQL7XjdD+N+0tw82n4r1q1ivz8fKZMmcKLL754wvYdO3Ywa9Ys8vLyWLBgAW53++U0S0tLmT17NlOnTuXOO++koaHrL+Lhw4e55JJLKC4u9mX5IgGlRMv6nrPoSBtpiVHa85eg57PwdzqdLFu2jOXLl1NQUMBLL73Enj17ujxm/vz5LFy4kDVr1mAYBitWrABg8eLF3HLLLRQWFjJ69Giefvrpzud4vV4WLFhAW5tW4RI5Vsfeqq7md26y7XE611+Cns/Cf/369UycOJGkpCRiYmLIy8ujsLCwc3tJSQnNzc2MGzcOgFmzZlFYWEhbWxsbN24kLy+vy/0dnn32WSZNmkRycrKvShcJSMWuehLjIoiLDje7lICWZY/lcFUjbo/X7FJEfMbmqxcuLy/Hbrd33nY4HGzbtu2U2+12O06nk+rqauLi4rDZbF3uB/j000/54IMPePbZZ086jNCd1NTA2COy2+PNLsHvqUcnOlzdxJB+iZ29UY+6d7IenT8kjX9uOEiLYSFTPdTnqAcCsUc+C3+v14vF8uXpRoZhdLl9qu3HPw7AYrHQ1NTE4sWLeeKJJ7Baz+6ARWVlPV6vf5+/a7fH43LVmV2GX1OPTuTxejl0uI5rLsrC5apTj3rgVD1KiAwDYPsuJ7G20D5lUp+j7vlzj6xWyyl3en122D8jIwOXy9V52+Vy4XA4Trm9oqICh8NBSkoKdXV1eDyeLs/btGkTlZWV3HnnncyYMYPy8nJuv/129u3b56u3IBIwyqubcHu8muzXCzJSYwizWjTuL0HNZ+E/adIkNmzYQFVVFU1NTaxdu5bc3NzO7VlZWURGRrJ582YAVq5cSW5uLuHh4eTk5LB69WoACgoKyM3N5corr+Stt95i5cqVrFy5EofDwf/+7/8yZMgQX70FkYDROdlP4X/ObGFWMlJiFP4S1HwW/unp6cybN485c+Ywc+ZMpk+fzpgxY5g7dy7bt28HYOnSpSxZsoSpU6fS2NjInDlzAFi0aBErVqwgPz+fTZs2cc899/iqTJGgUFxej8UC/dK0rG9vyLLH6tK+EtQshhE6i1hrzD84qEcnevL/24azupFH504E1KOeOF2PVq0/wKvr9vHUvFyiI302Ncrv6XPUPX/ukSlj/iLSd4rK6+mv8/t7TccqiR2XSBYJNgp/kQDX2NxGZW2zwr8XdVwfoUThL0FK4S8S4IrK28em+zsC71xjf5WWGEVkeJjG/SVoKfxFAtyX4a89/95itVjolxarGf8StBT+IgGuqLyeuOhwkuIizC4lqGTbY3WBHwlaCn+RANcx2e/4lTHl3GTZ46htbKO2odXsUkR6ncJfJIB5vF5KKhp0yN8HOmb8a+9fgpHCXySAOauaaHN7Ff4+0DHjv1jj/hKEFP4iAUyT/XwnMTaC+JhwSiq05y/BR+EvEsCKyusJs7bPTJfel5UWqz1/CUoKf5EAVlReT2ZqLLYw/Sr7QrY9jpKKBryhswq6hAh9Y4gEsKLyOh3y96EseywtrR4qa5rNLkWkVyn8RQJUbWMrR+pbFf4+1HGJZC32I8FG4S8SoDon+6Ur/H2lYy6FlvmVYNOj8P/BD37A+vXrfV2LiJyBIqdm+vtadKSNtMQoXeBHgk6Pwv/aa6/l6aefJi8vjz/+8Y8cOXLEx2WJSHeKyutJjIsgIUbL+vpS+4x/7flLcOlR+N9www389a9/5emnn6ayspIbb7yR+fPns23bNl/XJyKn0LGsr/hWlj2Ow5WNuD1es0sR6TU9HvP3er0cPHiQAwcO4PF4SE1N5aGHHuLJJ5/0ZX0ichJuj5eySi3r2xey7bF4vAaHqxrNLkWk19h68qBly5bxyiuv0L9/f2655RaeeOIJwsPDaWxs5KqrruLuu+/2dZ0icozSigY8XkPh3weyjpnx3zH7XyTQ9Sj8q6qq+MMf/sDIkSO73B8TE8OvfvUrnxQmIqf25bK+8SZXEvwyU2MIs1qOLvObbnY5Ir2iR4f9PR7PCcHfsbd/xRVX9H5VInJaReX12MKsZKREm11K0LOFWUlPiaG4XDP+JXicds9/0aJFOJ1ONm/eTFVVVef9breboqIinxcnIidXVF5Plj2WMKuW6ugL2fZY9pfVml2GSK85bfjfeOON7N69my+++IK8vLzO+8PCwhg3bpyvaxORkzAMg4OH67j4fIfZpYSMrLRYPtpRTnOrm6iIHo2Wivi1036KL7zwQi688EIuv/xy0tM11iXiDypqmmlscTMwXeP9faVjol9pRSND+iWYXI3IuTtt+P/whz/kiSee4D//8z9Pun3VqlU+KUpETu3g4ToABmYo/PtKlv3LZX4V/hIMThv+c+fOBeCnP/1pnxQjIt076KzDarGQfTSQxPfSkqKJCLfqAj8SNE47W2j06NEAXHLJJWRmZnLJJZfQ2NjIxo0bOf/88/ukQBHp6qCzjn5psYTbwswuJWRYLRYt8ytBpUdThRcuXMgf/vAH9u7dy4MPPkhxcTEPPPCAr2sTkeN0TPYbmKHFZvpalj1OF/iRoNGj8P/000956KGHeOONN/ja177GkiVLKCkp8XVtInKcI/Wt1DW2abKfCbLTYqltaKW2sdXsUkTOWY/C3zAMrFYr77//PhMnTgSgubnZp4WJyIk6JvsNytCks76W5fhymV+RQNej8B8wYABz586luLiYSy65hHvvvZcRI0b4ujYROc5BZx0W0Jr+JshO+3LGv0ig69FqFUuWLOGNN97goosuIjw8nJycHGbOnOnj0kTkeAcP15GRGkNkhCb79bWE2AjiosO15y9BoUd7/jExMeTk5FBbW8tnn33GmDFj2Ldvn69rE5HjHHTW6fx+k1iOnl5Zoj1/CQI92vN/4okneO6550hNTe28z2Kx8Oabb/qsMBHpqrahleq6Fk32M1GWPY73tpdhGAYWi8XsckTOWo/Cf+XKlaxdu1ZL/IqY6JDz6Mp+Cn/TZNljaWn1UFnTTFqSrqgogatHh/0zMzMV/CImO3g0/Aeka7KfWTrW+C/W+f4S4Hq053/ZZZfx+OOPc8011xAVFdV5/6hRo3xWmIh0dfBwHY6kaGKiws0uJWRlHZ3xX+KqZ9ywNJOrETl7PQr/V155BYDCwsLO+zTmL9K3DhyuY5Am+5kqOtJGakKUZvxLwOtR+L/11lu+rkNETqOusZWKmmaumpBldikhL8seS7HCXwJcj8b8GxoaePjhh7n11ls5cuQICxcupKFBH36RvrK/rH28f0imVvYzW7Y9jrLKBtwer9mliJy1HoX/I488Qnx8PJWVlURGRlJfX8/ChQt9XZuIHLW/rBaLBZ3j7wey7LF4vAbO6iazSxE5az0K/x07djBv3jxsNhvR0dEsXbqUHTt2+Lo2ETlqf1kt/VJjiYro0Uid+NCxk/5EAlWPwt9q7fowj8dzwn0i4huGYbCvtJbBOuTvFzJTY7FaLBr3l4DWo92Iiy++mF/+8pc0Nzfz7rvv8te//pVLL73U17WJCFBZ00x9UxuD+yn8/UG4zUp6SrT2/CWg9Wj3/b777iMmJob4+Hh+85vfMHLkSH70ox/5ujYRAfaV1QKa7OdPsu1xOt1PAlq3e/5vvPEGf/zjH/niiy+IiopixIgRTJgwgcjIyL6oTyTk7S+rxRZmJcsea3YpclSWPZZNO8tpafXoCosSkE4b/q+//jrLli3j7rvvZuTIkVgsFrZv386jjz5KS0sLU6ZM6as6RULW/tJaBmbEYQvTPBt/kW2PwwBKKxs0F0MC0mnD/4UXXuD555+nX79+nfcNHTqUsWPH8sADDyj8RXzM4/VywFlH7th+3T9Y+kzHUZji8nqFvwSk0+5KNDQ0dAn+DoMHD6alpcVnRYlIu9KKRlrbvBrv9zP2pGgibFZKdIEfCVCnDf+wsFOPZRmG0e2Lr1q1ivz8fKZMmcKLL754wvYdO3Ywa9Ys8vLyWLBgAW63G4DS0lJmz57N1KlTufPOOztXE9yzZw8333wzN9xwA9/5zncoKSnptgaRQLb/6GQ/zfT3L1aLhX5psRRrxr8EKJ8NIjqdTpYtW8by5cspKCjgpZdeYs+ePV0eM3/+fBYuXMiaNWswDIMVK1YAsHjxYm655RYKCwsZPXo0Tz/9dOf93/ve93jttdfIz8/n17/+ta/KF/EL+0priY2y4dC14/2OZvxLIDtt+H/xxRdMmDDhhH/jx49n165dp33h9evXM3HiRJKSkoiJiSEvL6/LVQFLSkpobm5m3LhxAMyaNYvCwkLa2trYuHEjeXl5Xe4H+NOf/kRubi5er5fS0lISErQ3JMFtb2kNgzMTsFgsZpcix8myx1LT0EpdY6vZpYicsdNO+HvjjTfO+oXLy8ux2+2dtx0OB9u2bTvldrvdjtPppLq6mri4OGw2W5f7AWw2G7W1teTn59Pc3Mxf/vKXs65PxN81NrdR6mrg4pEOs0uRk8i2xwFQ4mpg5MAIk6sROTOnDf+srLO/fKjX6+2yt2IYRpfbp9p+/OOALrcTEhJ47733WLduHXfeeSdvvvnmaecmHCs1Ne5s306fstt18ZbuhEKPNu90YgA5ozLP6v2GQo/O1bn0aGxkOADVjW1B3etgfm+9JRB75LOrhGRkZLBp06bO2y6XC4fD0WW7y+XqvF1RUYHD4SAlJYW6ujo8Hg9hYWFdnrd69Wquu+46LBYLubm5NDc3U1NTQ0pKSo9qqqysx+vtfqKimez2eFyuOrPL8Guh0qNNnx3GarGQEmM74/cbKj06F73Ro4TYCHbsq+Sy84Pz6Iw+R93z5x5ZrZZT7vT6bMLfpEmT2LBhA1VVVTQ1NbF27Vpyc3M7t2dlZREZGcnmzZsBWLlyJbm5uYSHh5OTk8Pq1asBKCgo6Hzec8891zkU8cEHH5CcnNzj4BcJNHuKj9DfEacr+fmxAY44DpX75xe/yOn4LPzT09OZN28ec+bMYebMmUyfPp0xY8Ywd+5ctm/fDsDSpUtZsmQJU6dOpbGxkTlz5gCwaNEiVqxYQX5+Pps2beKee+4B4Oc//zl/+tOfmDFjBr/97W958sknfVW+iKncHi/7ymoZlp1odilyGv3T4yitaMDt8ZpdisgZsRg9OWE/SOiwf3AIhR4dOFzLw89v4r9mjOKS89PP+Pmh0KNz1Rs9+vBzJ8+89hmLb7uE/o7AmFN0JvQ56p4/98iUw/4icvZ2F9cAMCxLe/7+bEB6+xfrIad/fvmLnIrCX8QP7SmuITUhkpSEKLNLkdNIT44hItzKIadW+pPAovAX8TOGYbCnpIah2uv3e1arhf72OIo06U8CjMJfxM9U1jZTXdfCedlJZpciPdA/PZ5DzvoeXe9ExF8o/EX8zBeHjgAwvH+SqXVIzwxwxNHY4qayttnsUkR6TOEv4md2HqwmLjq885rx4t/6H530V6RxfwkgCn8RP7Pz0BFGDEjCqov5BIRsexwWCxwqV/hL4FD4i/gR15EmKmubGTkg2exSpIciw8PISInR6X4SUBT+In5k58FqAEYOSDK3EDkj/R1xOt1PAorCX8SP7DxUTUJMOP3SNN4fSAakx1NZ20xDc5vZpYj0iMJfxE8YhnF0vD/5hMtai38b4NCkPwksCn8RP1F+pInquhZGDtR4f6Dpn95+PXdN+pNAofAX8RMa7w9cibERJMZGUKRJfxIgFP4ifmLHwWoS4yLISIkxuxQ5C/3T47TnLwFD4S/iB7xeg8/2VzF6cIrG+wPUwPR4SisacHu8Zpci0i2Fv4gf2H+4loZmNxcOSTW7FDlL/R1xeLwGpRUNZpci0i2Fv4gf+HRfFRbggkEpZpciZ2nA0Ul/BzXuLwFA4S/iBz7dV8ngfgnERYebXYqcJUdyNJERYRw6rHF/8X8KfxGT1Te1sa+sltGDtdcfyKwWCwMdcRw4XGt2KSLdUviLmOzzA1UYBhrvDwIDMxIoKq/H49WkP/FvCn8Rk23fW0lslI3BmQlmlyLnaFBGPK1uL2UVjWaXInJaCn8RE3m8XrburWTM0FSsVp3iF+gGZrRP+jtwWJP+xL8p/EVMtKe4hvqmNsafZze7FOkFGSkxREaEcVDhL35O4S9ioo93VWALszJ6iCb7BQOr9eikP6cm/Yl/U/iLmMQwDD7Z7eKCQclERdjMLkd6ycCMBIqcmvQn/k3hL2KSovJ6KmqamTBch/yDSeekv0pN+hP/pfAXMcknuyuwAGOHpZldivSijkl/GvcXf6bwFzGBYRhs3FnOsOxEEmMjzC5HelFGSgyR4WGa8S9+TeEvYoJiVwOlFQ1cekG62aVIL7NaLQxI10p/4t8U/iIm+ODzw1gtFnJGOswuRXxgYEa8Jv2JX1P4i/Qxr2Hw0efljBqcQkKMDvkHI036E3+n8BfpY3tLaqisbWaiDvkHrYEZ7Us1a9Kf+CuFv0gf++AzJxE2K+PO0yz/YJWpSX/i5xT+In2opc3Dh587GT/cTnSkFvYJVh2T/rTnL/5K4S/ShzbtLKexxc3ksf3MLkV8bGBGPIfK6zTpT/ySwl+kD63bWkp6cjQjBiSZXYr42OCMBFrbdHlf8U8Kf5E+UlrRwO7iGnLH9sNi0eV7g93gfu2T/vaV6Xx/8T8Kf5E+sm5rKWFWC5dfmGl2KdIH0pOjiY2ysa+0xuxSRE6g8BfpA00tbt7dVsaE4XYStJxvSLBYLAzOTGBfqSb9if9R+Iv0gfe2ldHU4mbKJf3NLkX60JB+CZRU1NPc6ja7FJEuFP4iPubxenljUxHDshMZ2i/R7HKkDw3OTMAwtNiP+B+Fv4iPfbKrgoqaZvIuHmB2KdLHNOlP/JXCX8SHDMPg9Q8PYk+KYrxW9As5CTER2JOi2Feq8Bf/ovAX8aGteyvZX1bHtMsGYbXq9L5Q1D7pT+Ev/kXhL+IjhmGw8t392JOimDQ6w+xyxCRD+iVSXddCdV2L2aWIdFL4i/jIlt0VHHTWcf2kwdjC9KsWqoYcHfffr3F/8SP6RhLxAY/Xyyvv7sORHM1lo3Xp3lA2MD2OMKtFh/7Fryj8RXzg3a1llLgauHHyUMKs+jULZeG2MLIdcVrpT/yKvpVEelljs5tX393H8OxELhphN7sc8QND+iWw/3AdXq9hdikigMJfpNf9Y8MB6hvbuPmr5+kCPgLAkMwEWlo9lFU2mF2KCODj8F+1ahX5+flMmTKFF1988YTtO3bsYNasWeTl5bFgwQLc7vYlMEtLS5k9ezZTp07lzjvvpKGh/Rdm7969zJ49mxkzZnDTTTexY8cOX5YvcsYOVzXyxsYiJl2YwaCMBLPLET/RMelvr8b9xU/4LPydTifLli1j+fLlFBQU8NJLL7Fnz54uj5k/fz4LFy5kzZo1GIbBihUrAFi8eDG33HILhYWFjB49mqeffhqABx98kLlz57Jy5UruuecefvzjH/uqfJEz5jUMnl+9g4jwML4+eajZ5YgfyUiJIS46nD3FGvcX/+Cz8F+/fj0TJ04kKSmJmJgY8vLyKCws7NxeUlJCc3Mz48aNA2DWrFkUFhbS1tbGxo0bycvL63I/wDe+8Q2uvPJKAEaMGEFZWZmvyhc5Y29/UsKu4hpuvnoYSXGRZpcjfsRisTAsK5HdJQp/8Q82X71weXk5dvuXk50cDgfbtm075Xa73Y7T6aS6upq4uDhsNluX+6H9D4EOTz75JF/96lfPqKbU1Lizei99zW6PN7sEv+dvPSqvbuTld/Yy7jw7X7tmuF+M9ftbj/xRX/Zo7AgHW/75ORHRESQG0B+H+hx1LxB75LPw93q9Xb4ADcPocvtU249/HHDC4x5//HG2bt3KCy+8cEY1VVbW+/1sW7s9HpdLVwA7HX/rkWEYLPv7Vjxeg29dM4yKinqzS/K7Hvmjvu5RZlIUAB9uLWH88MA4C0Sfo+75c4+sVsspd3p9dtg/IyMDl8vVedvlcuFwOE65vaKiAofDQUpKCnV1dXg8nhOe53a7ue+++9i+fTsvvPAC8fGB99eWBJ8Nnx3m031VfH3yUOxJ0WaXI35qcGY8tjCLDv2LX/BZ+E+aNIkNGzZQVVVFU1MTa9euJTc3t3N7VlYWkZGRbN68GYCVK1eSm5tLeHg4OTk5rF69GoCCgoLO5/3iF7+gvr6e5557TsEvfqGmoZW//Ws3Q7MSuGZCttnliB8Lt4UxMCNek/7EL/gs/NPT05k3bx5z5sxh5syZTJ8+nTFjxjB37ly2b98OwNKlS1myZAlTp06lsbGROXPmALBo0SJWrFhBfn4+mzZt4p577qGqqooXX3yR/fv3841vfIMZM2YwY8YMX5Uv0iMvvrGLljYP/++683XVPunWeVlJHDhcS5vbY3YpEuIshmH49yB4L9KYf3Dwlx5t/sLFU69uZ1buEKZPGmR2OV34S4/8mRk9+niXi9++sp2ffHsC52Un9enPPhv6HHXPn3tkypi/SDBraG7jr2u/YIAjjqmXDjC7HAkQw7ISAXToX0yn8Bc5Cy+9uYe6xjb+X/75ulyv9FhCbATpydHsVviLyfStJXKGPjtQxXvby5h66QAGZmjiqZyZYdmJ7CmpIYRGXMUPKfxFzkBLm4cXCneSnhzNjCsGmV2OBKDzspOob2rjcFWj2aVICFP4i5yB197fj+tIM7dOHUm4LczsciQAdY7763x/MZHCX6SHDjnrWPNhEVeMyWTkwGSzy5EAlZHafpGf3UUKfzGPwl+kB7xeg+df30lctI1vXjXM7HIkgFktFob3T+KLomqzS5EQpvAX6YF/f1LCgcN13HLtcOKiw80uRwLciP5JuI40U1nTbHYpEqIU/iLdqG9qo+DdfZw/MJmLRzq6f4JIN0YMSALQ3r+YRuEv0o1X391HU4uHW756nl9cqlcCX7YjjtgoGzsPHTG7FAlRCn+R0ygur+ftT0q4akIWWfaTL5MpcqY6x/0Pac9fzKHwFzkFwzBY/q9dxETamHHFYLPLkSAzckAyriPNVNVq3F/6nsJf5BS27qlk56EjfC13iCb5Sa/rHPfXoX8xgcJf5CS8hsEr6/aSnhxN7th+ZpcjQejLcX8d+pe+p/AXOYmPdjgpdjUw88ohunCP+MSX4/5HzC5FQpC+1USO4/Z4KVi3n2x7HBefr1P7xHdGDEim/EiTxv2lzyn8RY7z3vYyyo80MWvyEKw6tU98aOTRcX8d+pe+pvAXOUab28Oq9w8wNCuBsUNTzS5Hgly2I4646HA+P6Dwl76l8Bc5xvvbD1Nd18LMK4doQR/xOavFwgWDkvnsQBWGYZhdjoQQhb/IUR6vl9UfHGRwZgIX6Kp90kdGDUqhpr6VkooGs0uREKLwFzlq445yKmqamX7ZQO31S58ZNTgFgM/2V5lciYQShb8I7ef1//ODg/RLi2XseWlmlyMhJCUhiszUGIW/9CmFvwiwdU8FJa4Gpk0cqBn+0udGDUphV9ER2twes0uREKHwFwFWbzhIWmIUl1yg8/ql740anEKr28vu4hqzS5EQofCXkLe3pIa9pbXkXTKAMKt+JaTvjRiQRJjVokP/0mf0TSch741NRURH2rj8wgyzS5EQFRVhY1hWIp8dUPhL31D4S0irqm1m004XuWMziYqwmV2OhLBRg1M45KyntqHV7FIkBCj8JaS99XEJBgbXTMg2uxQJcR2n/H26v9LkSiQUKPwlZLW0eXhnSwkThttJS4o2uxwJcQMz4kmMjWDbXoW/+J7CX0LWhk8P09Ds5tqc/maXIoLVYmHM0FS276vC7fGaXY4EOYW/hCTDMHhjUxED0+M5LzvR7HJEABg7LI2mFrdO+ROfU/hLSNpxsJqyyka+mpOtpXzFb1wwKBlbmIWteyrMLkWCnMJfQtLbW0qJjbJxyfla1Ef8R1SEjZEDktmqcX/xMYW/hJya+hY+2eXiijGZhNvCzC5HpIuxw9JwVjVyuKrR7FIkiCn8JeS8t70Mj9dg8rgss0sROcHYoakAbNOhf/Ehhb+EFK/X4J0tpZw/MJmMlBizyxE5QVpSNFn2WD7ZrfAX31H4S0j5dH8VFTXNfGW89vrFf004z86u4iNa7U98RuEvIeWdLSUkxIQz/rw0s0sROaWckQ4MAz7e7TK7FAlSCn8JGVW1zWzZU8GVY/thC9NHX/xXtj0WR3I0m79Q+Itv6BtQQsa6raVgQO7YfmaXInJaFouFi0bY2XmwmvqmNrPLkSCk8JeQ4PF6eXdbGaOGpGDXOv4SAHJGOPB4DbZo4p/4gMJfQsK2PZVU17VwlU7vkwAxKCOe1IRINn1RbnYpEoQU/hIS/r2lhOT4SMYMSzW7FJEeaT/07+DzA1U0NrvNLkeCjMJfgp7rSBOf7aviyjGZhFn1kZfAcfFIB26PweZd2vuX3qVvQgl667aWgkUT/STwDOmXgCMpmg8+c5pdigQZhb8ENbfHy3vbyhg7NI2UhCizyxE5IxaLhYmj0tl5sJqq2mazy5EgovCXoLZ1TyU1Da3kjtNevwSmy0ZlYAAf7tDev/Qehb8EtXe2tk/0u3BIitmliJyV9JQYhvRLYMOnCn/pPQp/CVoVmugnQeKyURkUu+opKq83uxQJEvpGlKC1blsZAFeO0SF/CWwXn+8gzGphw6eHzS5FgoRPw3/VqlXk5+czZcoUXnzxxRO279ixg1mzZpGXl8eCBQtwu9vPZS0tLWX27NlMnTqVO++8k4aGhi7P+/vf/87999/vy9IlwLWv6FfKhUNTSU3URD8JbAkxEYwZmsr7n5bh9njNLkeCgM/C3+l0smzZMpYvX05BQQEvvfQSe/bs6fKY+fPns3DhQtasWYNhGKxYsQKAxYsXc8stt1BYWMjo0aN5+umnAWhpaWHp0qU89thjvipbgsS2PZXU1LcyWaf3SZCYPC6LusY2PtFyv9ILfBb+69evZ+LEiSQlJRETE0NeXh6FhYWd20tKSmhubmbcuHEAzJo1i8LCQtra2ti4cSN5eXld7gfYuHEjXq+X+fPn+6psCRLvbC0lMS5CK/pJ0Bg9OIXUhEje2VJidikSBGy+euHy8nLsdnvnbYfDwbZt20653W6343Q6qa6uJi4uDpvN1uV+gCuuuIIrrriCV1555axqSk2NO6vn9TW7Pd7sEvze6XpUXt3Ip/sq+cY1w8lIT+zDqvyLPkfdC7QeXTdpMH8t3InbYiUzLbZPfmag9cgMgdgjn4W/1+vFYrF03jYMo8vtU20//nHACbfPVmVlPV6v0Suv5St2ezwuV53ZZfi17nq08t19GAZcNCw1ZHupz1H3ArFH44emstxioeDfu7nxK0N9/vMCsUd9zZ97ZLVaTrnT67PD/hkZGbhcrs7bLpcLh8Nxyu0VFRU4HA5SUlKoq6vD4/Gc9Hkip3PspXvTdOleCTLJ8ZGMHZbKe9tKaXNr4p+cPZ+F/6RJk9iwYQNVVVU0NTWxdu1acnNzO7dnZWURGRnJ5s2bAVi5ciW5ubmEh4eTk5PD6tWrASgoKOjyPJHT2b6viuq6FiaP1aV7JThdNSGL2sY2PtKKf3IOfBb+6enpzJs3jzlz5jBz5kymT5/OmDFjmDt3Ltu3bwdg6dKlLFmyhKlTp9LY2MicOXMAWLRoEStWrCA/P59NmzZxzz33+KpMCTLrtpSSEBvBWE30kyA1alAKWWmxrPmoCMPw72FM8V8WI4Q+PRrzDw6n6lFVbTPzf7ee/IkD+fpk34+H+jN9jroXyD16d2spf3p9J/fdPI4LBvlu6epA7lFf8ecemTLmL9LX3t5SAoYu3SvBb+KodBJiwlm7scjsUiRAKfwlKLS5vazbUsrYYWnYNdFPgly4LYyrJ2SzbW8lpRUN3T9B5DgKfwkKm78op7axjasnaKKfhIavTMgi3GZl9QcHzS5FApDCX4LCWx+X4EiO5oLBunSvhIaEmAiuGp/FB585cVY3ml2OBBiFvwS8g4fr2FNSw9Xjs7D20oJQIoHguksHEBZm4R/vHzC7FAkwCn8JeG99XExEuJXLx2SaXYpIn0qMi+Sq8Vls0N6/nCGFvwS0huY2PvzcycQLMoiNCje7HJE+17H3v0p7/3IGFP4S0N7bVkar26uJfhKyvtz7P0xReb3Z5UiAUPhLwPJ6Dd76uJhh2YkMSA+8q2qJ9JbpkwYRE2ljxVu7teqf9IjCXwLWx7tcuI40MyWnv9mliJgqLjqc6y8fzGcHqtm+r8rsciQAKPwlYK3ZeAh7UhQThtvNLkXEdFdPyMKRHM1Lb+3G49UV/+T0FP4SkPaU1LC3pJZrc/pjter0PhFbmJVvXjWMsspG3tpcYnY54ucU/hKQ1nx0iJhIG1fo9D6RTuPPS2P0kBReWbePyppms8sRP6bwl4BTVtHAx7tcfGV8FlERNrPLEfEbFouF70wZgYHBi2/s0uQ/OSWFvwSclev2YrVYuOaibLNLEfE79qRoZl4xhC17Ktj8hcvscsRPKfwloBypb2Hthwe5bHQGyfGRZpcj4peuvTibAY44/rr2C2obWs0uR/yQwl8CypqPDuHxeJl22UCzSxHxW2FWK/85/QIaWzw8//pOHf6XEyj8JWDUNrby709KyJ2QTXpyjNnliPi1bEccN35lKFv2VLBua6nZ5YifUfhLwHhjYxFtbV6+ec1ws0sRCQhfzcnmgkHJ/O3N3ZRWNJhdjvgRhb8EhPqmNt7cXEzOSAf9tZSvSI9YLRb+Y9oFRIWH8dSr22lqcZtdkvgJhb8EhLUbi2hu9TB90iCzSxEJKMnxkfzXjNE4q5p47p87NP4vgMJfAkBNQytvbCzi4pEO+jvizC5HJOCMHJjMjV8ZyuZdLl7/8JDZ5YgfUPiL31v1/n7cHi+zcoeYXYpIwMq7pD8Xj3Tw8jt7+WS3zv8PdQp/8Wvl1Y28s6WUK8f2Iz1FM/xFzpbFYuG2/PMZmB7PMys/Y39ZrdkliYkU/uLXXn13P2FWC9drrF/knEVGhPHDb4wlITaCJ/6+FdeRJrNLEpMo/MVv7Smu4cPPnVx7cX+t5ifSSxJjI5j3zbF4vAa/XrGVGq0AGJIU/uKXvF6Dv77xBcnxkVrNT6SXZabGcveNY6iua+ZX//cJ9U1tZpckfUzhL35p3dZSDjnr+eZVw3TlPhEfOC87iR98fQyHq5r49UtbaGzWGgChROEvfqe+qY1X1u1jRP8kLjnfYXY5IkFr1KAU7vraaIrK6/nN37dqEaAQovAXv/PSW7tpbHZzy7XDsVgsZpcjEtTGDkvjjhtGsa+0ll+9tIWGZg0BhAKFv/iVbXsreX/7YfIvG6AFfUT6SM5IB3d9bTSHnHU8vvwTXQY4BCj8xW80tbj5c+FOMlNjuH7SYLPLEQkp44fb+eGNY3FWNfKL5R9TXddidkniQwp/8RsvvbWbI/Ut3DbtfMJt+miK9LVRg1P475vGUV3XwmN/2UyRs87sksRH9A0rfuGjHU7WbS1j6qUDGNov0exyRELW8P5J/OiW8bR5vMz/n3f54lC12SWJDyj8xXTl1Y08//pOhvZL4GtXav1+EbMNykjgwe9cRHJ8JL96aQsffHbY7JKklyn8xVRtbi+/W/kZYVYLd8wYhS1MH0kRf5CWFM0vf3AlQ/ol8r+rPucf6w/ocsBBRN+0YhrDMHj+9R0cPFzHbfnnk5YYbXZJInKMuJgI7r1pHJdekM4r6/bx+5Wf0dLqMbss6QVaOk1Ms2r9ATZ85uRruUMYP9xudjkichLhNiu3X38BAxxx/H/v7KWssoHvz7oQR7KushnItOcvptjw2WEK3t3PpNEZTNfa/SJ+zWKxcN3Egcz75liq61r42Z838em+SrPLknOg8Jc+t/kLF3/8xw5G9E/i1qkjtYqfSIAYPTiVn373YpLjI1m2Yit/f3sPbo/X7LLkLCj8pU9t2VPB71d+yuDMeO6+cYzO5xcJMI6kaBbMySF3XD9e/+AQj/1lM86qRrPLkjOkb17pM+9vL+OpV7aT7Yhj3jfHEh2pKScigSgyPIxbp47krq+NxnWkiYf+tJF3tpTobIAAom9f8TnDMFj9wUFefmcf5w9M5vuzLlTwiwSBi0Y4GJyZwLP/+Jw/F37Bh587ufW6kaRrMqDf056/+FRjs5unXv2Ul9/Zx6UXpHPPN7THLxJMUhKiuO9b47l16ggOOutY+MeP+OeGA7S5dUqgP9O3sPjMnpIa/viPz3Edaebmq4dx7cX9NblPJAhZLRYmj8tizNA0XnxjFy+/s493tpRy41eGcvFIh37v/ZDCX3pdc6ubV9bt481NxSQnRDL/W+MYMSDZ7LJExMeS4yP5/qwL+fxAFS+9tYffr/yMNzYWcf3lg7lwSIr+CPAjCn/pNW6Pl3e3lfHae/upaWjlqglZ3Dh5qA7zi4SYCwalsOi7F/Pe9jJee38/v/n7VgamxzPtsoFMGG7HatUfAWbTt7Kcs+ZWN+9vP8wbG4soP9LEsOxE7vrahQzL1tX5REKV1Wohd2w/Jo3OYMOnh1n9wUGeLviU5PhIrhyTyRVjMrWkt4kU/nJWvIbBnuIaPvzcyYefO2lscTM4M54fXHMh44al6fCeiABgC7Ny5dh+XH5hJp/sdvHOllJWvX+AVe8fYHj/JCYMtzN+eJr+EOhjPg3/VatW8bvf/Q63282tt97K7Nmzu2zfsWMHCxYsoKGhgZycHBYvXozNZqO0tJT58+dTWVnJ4MGDWbp0KbGxsdTW1nLfffdRVFRESkoKv/nNb7DbtSZ8X6ltaGXnoWo+P1DF9n1VVNe1EGGzMu68NL56UX+GZiUo9EXkpKxWCxeNcHDRCAcVR5p4b3sZm79w8bc3d/O3N3eTbY9lxIBkRvRP4rz+SSTGRphdclCzGD5alcHpdPKtb32LV155hYiICG6++WZ+/etfM2zYsM7HTJ8+nUceeYRx48bxwAMPMHr0aG655RbuuOMObrjhBqZNm8ZTTz1FY2Mj8+fP5+GHHyYjI4Pbb7+dgoIC3n77bX7zm9/0uKbKynq8Xv9ehMJuj8flqjPt5xuGQW1DK66aZipqmnBWNXHIWcchZx2VtS0AREfaGDkgiYtHOhh3XhpREX17AMnsHgUC9ah76lH3+qJHzqpGPt7l4rMDVewpqaG1rX254MTYCLIdcfS3x5GRGkNqYhRpCVGkJET51cqg/vw5slotpKbGnXSbz8L/1VdfZePGjTz22GMAPPXUUxiGwfe//30ASkpKuPXWW/nXv/4FwKZNm3jyySf54x//yKWXXspHH32EzWajrKyMb3/727z55ptcffXVvPjii2RmZuJ2u7nkkkv48MMPCQ8P71FNvRn+lTXNVNe3gAEG7a95bCePbathgHHsDdpvf3nfl6+RmBDDkZrGYx5qnOQ1vnw8x9xvHPOAjv/2GgatbV7aPF7a3F7a3J6j/+ulpc1DfVMbDU1t1De5qW9qo7axlTb3l2t1W4CM1BgGpMczID2OEf2TGZgRR5jVvF8+f/5l8xfqUffUo+71dY/cHi8HD9ext6SGIlc9xeUNlFQ0nHD9gLjo8C7/YqNtREfYCA+3EmELI8JmJdxmJSI8jHCbFavFgtVqwWppPy3RcsJ/t98+myOXyckxHDly8uWNLZzi9U5xd1x0OBkpvbdA0unC32e7bOXl5V0OyTscDrZt23bK7Xa7HafTSXV1NXFxcdhsti73H/8cm81GXFwcVVVVpKen++ptnNKCP3xAqztwL2gRbrMSYbMSe/SXJzEugn5pscTHhGNPiiY1MQp7YhRpSdFEhoeZXa6IhABbmJWhWYkMzfpysrDH66WqtoXKmmYqa5uprGnmSENr545LZW0zB51tNLd6aHN7cHv8++hud5Z+bxIpCVE+/zk+C3+v19vlryjDMLrcPtX24x8Hp/5rzDAMrGewB3qqv4DOxrJ5k6k40tx+w/LlH3IWyzF/7Vnab7f/55cP+vKxX76vY59nsdDlscc/7mSv1/GYY1tlOfrXbER42Jf/jv5FHOhj83Z7vNkl+D31qHvqUff8oUcZZ7B/5/EatLV5aDn6r83txes12v8ZBh6vgWEcve1tPzrasf1UDE6+7XTHzU+56TTPiY8N57z+fbMmis/CPyMjg02bNnXedrlcOByOLttdLlfn7YqKChwOBykpKdTV1eHxeAgLC+vyPIfDQUVFBRkZGbjdbhoaGkhKSupxTb152D86zEL/1N6fneqTw2xeL54WL00tbTT17iubQodru6cedU896l6g98gCRED7QvbWY/aqelFv96g3X+t0h/19NnA7adIkNmzYQFVVFU1NTaxdu5bc3NzO7VlZWURGRrJ582YAVq5cSW5uLuHh4eTk5LB69WoACgoKOp83efJkCgoKAFi9ejU5OTk9Hu8XERGRdj6b8Aftp/o988wztLW1ceONNzJ37lzmzp3L3XffzYUXXsjOnTt58MEHqa+vZ9SoUSxZsoSIiAhKSkq4//77qaysJDMzk1//+tckJiZy5MgR7r//foqKioiPj2fp0qVkZ2f3uB7N9g8O6lH31KPuqUfdU4+65889MmW2vz9S+AcH9ah76lH31KPuqUfd8+cemXLYX0RERPyTwl9ERCTEKPxFRERCjMJfREQkxCj8RUREQozCX0REJMQo/EVEREKMwl9ERCTEKPxFRERCjMJfREQkxCj8RUREQozCX0REJMQo/EVEREKMzewC+pLVajG7hB4JlDrNpB51Tz3qnnrUPfWoe/7ao9PVFVKX9BUREREd9hcREQk5Cn8REZEQo/AXEREJMQp/ERGREKPwFxERCTEKfxERkRCj8BcREQkxCn8REZEQo/AXEREJMQp/ERGREKPw70W//e1vmTZtGtOmTePxxx8H4JVXXiE/P5/rr7+eRx55BLfbDcA777zD9ddfz/XXX8+9995LQ0MDAK+++ipXXHEFM2bMYMaMGSxbtgyA2tpabr/9dq677jpmz56Ny+UCoLW1lfnz53Pdddfxta99jb1795rwznuuN3pUXl7O7bffzsyZM7n55pspLi4G1KOOHlVWVnZ+fmbMmMHVV1/N+PHjAfXo2M9RcXExs2fPZsaMGXznO9+hpKQEUI+O7dG2bdv4+te/zvXXX88dd9zR2Ytg6RHAE088QX5+PtOmTeNPf/oTAOvXr+f6669nypQpnd/BADt27GDWrFnk5eWxYMGCzv6VlpYye/Zspk6dyp133tnZP7/ukyG94v333zduuukmo6WlxWhtbTXmzJljPPPMM8aVV15pOJ1OwzAMY9GiRcZzzz1n1NTUGBMnTjR2795tGIZh/O///q/xs5/9zDAMw3j44YeNVatWnfD6ixcvNp555hnDMAzj1VdfNX74wx8ahmEYzz77rPHTn/7UMAzD+Oijj4xvfOMbvn6rZ623enTrrbcay5cvNwzDMJYvX97ZC/Xoyx518Hg8xre//W3jtddeMwxDPTq2R/fdd5/x4osvGoZhGC+88IJx7733GoahHnX0yOv1GpMnTzY2bNhgGIZh/POf/zTuuOMOwzCCo0eGYRgffvihcfPNNxttbW1GU1OTcdVVVxk7duwwJk+ebBw6dMhoa2szbrvtNuPtt982DMMwpk2bZnzyySeGYRjGT37yk87Pz+2332784x//MAzDMH77298ajz/+uGEY/t0n7fn3Ervdzv33309ERATh4eEMHTqU1tZWxo0bh8PhAOCqq67iX//6FwcOHKBfv34MGzasy/0A27dv59VXX+X666/nvvvuo6amBoC3336b66+/HoDp06ezbt062traePvtt7nhhhsAuPjii6mqqqK0tLSv336P9EaPqqqq2LlzJzfffDMAX//617nnnnsA9ejYz1GHl19+mejo6M6+qEdf9sjr9VJfXw9AU1MTUVFRgHrUcX91dTXNzc1MnDix8/733nuP1tbWoOgRwCWXXMILL7yAzWajsrISj8dDbW0tAwcOpH///thsNq6//noKCwspKSmhubmZcePGATBr1iwKCwtpa2tj48aN5OXldbkf/PuzpPDvJeedd17nh+LAgQO8/vrr5Ofns3XrVsrKyvB4PBQWFlJRUcGgQYM4fPgwO3fuBOD111+noqICaP+l/d73vsdrr71GZmYmDz/8MNB+qNtutwNgs9mIi4ujqqqqy/0dzz98+HAfvvOe640eFRUV0a9fP37+85/z9a9/nbvvvpvw8HBAPTr2cwTg8Xj4/e9/z7333tt5n3r0ZY9++MMf8vzzz3PllVfy3HPPMXfuXEA96uhRcnIyMTExvPfeewD885//pK2tjerq6qDoUYfw8HCefPJJpk2bxmWXXXbCe3A4HDidzpO+N6fTSXV1NXFxcdhsti73g39/lhT+vWz37t3cdttt/OhHP2LIkCHce++93HnnncyePZsRI0YQHh5OQkICv/jFL/jpT3/K17/+dRwOR2eAPfXUU1x00UVYLBb+8z//k3ffffekP8cwDKxWK4ZhYLFYTrjfn51Lj9xuN59//jkTJ07k5Zdf5pprruH+++8/6c8J1R51ePfddxk0aBAjRow45c8J5R79+Mc/5uGHH+bdd99l8eLFfP/738c4yRXOQ7VHFouFJ598kmeeeYaZM2dSV1dHUlJSl89Yh0DuEcDdd9/Nhg0bKCsr48CBAye8B4vFgtfrPen9x79n4ITbxz7HX/rk//+vBJDNmzfz3e9+l3vvvZevfe1rtLS0MGbMGAoKCvi///s/0tPT6d+/Px6Ph4yMDP7+97/z8ssvc/7559O/f3/q6up4/vnnO1/PMAzCwsKA9r8+O/ZY3G43DQ0NJCUlkZ6eTnl5eedzKioqOg/r+aNz7ZHdbic2NparrroKaD+Utm3bNkA96uhRh3/961/k5+d3eW31qL1HVVVV7Nu3j69+9asA5OXl4XK5qK6uVo+O+RzZbDb+8pe/UFBQwA033IDX6yUpKSloerR371527NgBQHR0NFOmTOHDDz/snJgH4HK5cDgcZGRkdLm/472lpKRQV1eHx+Pp8njw7983hX8vKSsr46677mLp0qVMmzYNgMbGRr773e9SX19Pa2srf/3rX8nPz8disXDbbbfhdDoxDIPnn3+e/Px8YmJiePbZZ9m6dSsAf/3rX7n22msBmDx5MgUFBQCsXr2anJwcwsPDmTx5MitXrgRg06ZNREZG0q9fv75vQA/0Ro8GDBhARkYG77zzDgD//ve/GTVqFKAedfSow5YtW8jJyeny+upRe4+Sk5OJjIxk06ZNQHtQxsbGkpKSoh4d8zl64IEHOv+4/tOf/sTUqVOxWq1B0SNoP+PjwQcfpLW1ldbWVt58801uvvlm9u/fz8GDB/F4PPzjH/8gNzeXrKwsIiMj2bx5MwArV64kNzeX8PBwcnJyWL16NQAFBQXk5uYC/v37ZjFOdpxLztgjjzzCyy+/zIABAzrvu/nmm7HZbDz//PO43W6mT5/OD37wA6B9IsivfvUrWltbueyyy1iwYAHh4eFs2rSJRx99lObmZgYNGsTjjz9OfHw8R44c4f7776eoqIj4+HiWLl1KdnY2LS0tLFy4kE8//ZSIiAgeeeSRzjD0N73Vo3379rFo0aLOsbaf//znDBo0SD06pkcAY8eO5aOPPiIyMrLztdSjL3u0bds2fvazn9Hc3ExsbCwLFy7kggsuUI+O69GiRYtoampixIgRPProo8TFxQVFjzr8z//8D6+//jphYWFMmTKFH/zgB2zYsIElS5bQ0tLC5MmT+clPfoLFYmHnzp08+OCD1NfXM2rUKJYsWUJERAQlJSXcf//9VFZWkpmZya9//WsSExP9uk8KfxERkRCjw/4iIiIhRuEvIiISYhT+IiIiIUbhLyIiEmIU/iIiIiFG4S8iIhJiFP4iIiIh5v8HVWXe1HdYbiMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_newcomb.plot(kind='density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Despite a small wobble, the distribution looks close to a normal distribution.\n",
    "\n",
    "#### Q-Q Plot\n",
    "\n",
    "While a kernel density plot gives a global overview and can easily indicate patterns in the data like two groups or asymmetry, you cannot see whether the normal distribution really fits (e.g., you cannot judge from it whether tails decay sufficiently fast). This is where a Q-Q plot can be used.\n",
    "\n",
    "In a Q-Q plot, the data are transformed such that a normal distribution would follow a straight line at 45 degrees. The straight line is convenient since it is easy to check visually whether points are on a straight line.\n",
    "\n",
    "You can create Q-Q plots using **`sm.qqplot()`**\n",
    "([documentation](https://www.statsmodels.org/stable/generated/statsmodels.graphics.gofplots.qqplot.html)).\n",
    "\n",
    "> **Note:** Unlike the other plotting methods we used in this course, `sm.qqplot()` does not return an `axes` object. Therefore, to assign a title using `.set_title()` we create a 1x1 subplot.\n",
    "\n",
    "Let us we create a Q-Q plot for the speed of light data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=1, ncols=1, sharex=True, sharey=True, squeeze=False)\n",
    "sm.qqplot(df_newcomb['Speed [km/s]'], fit=True, line='45', ax=ax[0,0])\n",
    "ax[0,0].set_title('Q-Q plot for Newcombs measurements');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a Q-Q plot, the closer the data points stay to the diagonal (45-degree line in red),\n",
    "the more the data follows a normal distribution.\n",
    "\n",
    "Here, the data again seems to be reasonably normally distributed.\n",
    "\n",
    "#### Anderson-Darling Normality Test\n",
    "\n",
    "We can also compute a (numerical) test statistic that tests for normality,\n",
    "using **`sm.stats.normal_ad()`**\n",
    "([documentation](https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.normal_ad.html)).\n",
    "It returns a pair: the **Anderson-Darling test statistic** (a floating-point number) and\n",
    "its **p-value**.\n",
    "\n",
    "When applying an Anderson Darling test, we assume that the data is normally distributed. This is our null hypothesis. The first number is the test statistic. The second number is the p-value. This p-value expresses the likelihood that the test statistic has this value under the null hypothesis. If this p-value is lower than 0.05, there is a less than 5% chance that this data would occur when drawn from a normal distribution. In that case we reject the null hypothesis and thus normality of our data.\n",
    "\n",
    "We compute the Anderson-Darling test statistic and the p-value for the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.16635374494890343, 0.8327921522120103)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.stats.normal_ad(df_newcomb['Speed [km/s]'])\n",
    "sm.stats.normal_ad(np.array([0.430, 0.712, 0.885, 1.08]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our case,\n",
    "the p-value is much larger than 0.05,\n",
    "indicating that this data set is **not** unlikely under the assumption\n",
    "that it is from a normal distribution.\n",
    "\n",
    "Hence from all three methods we see no evidence which indicates that the normality assumption has been violated and we can thus safely apply the **t-test for equality of means**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4 (Speed of Light): Apply Appropriate Test\n",
    "\n",
    "We defined a **two-sided** hypothesis for **equality of means** on **one-sample** data and verified that the assumption of normality does not appear to be violated. Now we can apply the appropriate test. In our case this is:\n",
    "* **t-test for equality of means**\n",
    "\n",
    "We wish to test whether the mean of the sample is equal to the currently known value for the speed of light or there is a significant difference.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### t-test for Equality of Means (One-sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, we repeat our hypothesis\n",
    "\n",
    "$$H_0:\\mu_{newcomb}=299792.458$$\n",
    "\n",
    "$$H_a:\\mu_{newcomb}\\neq 299792.458$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Carrying out this kind of test in Python with _StatsModels_ involves three steps:\n",
    "\n",
    "1. **Preprocess the data** using **ds = `sm.stats.DescrStatsW()`**.\n",
    "1. **Extract test parameters** using\n",
    "\n",
    "    * **`ds.ttest_mean(value, alternative='...')`** for **t-test statistic**, **p-value**, and\n",
    "        **degrees of freedom**,\n",
    "    * **`ds.tconfint_mean(alpha=..., alternative='...')`** for the **confidence interval**\n",
    "    \n",
    "    where\n",
    "    \n",
    "        * `value` is the value we are comparing the sample mean to,\n",
    "        * `alternative=` argument is one of \n",
    "\n",
    "            - `'two-sided'` (meaning the alternative hypothesis is $\\mu \\neq \\mu_0$),\n",
    "            - `'larger'` (meaning the alternative hypothesis is $\\mu > \\mu_0$),\n",
    "            - `'smaller'` (meaning the alternative hypothesis is $\\mu < \\mu_0$),\n",
    "\n",
    "        * `alpha=` argument is the significance level, e.g. `alpha=0.05` corresponding to the 95% confidence interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Preprocess the data (one-sample)**\n",
    "\n",
    "First, we preprocess the data sample and its expected mean separately.\n",
    "The resulting objects will be inputs to the actual comparison test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_newcomb = sm.stats.DescrStatsW(df_newcomb['Speed [km/s]'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract t-test statistic and p-value (one-sample)**\n",
    "\n",
    "The function `ds.ttest_mean(alternative='...')`\n",
    "returns the value of the t-test statistic and its p-value.\n",
    "It also returns as third value the *degrees of freedom*,\n",
    "but this value can be ignored, since we will not use it.\n",
    "\n",
    "Here are these values for the two-sided test, as we are considering the following alternative hypothesis:\n",
    "$𝐻_𝑎:\\mu_{newcomb}\\neq 299792.458$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.957593962870322, 1.8835359208278103e-07, 55.0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_newcomb.ttest_mean(299792.458, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **p-value** is the one in the middle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract confidence interval (one-sample)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `ds.tconfint_mean(alpha=..., alternative='...')` returns the\n",
    "confidence interval for the mean of the sample, with a confidence level of $1 - \\alpha$.\n",
    "For $\\alpha=0.05$ the interval gives a range where the mean is in with a probability of 0.95. Note that a one-sided interval with $\\alpha=0.025$ has one boundary similar to the two-sided interval with $\\alpha=0.05$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(299731.10613570415, 299761.9922101517)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_newcomb.tconfint_mean(alpha=0.05, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### t-test for Equality of Means (Two-sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now compare the measurements by Newcomb to those by Michelson to see if their speed of light estimates were actually that different.\n",
    "\n",
    "Our hypothesis becomes\n",
    "\n",
    "$$H_0:\\mu_{newcomb} = \\mu_{michelson}$$\n",
    "\n",
    "$$H_a:\\mu_{newcomb} \\neq \\mu_{michelson}$$\n",
    "\n",
    "This is an example of a **two-sided** hypothesis for **equality of means** on **two-sample** data.\n",
    "\n",
    "> **Note:** Before we apply the test we must check that all the assumptions are met, i.e. that both samples (Newcomb's and Michelson's) come from a normal distribution or that they are large. We did the check for Newcomb data already. If you do the check for Michelson data you will see that it is also met."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Carrying out this kind of test in Python with _StatsModels_ involves two steps:\n",
    "\n",
    "1. **Preprocess the data** using **`sm.stats.DescrStatsW()`**, creating *descriptive statistics objects* **`d1`** and **`d2`** for the two samples we want to compare,\n",
    "1. **Extract test parameters** using\n",
    "    * **`cm = sm.stats.CompareMeans(d1, d2)`** to create a *test object* **`cm`**, comparing **`d1`** to **`d2`**,\n",
    "    * **`cm.ttest_ind(alternative='...')`** for **t-test statistic**, **p-value**, and\n",
    "        **degrees of freedom**,\n",
    "    * **`cm.tconfint_diff(alpha=..., alternative='...')`** for the **confidence interval**,\n",
    "    \n",
    "    where\n",
    "        * `alternative=` is one of\n",
    "            - `'two-sided'` (meaning the alternative hypothesis is $\\mu_1 \\neq \\mu_2$),\n",
    "            - `'larger'` (meaning the alternative hypothesis is $\\mu_1 > \\mu_2$),\n",
    "            - `'smaller'` (meaning the alternative hypothesis is $\\mu_1 < \\mu_2$),\n",
    "        * `alpha=` argument is the significance level, e.g. `alpha=0.05` corresponding to the 95% confidence interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Preprocess the data (two-sample)**\n",
    "\n",
    "First, we preprocess the data sample and its expected mean separately.\n",
    "The resulting objects will be inputs to the actual comparison test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_newcomb = sm.stats.DescrStatsW(df_newcomb['Speed [km/s]'])\n",
    "d_michelson = sm.stats.DescrStatsW(df_michelson['Speed [km/s]'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create the test object using the preprocessed data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "cm = sm.stats.CompareMeans(d_newcomb, d_michelson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract t-test statistic and p-value (two-sample)**\n",
    "\n",
    "The function `cm.ttest_ind(alternative='...')`\n",
    "returns the value of the t-test statistic and its p-value.\n",
    "It also returns as third value the *degrees of freedom*,\n",
    "but this value can be ignored, since we will not use it.\n",
    "\n",
    "Here are these values for the two-sided test, as we are considering the following alternative hypothesis:\n",
    "$𝐻_𝑎:\\mu_{newcomb} \\neq \\mu_{michelson}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-16.437497750224615, 1.0487810072421076e-35, 154.0)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm.ttest_ind(alternative='two-sided')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **p-value** is the one in the middle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract confidence interval (two-sample)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `cm.tconfint_diff(alpha=..., alternative='...')` returns the\n",
    "confidence interval for the _difference between the means_ of the two samples (first minus second),\n",
    "with a confidence level of $1 - \\alpha$.\n",
    "For $\\alpha=0.05$ the interval gives a range where the difference is in with a probability of 0.95."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-221.6288954940909, -174.07275865012264)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm.tconfint_diff(alpha=0.05, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5 (Speed of Light): Decision\n",
    "\n",
    "The **p-value** and the **confidence interval** both express the same information in a different form. \n",
    "\n",
    "#### p-value\n",
    "\n",
    "The **p-value** is the easiest to interpret. When it is lower than a chosen $\\alpha$ (typically $0.05$) we reject the null hypothesis.\n",
    "\n",
    "From the p-value calculated in step 4 for the *one-sample* case, \n",
    "we see that in the case of a two-sided test with $\\alpha=0.05$,\n",
    "the *null hypothesis is rejected* (p-value is smaller than $\\alpha$).\n",
    "\n",
    "From the p-value calculated in step 4 for the *two-sample* case, \n",
    "we see that in the case of a two-sided test with $\\alpha=0.05$,\n",
    "the *null hypothesis is also rejected*.\n",
    "\n",
    "#### Confidence Interval\n",
    "\n",
    "For the *one-sample* case, the **confidence interval** can be interpreted in the following way. The confidence interval expresses the values between which the *mean* lies with 95% confidence. If the confidence interval contains the reference value (no difference in means) we cannot reject the null hypothesis. Otherwise, we reject the null hypothesis.\n",
    "\n",
    "From the confidence interval calculated in step 4 for the *one-sample* case, we can see that the *null hypothesis is rejected*, because it does not contain the reference value for speed of light 299792.458.\n",
    "\n",
    "For the *two-sample* case, the **confidence interval** can be interpreted in the following way. The confidence interval expresses the values between which the *difference between means* lies with 95% confidence. If the confidence interval contains 0 (no difference in means) we cannot reject the null hypothesis. Otherwise, we reject the null hypothesis.\n",
    "\n",
    "From the confidence interval calculated in step 4 for the *two-sample* case, we can see that the *null hypothesis is rejected*, because it does not contain the value 0, meaning that means are different."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Cloud Seeding\n",
    "\n",
    "You are now going to repeat the preceding tests for equality of the mean for a different dataset on _cloud seeding_.\n",
    "\n",
    "To improve rain fall in dry areas, an experiment was carried out with 52 clouds.\n",
    "Scientists investigated whether the addition of _silver nitrate_ __increases__ the rainfall.\n",
    "They chose 26 out of a sample of 52 clouds and seeded it with silver nitrate.\n",
    "The remaining 26 clouds were not treated with silver nitrate.\n",
    "\n",
    "The data set `./datasets/clouds.csv` records the rainfall in _feet per acre_.\n",
    "The dataset was constructed to test whether the addition of silver nitrate on clouds causes more rainfall.\n",
    "There are two samples: one column _with_ the silver nitrate treatment and one column _without_ the treatment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>without</th>\n",
       "      <th>with</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1202.6</td>\n",
       "      <td>2745.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>830.1</td>\n",
       "      <td>1697.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>372.4</td>\n",
       "      <td>1656.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>345.5</td>\n",
       "      <td>978.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>321.2</td>\n",
       "      <td>703.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>244.3</td>\n",
       "      <td>489.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>163.0</td>\n",
       "      <td>430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>147.8</td>\n",
       "      <td>334.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>95.0</td>\n",
       "      <td>302.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>87.0</td>\n",
       "      <td>274.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>81.2</td>\n",
       "      <td>274.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>68.5</td>\n",
       "      <td>255.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>47.3</td>\n",
       "      <td>242.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>41.1</td>\n",
       "      <td>200.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>36.6</td>\n",
       "      <td>198.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>29.0</td>\n",
       "      <td>129.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>28.6</td>\n",
       "      <td>119.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>26.3</td>\n",
       "      <td>118.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>26.1</td>\n",
       "      <td>115.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>24.4</td>\n",
       "      <td>92.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21.7</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>17.3</td>\n",
       "      <td>32.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>11.5</td>\n",
       "      <td>31.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>4.9</td>\n",
       "      <td>17.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4.9</td>\n",
       "      <td>7.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    without    with\n",
       "0    1202.6  2745.6\n",
       "1     830.1  1697.8\n",
       "2     372.4  1656.0\n",
       "3     345.5   978.0\n",
       "4     321.2   703.4\n",
       "5     244.3   489.1\n",
       "6     163.0   430.0\n",
       "7     147.8   334.1\n",
       "8      95.0   302.8\n",
       "9      87.0   274.7\n",
       "10     81.2   274.7\n",
       "11     68.5   255.0\n",
       "12     47.3   242.5\n",
       "13     41.1   200.7\n",
       "14     36.6   198.6\n",
       "15     29.0   129.6\n",
       "16     28.6   119.0\n",
       "17     26.3   118.3\n",
       "18     26.1   115.3\n",
       "19     24.4    92.4\n",
       "20     21.7    40.6\n",
       "21     17.3    32.7\n",
       "22     11.5    31.4\n",
       "23      4.9    17.5\n",
       "24      4.9     7.7\n",
       "25      1.0     4.1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clouds = pd.read_csv(\"./datasets/clouds.csv\")\n",
    "df_clouds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your task in this exercise is to perform the correct statistical test corresponding to the question whether cloud seeding has effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 (Cloud Seeding): Define Quantitative Question\n",
    "\n",
    "#### Exercise 1.a\n",
    "Choose the option that matches our situation best and assign either `'a'`, `'b'`, `'c'` or `'d'` to the variable `question_cloud`.\n",
    "\n",
    "> a. Does cloud seeding work? <br>\n",
    "> b. Is there a difference in average rainfall when cloud seeding has been applied? <br>\n",
    "> c. Does application of cloud seeding increase average rainfall?<br>\n",
    "> d. Does application of cloud seeding increase proportion of rainfall?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_1a] Define quantitative question (1 point)\n",
    "\n",
    "question_cloud = 'c'\n",
    "\n",
    "#// END_TODO [HYP_1a]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 (Cloud Seeding): Formulate Hypothesis\n",
    "\n",
    "#### Exercise 1.b\n",
    "Formulate the question you chose above as statistical hypotheses. Encode them as strings in the following way:\n",
    "\n",
    "- For the null hypothesis use `'mu_with=mu_without'`, using `mu` for comparing means.\n",
    "- For the alternative hypothesis use `!=`, `>` or `<`, e.g. `'mu_with<mu_without'`.\n",
    "\n",
    "Assign the null and alternative hypotheses encoded as strings to variables `H_0_cloud` and `H_a_cloud`, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('mu_with=mu_without', 'mu_with!=mu_without')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1b] Formulate hypothesis(1 point)\n",
    "\n",
    "H_0_cloud = 'mu_with=mu_without'\n",
    "H_a_cloud = 'mu_with!=mu_without'\n",
    "\n",
    "#// END_TODO [HYP_1b]\n",
    "H_0_cloud, H_a_cloud"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 (Cloud Seeding): Check Assumptions\n",
    "\n",
    "The t-test is valid for large datasets, or for small datasets that follow the normal distribution. Our rule of thumb in these exercises says that a dataset is considered small when it contains fewer than 50 samples. If we look at the number of samples in the `df_clouds` dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_clouds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see that there are relatively few samples, so we should check for normality. We will use the three techniques to test for normality:\n",
    "\n",
    "* A **kernel density plot**\n",
    "* A **Q-Q plot** \n",
    "* The **Anderson-Darling normality test**\n",
    "\n",
    "Note that if the dataset is large, we do not need to check for normality before applying the t-test for equality of means."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.c\n",
    "\n",
    "Create, in one figure, density plots of the data _with_ and _without_ seeding.\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Select both columns separately, and apply a density plot on each.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1c] Density plots of data (1 point)\n",
    "\n",
    "ax = df_clouds['with'].plot(kind='density', label='With Seeding')\n",
    "df_clouds['without'].plot(kind='density', label='Without Seeding', ax=ax)\n",
    "ax.set_title(\"Density Plots of Data with and without Cloud Seeding\", fontsize=14)\n",
    "ax.set_xlabel(\"Values\", fontsize=12)\n",
    "ax.legend(title=\"Legend\")\n",
    "\n",
    "#// END_TODO [HYP_1c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.d\n",
    "\n",
    "Create two Q-Q plots for the data _with_ and _without_ seeding. Place the plots next to each other and do not forget to add titles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Without Seeding')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1d] Q-Q plot for data with and without seeding (1 point)\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2,sharex=True,squeeze=False,figsize=(16,8))\n",
    "sm.qqplot(df_clouds['with'],fit=True,ax=ax[0,0],line='45')\n",
    "sm.qqplot(df_clouds['without'],fit=True,ax=ax[0,1],line='45')\n",
    "\n",
    "ax[0,0].set_title(\"With Seeding\")\n",
    "\n",
    "ax[0,1].set_title(\"Without Seeding\")\n",
    "#// END_TODO [HYP_1d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.e\n",
    "\n",
    "Apply Anderson-Darling normality test to the data _with_ and _without_ seeding, and assign the resulting objects to `anderson_darling_with` and `anderson_darling_without` variables, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3.391069805893679, 9.605483420175515e-09),\n",
       " (3.801896473412558, 9.048556290228121e-10))"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1e] Anderson-Darling normality test for data with and without seeding (1 point)\n",
    "\n",
    "anderson_darling_with = sm.stats.normal_ad(df_clouds['with'])\n",
    "anderson_darling_without = sm.stats.normal_ad(df_clouds['without'])\n",
    "\n",
    "p_anderson_darling_with = anderson_darling_with[1]\n",
    "p_anderson_darling_without = anderson_darling_without[1]\n",
    "\n",
    "#// END_TODO [HYP_1e]\n",
    "\n",
    "anderson_darling_with, anderson_darling_without"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From above results you should notice the following things:\n",
    " * The long wobbly tails on the right in the kernel density plot indicate that this is not really a normal distribution. \n",
    " * In the Q-Q plots, the points stray far from the line\n",
    " * In the Anderson-Darling test in both cases, the p-values are extremely small, indicating that these data sets are very unlikely under the assumption that they are from a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This indicates a problem: since the dataset is relatively small and the assumption of normality appears to be violated, we should **not** apply a t-test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A distribution skewed to the right can in some cases be transformed into in a normal distribution by taking the log of the data.\n",
    "We add two columns to the data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>without</th>\n",
       "      <th>with</th>\n",
       "      <th>with_log</th>\n",
       "      <th>without_log</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>26.000000</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>26.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>164.588462</td>\n",
       "      <td>441.984615</td>\n",
       "      <td>5.134187</td>\n",
       "      <td>3.990406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>278.426404</td>\n",
       "      <td>650.787171</td>\n",
       "      <td>1.599514</td>\n",
       "      <td>1.641847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.100000</td>\n",
       "      <td>1.410987</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>24.825000</td>\n",
       "      <td>98.125000</td>\n",
       "      <td>4.581480</td>\n",
       "      <td>3.211421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>44.200000</td>\n",
       "      <td>221.600000</td>\n",
       "      <td>5.396406</td>\n",
       "      <td>3.786259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>159.200000</td>\n",
       "      <td>406.025000</td>\n",
       "      <td>6.000699</td>\n",
       "      <td>5.069278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1202.600000</td>\n",
       "      <td>2745.600000</td>\n",
       "      <td>7.917755</td>\n",
       "      <td>7.092241</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           without         with   with_log  without_log\n",
       "count    26.000000    26.000000  26.000000    26.000000\n",
       "mean    164.588462   441.984615   5.134187     3.990406\n",
       "std     278.426404   650.787171   1.599514     1.641847\n",
       "min       1.000000     4.100000   1.410987     0.000000\n",
       "25%      24.825000    98.125000   4.581480     3.211421\n",
       "50%      44.200000   221.600000   5.396406     3.786259\n",
       "75%     159.200000   406.025000   6.000699     5.069278\n",
       "max    1202.600000  2745.600000   7.917755     7.092241"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clouds['with_log'] = np.log(df_clouds['with'])\n",
    "df_clouds['without_log'] = np.log(df_clouds['without'])\n",
    "df_clouds.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are now going to repeat the preceding normality tests on the transformed data to see if the data now indeed resembles a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.f\n",
    "Create density plots of the  log-transformed data\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Select both columns separately, and apply a density plot. Add a legend to keep both density plots apart.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2694892e1f0>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1f] Density plots of  log-transformed data (1 point)\n",
    "\n",
    "ax = df_clouds['with_log'].plot(kind='density', label='with', figsize=(8, 6))\n",
    "df_clouds['without_log'].plot(kind='density', ax=ax, label='without')\n",
    "ax.set_title(\"Density Plots of Log-Transformed Data (with and without cloud seeding)\")\n",
    "ax.set_xlabel(\"Log-Transformed Values\")\n",
    "ax.set_ylabel(\"Density\")\n",
    "ax.legend()\n",
    "\n",
    "#// END_TODO [HYP_1f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.g\n",
    "\n",
    "Create two Q-Q plots for the log-transformed data _with_ and _without_ seeding. Place the plots next to each other and do not forget to add titles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Without Seeding')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1g] Q-Q plot for log-transformed data with and without seeding (1 point)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2,sharex=True,squeeze=False,figsize=(16,8))\n",
    "sm.qqplot(df_clouds['with_log'],fit=True,ax=ax[0,0],line='45')\n",
    "sm.qqplot(df_clouds['without_log'],fit=True,ax=ax[0,1],line='45')\n",
    "\n",
    "ax[0,0].set_title(\"With Seeding\")\n",
    "\n",
    "ax[0,1].set_title(\"Without Seeding\")\n",
    "\n",
    "#// END_TODO [HYP_1g]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.h\n",
    "Apply the Anderson-Darling normality test to the log-transformed data with and without cloud seeding. Assign the resulting objects to `anderson_darling_with_log` and `anderson_darling_without_log`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0.37033204575403644, 0.3986895582917981),\n",
       " (0.23405725120319332, 0.771739527759551))"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1h] Anderson-Darling normality tests for log-transformed data (1 point)\n",
    "\n",
    "p_anderson_darling_with_log = sm.stats.normal_ad(df_clouds['with_log'])\n",
    "p_anderson_darling_without_log = sm.stats.normal_ad(df_clouds['without_log'])\n",
    "\n",
    "#// END_TODO [HYP_1h]\n",
    "\n",
    "p_anderson_darling_with_log, p_anderson_darling_without_log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.i\n",
    "\n",
    "Does the log-scaled data seem to follow a normal distribution? Assign your (boolean) answers to the variables `normal_cloud_with` and `normal_cloud_without`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_1i] Does the log-scaled data follow a normal distribution (1 point)\n",
    " \n",
    "normal_cloud_with = True\n",
    "normal_cloud_without = True\n",
    "\n",
    "#// END_TODO [HYP_1i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4 (Cloud Seeding): Apply Appropriate Test\n",
    "\n",
    "#### Exercise 1.j\n",
    "Preprocess each of the two data samples separately. \n",
    "Use the **log-transformed** data! Assign the results to `d_with_log` and `d_without_log`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_1j]  Preprocess the log-transformed data (1 point)\n",
    "\n",
    "d_with_log = sm.stats.DescrStatsW(df_clouds['with_log'])\n",
    "d_without_log = sm.stats.DescrStatsW(df_clouds['without_log'])\n",
    "\n",
    "#// END_TODO [HYP_1j]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.k\n",
    "Create the test object using the preprocessed data:\n",
    "Assign the test object to `cm_cloud_log`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_1k] Create test object (1 point)\n",
    "\n",
    "cm_cloud_log = sm.stats.CompareMeans(d_with_log,d_without_log)\n",
    "\n",
    "#// END_TODO [HYP_1k]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.l\n",
    "\n",
    "Perform the appropriate test for the hypothesis you chose. Assign the resulting p-value to `p_cloud_log`.\n",
    "\n",
    "Make sure you only save the p-value in the mentioned variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007041329483603202"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_1l] apply test on (1 point)\n",
    "\n",
    "p_cloud_log = cm_cloud_log.ttest_ind(alternative ='larger')[1]\n",
    "\n",
    "#// END_TODO [HYP_1l]\n",
    "\n",
    "p_cloud_log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5 (Cloud Seeding): Decision\n",
    "\n",
    "#### Exercise 1.m\n",
    "\n",
    "What is your conclusion? Is there sufficient evidence to reject the null hypothesis (at significance level $\\alpha=0.05$) based on the log-transformed data? Assign your (boolean) answer to the variables `reject_null_cloud_log`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_1m] Decision for confidence limits (1 point)\n",
    "\n",
    "reject_null_cloud_log = True\n",
    "\n",
    "#// END_TODO [HYP_1m]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 2. Hypothesis Testing on Proportions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning Objectives of This Section\n",
    "\n",
    "After this section, you should\n",
    "\n",
    "* know how to do _one-sided_ and _two-sided_ tests for **equality of proportions**\n",
    "    of _one-sample_ and _two-sample_ data\n",
    "* know how to draw conclusions about acceptance or rejection of the null hypothesis based on:\n",
    "  * p-value resulting from the z-test\n",
    "  * confidence intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Exams\n",
    "\n",
    "We now visit hypothesis testing on proportions.\n",
    "For these tests we only need the number of observations and the number of successes.\n",
    "\n",
    "Let us look at a class of students following a course.\n",
    "The class has 100 students, and 88 pass their exam.\n",
    "The previous year, there were 89 students and 70 passed the exam.\n",
    "The teacher has made large improvements to her course according to the feedback she has gotten from student reviews. The expectation is therefore that the passing rate has gone up.\n",
    "\n",
    "We set up the data in these variables:\n",
    "\n",
    "* `students` for the total number of students\n",
    "* `passes` for the number of students who passed on the exam\n",
    "* `students_previous` for the total number of students in the previous year\n",
    "* `passes_previous` for the number of students that passed in the previous year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.88, 0.7865168539325843)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "students = 100\n",
    "passes = 88\n",
    "\n",
    "rate = passes/students\n",
    "\n",
    "students_previous = 89\n",
    "passes_previous = 70\n",
    "\n",
    "rate_previous = passes_previous / students_previous\n",
    "\n",
    "rate, rate_previous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again we will follow the four steps as explained above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 (Exams): Define Quantitative Question\n",
    "\n",
    "From the introduction above we can conclude that we want to investigate whether or not the passing rate has improved. We can define the following quantitative question.\n",
    "\n",
    "> Is the proportion of students which passed the exam this year significantly larger than the proportion of students that passed last year?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 (Exams): Formulate Hypothesis\n",
    "\n",
    "Again we should pay attention to the following: do we want to test for the equality of means or the equality of proportions. \n",
    "\n",
    "In this case we are interested in the **fraction** of the students that have failed. Hence we are interested in the **equality of proportions**\n",
    "\n",
    "As defined in step 1, we want to investigate whether or not the passing rate has improved. From the context we have a clear indication of a direction in which we expect the proportion to change. Therefore we should formulate a **one-sided** alternative hypothesis. \n",
    "\n",
    "In short, we will define a **one-sided** hypothesis for **equality of proportion** on **two-sample** data\n",
    "\n",
    "The corresponding hypotheses are\n",
    "\n",
    "$$H_0: p_{new} = p_{old}$$\n",
    "\n",
    "$$H_a: p_{new} > p_{old}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 (Exams): Check Assumptions\n",
    "\n",
    "In the case of testing for equality of proportion we do not assume our data to come from a normal distribution. Therefore we do not have to check for normality and can thus ignore this step. There are other assumptions when testing proportions and ways to check these assumptions, but they are outside the scope of this course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4 (Exams): Apply Appropriate Test\n",
    "\n",
    "We defined a **one-sided** hypothesis for **equality of proportions** on **two-sample data**. Now we can apply the appropriate test. In our case this is the\n",
    "\n",
    "* **z-test for equality of proportions**\n",
    "\n",
    "We can extract the z-test statistic and p-value using\n",
    "\n",
    "**`sm.stats.proportions_ztest(count, number_observations, value=..., alternative=...)`**\n",
    "\n",
    "The `proportions_ztest()` function returns a pair: the z-test statistic and the corresponding **p-value**.\n",
    "\n",
    "#### z-test for Equality of Proportions (One-sample)\n",
    "\n",
    "In case of a **one-sample** test, the `proportions_ztest()` function takes the following arguments:\n",
    "- **`count`**: the number of positive observations\n",
    "- **`number_observations`**: the total number of observations\n",
    "- **`value=`**: the reference proportion you want to compare with\n",
    "- **`alternative=`**: one of `'two-sided'`, `'larger'`, or `'smaller'`\n",
    "\n",
    "#### z-test for Equality of Proportions (Two-sample)\n",
    "\n",
    "In case of a **two-sample** test, the `proportions_ztest()` function takes the following arguments:\n",
    "    \n",
    "- **`count`**: a list `[num_new_positive_observations, num_old_positive_observations]` containing the number of positive observations in the new and old samples\n",
    "- **`number_observations`**: a list `[num_new_observations, num_old_observations]` containing the total number of observations in the new and old samples\n",
    "- **`alternative=`**: one of `'two-sided'`, `'larger'`, or `'smaller'`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wish to test whether the proportion of students that passed the last exam is larger than the proportion of students that passed in the past (i.e. a two-sample test).\n",
    "\n",
    "For convenience, we repeat our hypothesis:\n",
    "\n",
    "$$H_0: p_{new}=p_{old}$$\n",
    "\n",
    "$$H_a: p_{new}> p_{old}$$\n",
    "\n",
    "We can compute the p-value for a z-test in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.7324066201653368, 0.041600595056627936)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ztest_exam = sm.stats.proportions_ztest([passes, passes_previous], [students, students_previous], alternative='larger')\n",
    "ztest_exam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extract the p-value\n",
    "\n",
    "The **p-value** is the second number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.041600595056627936"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ztest_exam[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Extract the Confidence Interval (One-sample)\n",
    "\n",
    "We can compute a 95%-confidence interval `CI_exam` for the proportion of passing students,\n",
    "using function **`sm.stats.proportion_confint(count, number_observations, alpha=...)`**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8163087092715731, 0.943691290728427)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CI_exam = sm.stats.proportion_confint(passes, students, alpha=0.05)\n",
    "CI_exam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Extract the Confidence Interval (Two-sample)\n",
    "\n",
    "The function **`statsmodels.stats.proportion.confint_proportions_2indep(count1, n1, count2, n2, alpha=...)`** returns the confidence interval for the difference between the proportions `count1/n1` and `count2/n2` of the two samples (first minus second), with a confidence level of  1−𝛼 . For  𝛼=0.05  the interval gives a range where the difference is in with a probability of 0.95."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.01298407030544961, 0.20176657139343457)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "statsmodels.stats.proportion.confint_proportions_2indep(passes, students, passes_previous, students_previous, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5 (Exams): Decision\n",
    "\n",
    "The **p-value** and the **confidence interval** both express the same information in a different form. \n",
    "\n",
    "#### p-value\n",
    "\n",
    "The **p-value** is the easiest to interpret. When it is lower than a chosen $\\alpha$ (typically $0.05$) we reject the null hypothesis.\n",
    "\n",
    "For the p-value calculated in step 4, we can see that in the case of $\\alpha=0.05$ the *null hypothesis is rejected*, because the p-value is below 0.05.\n",
    "\n",
    "#### Confidence Interval\n",
    "\n",
    "For the *one-sample* case, the **confidence interval** can be interpreted in the following way. The confidence interval expresses the values between which the *proportion* lies with 95% confidence. If the confidence interval contains the reference value we cannot reject the null hypothesis. Otherwise, we reject the null hypothesis.\n",
    "\n",
    "For the *two-sample* case, the **confidence interval** can be interpreted in the following way. The confidence interval expresses the values between which the *difference between proportions* lies with 95% confidence. If the confidence interval contains 0 (no difference in means) we cannot reject the null hypothesis. Otherwise, we reject the null hypothesis.\n",
    "\n",
    "From the confidence interval calculated in step 4 for the *two-sample* case, we can see that the *null hypothesis is rejected*, because it does not contain the value 0, meaning that means are different."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Exercise: Silicon Wafers\n",
    "\n",
    "An important quality characteristic in integrated-circuit manufacturing is\n",
    "the thickness of the wafer\n",
    "(a wafer is a slice of silicon from which chips are made\n",
    "for use as integrated circuits in devices like smart phones).\n",
    "As a routine, the thickness is measured in a gage, only giving two results: good, or bad.\n",
    "\n",
    "It is known from previous years that $15\\%$ of the wafers are bad.\n",
    "A new batch arrives and a sample of $50$ wafers is taken from this new batch.\n",
    "The number of bad wafers in this sample equals $13$.\n",
    "We would like to know whether or not there is a difference in the fraction of bad wafers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2.a\n",
    "\n",
    "Compute the fraction of bad wafers in the new sample. Assign the number of wafers and number of bad wafers to the variables `num_wafers` and `num_bad_wafers`,\n",
    "and the old and the new proportion to the variables\n",
    "`prop_bad_wafers_old` and `prop_bad_wafers_new`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 13, 0.15, 0.26)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_2a] Wafers, bad wafers, old and new proportion (1 point)\n",
    "\n",
    "num_wafers = 50\n",
    "num_bad_wafers = 13\n",
    "prop_bad_wafers_new = num_bad_wafers/num_wafers\n",
    "prop_bad_wafers_old = 0.15\n",
    "\n",
    "#// END_TODO [HYP_2a]\n",
    "\n",
    "num_wafers, num_bad_wafers, prop_bad_wafers_old, prop_bad_wafers_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 (Silicon Wafers): Define a Quantitative Question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2.b\n",
    "Choose the most appropriate quantitative question for our example.\n",
    "\n",
    "Assign `'a'`, `'b'` or `'c'` to the variable `question_wafers`\n",
    "\n",
    "> a. Has the proportion of bad wafers in the new batch changed compared to previous years?<br>\n",
    "> b. Has the average of bad wafers in the new batch changed compared to previous years?<br>\n",
    "> c. Is the proportion of bad wafers in the new batch greater than previous years?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_2b] Choose quantitative question (1 point)\n",
    "\n",
    "question_wafers = 'a'\n",
    "\n",
    "#// END_TODO [HYP_2b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 (Silicon Wafers): Formulate Hypothesis\n",
    "\n",
    "#### Exercise 2.c\n",
    "\n",
    "Formulate the question you chose above as statistical hypotheses. Encode them as strings in the following way:\n",
    "\n",
    "- For the null hypothesis use `'mu_old=mu_new'` or `'p_old=p_new'`, using `mu` for comparing means and `p` for comparing proportions.\n",
    "- For the alternative hypothesis use `!=`, `>` or `<`, e.g. `'mu_old<mu_new'`.\n",
    "\n",
    "Assign the null and alternative hypotheses encoded as strings to variables `H_0_wafers` and `H_a_wafers`, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_2c] Formulate Hypothesis (1 point)\n",
    "\n",
    "H_0_wafers = 'p_old=p_new'\n",
    "H_a_wafers = 'p_old!=p_new'\n",
    "#// END_TODO [HYP_2c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 (Silicon Wafers): Check Assumptions\n",
    "#### Exercise 2.d\n",
    "If there are assumptions you can check please do so.\n",
    "\n",
    "Assign **True** to the variable `check_assump_wafers` if assumptions need to be checked, **False** if not.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_2d] Check Assumptions (1 point)\n",
    "\n",
    "check_assump_wafers = False\n",
    "\n",
    "#// END_TODO [HYP_2d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4 (Silicon Wafers): Apply Correct Test\n",
    "\n",
    "#### Exercise 2.e\n",
    "\n",
    "Choose and apply the correct test. Assign the resulting p-value to `p_wafers`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07618378378160437"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_2e] Apply test (1 point)\n",
    "ztest = sm.stats.proportions_ztest(num_bad_wafers,num_wafers,value=prop_bad_wafers_old, alternative = 'two-sided')\n",
    "p_wafers = ztest[1]\n",
    "\n",
    "#// END_TODO [HYP_2e]\n",
    "p_wafers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2.f\n",
    "\n",
    "Is there sufficient evidence to reject the null hypothesis (at significance level $\\alpha=0.05$)? Assign your (boolean) answer to the variable `reject_null_wafers`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_2f] Has the fraction of bad wafers changed? (1 point)\n",
    "\n",
    "reject_null_wafers=False\n",
    "\n",
    "#// END_TODO [HYP_2f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 3. Performing Diagnostics on Regression Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning Objectives of This Section\n",
    "\n",
    "After this section, you should\n",
    "\n",
    "* know how to inspect normalized residuals of a linear model\n",
    "* know how to interpret normalized residual values to indicate wrong model assumption or suspected outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Boiling Point of Water\n",
    "\n",
    "In this exercise we use the data set `./datasets/water.csv`. This data set describes an experiment conducted by James David Forbes in 1844 in the Alps to use the boiling point of water to estimate the altitude (through the pressure). The idea is that it is easy to measure the boiling point of water. The boiling point is available in the column `'bp'` (in degrees Celsius) and the pressure (in inches of mercury) is available in the column `'pres'`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bp</th>\n",
       "      <th>pres</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90.277778</td>\n",
       "      <td>20.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>90.166667</td>\n",
       "      <td>20.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>92.166667</td>\n",
       "      <td>22.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>92.444444</td>\n",
       "      <td>22.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>93.000000</td>\n",
       "      <td>23.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>93.277778</td>\n",
       "      <td>23.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>93.833333</td>\n",
       "      <td>23.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>93.944444</td>\n",
       "      <td>23.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>94.111111</td>\n",
       "      <td>24.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>94.055556</td>\n",
       "      <td>24.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>95.333333</td>\n",
       "      <td>25.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>96.400000</td>\n",
       "      <td>26.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>98.611111</td>\n",
       "      <td>28.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>98.111111</td>\n",
       "      <td>27.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>99.277778</td>\n",
       "      <td>29.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>99.944444</td>\n",
       "      <td>29.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>100.111111</td>\n",
       "      <td>30.06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            bp   pres\n",
       "0    90.277778  20.79\n",
       "1    90.166667  20.79\n",
       "2    92.166667  22.40\n",
       "3    92.444444  22.67\n",
       "4    93.000000  23.15\n",
       "5    93.277778  23.35\n",
       "6    93.833333  23.89\n",
       "7    93.944444  23.99\n",
       "8    94.111111  24.02\n",
       "9    94.055556  24.01\n",
       "10   95.333333  25.14\n",
       "11   96.400000  26.57\n",
       "12   98.611111  28.49\n",
       "13   98.111111  27.76\n",
       "14   99.277778  29.04\n",
       "15   99.944444  29.88\n",
       "16  100.111111  30.06"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_forbes= pd.read_csv(\"./datasets/water.csv\")\n",
    "df_forbes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we inspect our data using a scatter plot. In this way we can get an idea of what order polynomial we should fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df_forbes.plot(kind='scatter', x='bp', y='pres', c='b')\n",
    "ax.set_xlabel('Boiling point (in degrees Celcius)')\n",
    "ax.set_ylabel('Pressure (in inches of mercury)')\n",
    "ax.set_title(\"Pressure vs boiling point of water\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot suggests that a first order polynomial might be a good fit. Let's fit a regression model and investigate these observations.\n",
    "\n",
    "We estimate a linear regression model with the pressure as dependent variable and the boiling point as independent variable. \n",
    "\n",
    "Remember that a simple linear regression model tries to find the best fit for $a$ and $b$ in $$dependent\\_var = a * independent\\_var + b $$\n",
    "\n",
    "For this we use the **Ordinary Least Squares** (OLS) method from the SciKit Learn library that we used in the DMM exercises."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_forbes[['bp']]\n",
    "y = df_forbes['pres']\n",
    "linear_model = LinearRegression()\n",
    "linear_model.fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Note:** `X` is a `DataFrame` and `y` is a `Series`.\n",
    "\n",
    "We can visualize the regression model with the _Seaborn_ library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Ben\\anaconda3\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.regplot(df_forbes['bp'], df_forbes['pres'])\n",
    "ax.set_xlabel('Boiling point (in degrees Celcius)')\n",
    "ax.set_ylabel('Pressure (in inches of mercury)')\n",
    "ax.set_title(\"Pressure vs boiling point of water\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Evaluation\n",
    "\n",
    "Let us check how well we fit our training data by computing the $R^2$ score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9972253366738393"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_model.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$R^2$ is almost 1. Does this mean we fitted the correct linear model?\n",
    "\n",
    "To evaluate the quality of our linear model, we plot the normalized residuals. Let us compute the residuals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = linear_model.predict(X)\n",
    "residuals = (y - y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and normalize them using the `scale()` method from the SciKit Learn library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import scale\n",
    "\n",
    "residuals_norm = scale(residuals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the normalized residuals against the independent variable (i.e. the boiling point)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_forbes_vis = df_forbes.copy()\n",
    "df_forbes_vis['residuals'] = residuals_norm\n",
    "\n",
    "ax = df_forbes_vis.plot(kind='scatter', x='bp', y='residuals', c='b')\n",
    "ax.set_xlabel('Boiling point (in degrees Celcius)')\n",
    "ax.set_ylabel('Normalized residuals')\n",
    "ax.set_title('Normalized residuals for pressure', fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two things we should note from the above plot. First, the residuals do not seem unstructured. There might be a parabolic shape. This is not completely clear from the plot but a doubt like this indicates that we should at least investigate other regression models.\n",
    "\n",
    "Secondly, if we assume this parabolic shape, there might be an outlier: the point at around 96.5. This is an interesting find, as it was not visible from the visual inspection of the data.\n",
    "\n",
    "The first thing we should do here is investigating if there is a better fitting model. Theory around the phenomenon you are studying is usually a good place to start. Theory tells us that there is a linear relation between the temperature and the _log_ of the pressure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first fit a linear model on the logarithm of the pressure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_log = np.log(df_forbes['pres'])\n",
    "linear_model_log = LinearRegression()\n",
    "linear_model_log.fit(X, y_log);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then draw a scatter plot of the normalized residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_log_pred = linear_model_log.predict(X)\n",
    "residual_log = scale(y_log - y_log_pred)\n",
    "\n",
    "df_forbes_log_vis = df_forbes.copy()\n",
    "df_forbes_log_vis['residuals'] = residual_log\n",
    "\n",
    "ax = df_forbes_log_vis.plot(kind='scatter', x='bp', y='residuals', c='b')\n",
    "ax.set_xlabel('Boiling point')\n",
    "ax.set_ylabel('Normalized residuals')\n",
    "ax.set_title('Normalized residuals for logarithm of pressure', fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residuals seem less structured, which indicates that the new model fits the data better.\n",
    "\n",
    "As indicated in the lecture a normalized residual value higher than 2.5 might indicate an outlier (rule of thumb). Since the normalized residual for the point with pressure 96.4 (log pressure 4.57) is larger than 2.5, this point should be investigated further.\n",
    "\n",
    "Ideally we would check with the data collector, if there is a reason to exclude this point. Perhaps equipment malfunctioned. Since we can no longer ask Dr. Forbes, rules of scientific integrity dictate that we just have to accept this data point, as we have no solid arguments for removing it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Timber"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value of a timber tree is determined by the volume of it, but this can only be determined after the tree is cut down and sawn up. We somehow would like to predict the volume of the tree from the girth (the circumference) of the tree, and its height, which are easy to measure when the tree is still standing. We will use the dataset in `./datasets/trees.csv` which contains a table with three columns:\n",
    "\n",
    "- **`girth`**: the girth of a tree at breast height, in inches (1 foot = 12 inches)\n",
    "- **`height`**: the height of a tree, in feet\n",
    "- **`volume`**: the volume of timber produced from the tree, in cubic feet\n",
    "\n",
    "We will fit a regression model with girth and height as independent variables. \n",
    "\n",
    "(This exercise was adapted from Bingham and Fry (2010))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>girth</th>\n",
       "      <th>height</th>\n",
       "      <th>volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.3</td>\n",
       "      <td>70</td>\n",
       "      <td>10.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.6</td>\n",
       "      <td>65</td>\n",
       "      <td>10.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.8</td>\n",
       "      <td>63</td>\n",
       "      <td>10.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.5</td>\n",
       "      <td>72</td>\n",
       "      <td>16.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10.7</td>\n",
       "      <td>81</td>\n",
       "      <td>18.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10.8</td>\n",
       "      <td>83</td>\n",
       "      <td>19.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11.0</td>\n",
       "      <td>66</td>\n",
       "      <td>15.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11.0</td>\n",
       "      <td>75</td>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>11.1</td>\n",
       "      <td>80</td>\n",
       "      <td>22.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11.2</td>\n",
       "      <td>75</td>\n",
       "      <td>19.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11.3</td>\n",
       "      <td>79</td>\n",
       "      <td>24.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>11.4</td>\n",
       "      <td>76</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>11.4</td>\n",
       "      <td>76</td>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>11.7</td>\n",
       "      <td>69</td>\n",
       "      <td>21.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>12.0</td>\n",
       "      <td>75</td>\n",
       "      <td>19.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>12.9</td>\n",
       "      <td>74</td>\n",
       "      <td>22.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>12.9</td>\n",
       "      <td>85</td>\n",
       "      <td>33.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>13.3</td>\n",
       "      <td>86</td>\n",
       "      <td>27.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>13.7</td>\n",
       "      <td>71</td>\n",
       "      <td>25.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>13.8</td>\n",
       "      <td>64</td>\n",
       "      <td>24.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>14.0</td>\n",
       "      <td>78</td>\n",
       "      <td>34.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>14.2</td>\n",
       "      <td>80</td>\n",
       "      <td>31.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>14.5</td>\n",
       "      <td>74</td>\n",
       "      <td>36.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>16.0</td>\n",
       "      <td>72</td>\n",
       "      <td>38.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>16.3</td>\n",
       "      <td>77</td>\n",
       "      <td>42.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>17.3</td>\n",
       "      <td>81</td>\n",
       "      <td>55.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>17.5</td>\n",
       "      <td>82</td>\n",
       "      <td>55.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>17.9</td>\n",
       "      <td>80</td>\n",
       "      <td>58.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>18.0</td>\n",
       "      <td>80</td>\n",
       "      <td>51.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>18.0</td>\n",
       "      <td>80</td>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>20.6</td>\n",
       "      <td>87</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    girth  height  volume\n",
       "1     8.3      70    10.3\n",
       "2     8.6      65    10.3\n",
       "3     8.8      63    10.2\n",
       "4    10.5      72    16.4\n",
       "5    10.7      81    18.8\n",
       "6    10.8      83    19.7\n",
       "7    11.0      66    15.6\n",
       "8    11.0      75    18.2\n",
       "9    11.1      80    22.6\n",
       "10   11.2      75    19.9\n",
       "11   11.3      79    24.2\n",
       "12   11.4      76    21.0\n",
       "13   11.4      76    21.4\n",
       "14   11.7      69    21.3\n",
       "15   12.0      75    19.1\n",
       "16   12.9      74    22.2\n",
       "17   12.9      85    33.8\n",
       "18   13.3      86    27.4\n",
       "19   13.7      71    25.7\n",
       "20   13.8      64    24.9\n",
       "21   14.0      78    34.5\n",
       "22   14.2      80    31.7\n",
       "23   14.5      74    36.3\n",
       "24   16.0      72    38.3\n",
       "25   16.3      77    42.6\n",
       "26   17.3      81    55.4\n",
       "27   17.5      82    55.7\n",
       "28   17.9      80    58.3\n",
       "29   18.0      80    51.5\n",
       "30   18.0      80    51.0\n",
       "31   20.6      87    77.0"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_timber = pd.read_csv('./datasets/trees.csv', index_col=0)\n",
    "df_timber"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.a\n",
    "Plot a scatter diagram of volume vs. height. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_3a] Height vs volume (1 point)\n",
    "\n",
    "ax=df_timber.plot(kind='scatter' , x='height', y= 'volume' , c='m')\n",
    "ax.set_title(\"Scatter Plot of Volume vs. Height\")\n",
    "ax.set_xlabel(\"Height\")\n",
    "ax.set_ylabel(\"Volume\")\n",
    "\n",
    "#// END_TODO [HYP_3a]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.b\n",
    "Plot a scatter diagram of volume vs. girth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y9Pvf/37MfXEAAJBckwb4rl279Pjjjys/P1+WZUmSPB6PXnzxRceLAwAAFzdpgP/qV7/SCy+8oCuuuCIZ9QAAgARM+hT6pz/9aX3yk59MRi0AACBBk47AV69erVWrVqmsrExe7x9O/9a3vuVoYQAAYHyTBvijjz6qvLw89fb2JqMeAACQgEkDvL+/X//yL/+SjFoAAECCJr0H/id/8ic6duxYMmoBAAAJmnQEfvr0ad1+++0qLi7WjBkzRo//4he/cLQwAAAwvkkDfOPGjcmoAwAATMGkAT5//vxk1AEAAKZg0gD/sz/7M3k8HlmWNbojWSAQ0H/91385XhwAALi4SQP8/AfYBgcH1djYqPb2dkeLAgAAE5v0KfTzzZgxQ8uXL9eRI0ecqgcAXBeNRtXW9oai0ajbpQDjmnQE/v7774/+2bIstbW16cMPP3SyJgBwTVNTo8LhbfL5vIrHhxQO71QoVOV2WcDHTOkeuCQVFBRo69atjhcGAMkWjUYVDm9TLDagWMw+Fg5vVVlZufx+v7vFAReY0j1wAEhnXV2d8vm8o+EtST6fV11dnQQ4Us64Ad7Q0DDhf3jPPfdMezEA4KaiomLF40NjjsXjQyoqKnapImB84wb4//7v/yazDgBwnd/vVzi8U+Hw1jH3wBl9IxWNG+C7du0a87qzs1NDQ0MqLS11vCgAcEsoVKWysnJ1dXWqqKiY8EbKmvQeeEdHh/76r/9aZ86c0cjIiK644gr9+Mc/1ty5c5NRHwAknd/vJ7iR8ib9HviOHTt033336Te/+Y1effVV3X///frud7+bjNoAAMA4Jg3wnp4e3XbbbaOvV6xYoffee8/RogAAwMQmDfDh4eExi7mwMhEAAO6b9B746tWrdeeddyoUCsnj8ejgwYP62te+lozaAADAOCYdgf/617/W9u3bNTg4qIGBAW3fvl133XVXMmoDAADjmDTAr732Wv3gBz/Qs88+q0996lOaN29eMuoCAAATmDTAV65cqf379+vHP/6xPvjgA9XU1GjdunXJqA0AAIwj4e1EBwYGNDg4KMuylJ2dnfAHPPTQQ9q8ebMkqbW1VdXV1aqoqFB9ff3UqwUAAJISeIitoaFBBw4c0ODgoG6//Xbt379fV155ZUIXf/HFF/Xkk0/qxhtv1MDAgLZs2aJ9+/Zpzpw5WrNmjVpaWhQMBi/7LwEAQKaZNMDb2tq0bds2lZWVTenC77//vurr67V27VodO3ZMR48eVWlpqUpKSiRJ1dXVam5uJsABALgEkwb43r17L+nC3/nOd7RhwwadPn1aknTmzBkFAoHR9wsLC9Xd3T3l6xYU5CV0XiCQP+VrpyP6YKMPNvpgow82+mAztQ+TBvil+NnPfqY5c+aovLxcBw4ckCSNjIzI4/GMnmNZ1pjXierp6dPIiDXhOYFAviKR3ilfO93QBxt9sNEHG32w0QdbKvchK8sz4aDVkQA/ePCgIpGIbrnlFn3wwQc6e/asOjs7xzz8FolEVFhY6MTHAwCQ9hwJ8IaGhtE/HzhwQC+//LK++93vqqKiQh0dHbrqqqvU2NioFStWOPHxAACkPUcC/GJycnJUV1en2tpaxWIxBYNBVVZWJuvjAQBIKx7Lsia+oZxiuAeeOPpgow82+mCjDzb6YEvlPkx2DzzhhVwAAEDqSNoUOgC4LRqNqrPzbeXmXiG/3+92OcBlYQQOICM0NTUqFFqimpoahUJL1NT0jNslAZeFAAeQ9qLRqMLhbYrFBtTb26tYbEDh8FZFo1G3SwMuGQEOIO11dXXK5xt7x9Dn86qrq9OlioDLR4ADSHtFRcWKx4fGHIvHh1RUVOxSRcDlI8ABpD2/369weKdycmYqPz9fOTkzFQ7v5EE2GI2n0AFkhFCoSmVl5ervf4+n0JEWCHAAGcPv9ysQKE3ZhTuAqWAKHQAAAxHgAAAYiAAHAMBABDgAAAYiwAEkJBqNqq3tDVYvA1IEAQ5gUufWEV+79h7WEQdSBAEOYELnryPe19fHOuJAiiDAAUyIdcSB1ESAA5gQ64gDqYkABzCh89cRz8vLYx1xIEWwlCqASZ1bR7yrq1NFRcWEN5ACCHAACfH7/QQ3kEKYQgcAwEAEOAAABiLAAQAwEPfAgQwQjUbV2fm2cnOv4D42kCYYgQNp7twyqDU1NSyDCqQRAhxIY+cvg9rb28syqEAaIcCBNMYyqED6IsABB6TK1pssgwqkLwIcmGaptPXm+cug5ufnswwqkEY8lmVZbhcxFT09fRoZmbjkQCBfkUhvkipKXfTBlsw+RKNRhUJLFIsNjB7LyZmppqZDroZmNBpVf/97PIUu/r84hz7YUrkPWVkeFRTkjfs+XyMDptG5e86x2B+Onbvn7GZw+v1+BQKlKfuLCsDUMYUOTCPuOQNIFgIcmEZsvQkgWZhCB6YZW28CSAYCHHAAW28CcBpT6AAAGIgABwDAQAQ4AAAGIsABADAQAQ5kuFRZtx3A1BDgQAZLpXXbAUwNAQ5kqPP3Cu/r62OvcMAwBDiQodgrHDAbAQ5kKNZtB8xGgAMZinXbAbOxlCqQwVi3HTAXAQ5kONZtB8zEFDoAAAYiwAEAMJCjAf7DH/5QS5cuVVVVlRoaGiRJra2tqq6uVkVFherr6538eAAA0pZj98Bffvll/frXv9bTTz+toaEhLV26VOXl5dqyZYv27dunOXPmaM2aNWppaVEwGHSqDAAA0pJjI/DrrrtO//zP/yyv16uenh4NDw/rww8/VGlpqUpKSuT1elVdXa3m5manSgAAIG05+hS6z+fTj370I/3kJz9RZWWlzpw5o0AgMPp+YWGhuru7p3TNgoK8hM4LBPKndN10RR9s9MFGH2z0wUYfbKb2wfGvkX3729/WN7/5Ta1du1YnT56Ux+MZfc+yrDGvE9HT06eREWvCcwKBfEUivZdUbzqhDzb6YKMPNvpgow+2VO5DVpZnwkGrY1Pob7/9tn73u99JknJzc1VRUaGXXnpJkUhk9JxIJKLCwkKnSgAAIG05FuDvvPOOtm3bpsHBQQ0ODuq5555TTU2N2tvb1dHRoeHhYTU2Nmrx4sVOlQAAQNpybAo9GAzq6NGjuvXWW5Wdna2KigpVVVXJ7/ertrZWsVhMwWBQlZWVTpUAAEDa8liWNfEN5RTDPfDE0QcbfbDRBxt9sNEHWyr3wbV74AAAwDkEOAAABiLAAQAwEAEOAICBCHAAAAxEgAMAYCACHAAAAxHgQIqIRqNqa3tD0WjU7VIAGIAAB1JAU1OjQqElWrv2HoVCS9TU9IzbJQFIcQQ44LJoNKpweJtisQH19fUpFhtQOLyVkTiACRHggMu6ujrl843dlsDn86qrq9OligCYgAAHXFZUVKx4fGjMsXh8SEVFxS5VBMAEBDjgMr/fr3B4p3JyZiovL085OTMVDu+U3+93uzQAKcyx7UQBJC4UqlJZWbm6ujpVVFRMeAOYFAEOpAi/309wA0gYU+gAABiIAAcAwEAEOGAwVm8DMhcBDhiK1duAzEaAAwZi9TYABDhgIFZvA0CAAwYab/W2WbNmcU8cyBAEOGCgi63eduutK7Ry5QruiQMZgoVcAEOdv3rbrFmztHLlCsViA4rF7PfD4a0qKytncRggTTECBwzm9/u1YMFCnT17lnviQIYhwIE0wI5mQOYhwOE6FiO5fOxoBmQe7oHDVU1NjQqHt8nn8yoeH1I4vFOhUJXbZRmJHc2AzEKAwzXnL0bCg1fTgx3NgMzBFDpcw2IkAHDpCHC4hgevAODSEeBwDQ9eAcCl4x44XMWDVwBwaQhwuI4HrwBg6phCBwDAQAQ4koYFWwBg+hDgSIqmpkaFQkvYKQsApgkBDsedv2BLX1+fYrEBhcNb03okzmwDAKcR4HBcpi3YwmwDgGQgwOG4TFqwJRNnGwC4gwCH4zJpwZZMm20A4B6+B46kyJQFWzJptgGAuxiBI2n8fr8WLFg4aXib/ABYJs02AHAXI3CklET3B49Goyk7ms+U2QYA7mIEjpSR6ANgJjzlnehsAwBcKgIcKSORB8B4yhsAbAQ4UkZRUbFisdiYY7FYbMwDYDzlDQA2AhwpZWTEmvA1T3kDgI0AR8ro6upUbu7MMcdyc2eOGV3zlDcA2HgKHSkj0dE1T3kDgMMj8IcfflhVVVWqqqrS7t27JUmtra2qrq5WRUWF6uvrnfx4GGYqo2ue8gaQ6Rwbgbe2turw4cN68skn5fF4dN9996mxsVF79uzRvn37NGfOHK1Zs0YtLS0KBoNOlYEUNd73uBldA0BiHBuBBwIBbd68WTNmzJDP59PcuXN18uRJlZaWqqSkRF6vV9XV1WpubnaqBCTJVFdOm+x73IyuAWByHsuyrMlPuzwnT57UypUrtWrVKrW3t2vPnj2S7FH6P/7jP+onP/mJ0yXAIU8++aQefPBB+Xw+xeNx7d27V7feeuu45/f09Oi6667TwMDA6LGZM2fq5ZdfVkFBQRIqBoD04PhDbMePH9eaNWu0adMmZWdn6+TJk6PvWZYlj8czpev19PR97KtFFwoE8hWJ9F5KuWnF6T5Eo1E98MCDisUGRgN548YH9LnPXTPu6Lmt7S15vWN/7Lxer44efUsLFix0pE5+Hmz0wUYfbPTBlsp9yMryqKAgb/z3nfzwV199VV//+tf1wAMP6LbbbtPs2bMViURG349EIiosLHSyBDjoUhZV4XvcADA9HAvw06dPa926ddqzZ4+qquzNKBYtWqT29nZ1dHRoeHhYjY2NWrx4sVMlwGGXEsbJ/h53NBrVa6+9xlKrANKOY1Pojz32mGKxmOrq6kaP1dTUqK6uTrW1tYrFYgoGg6qsrHSqBDjsXBiHw1vH7B42WRgn60nzczubzZjh0+BgfNydzQDAREl5iG06cQ88cU714cKvgKXi1p7RaFSh0BLFYn94WC4nZ6aamg6lTI3Jxv8XNvpgow+2VO7DZPfAWYkNUzLeft2pForn7s+fvzfKufvzqVYrAFwK1kJHwkzaypOH5QCkOwIcCZvqU+dTXeBlOp3/sFx+fj6bngBIO0yhI2FTGdWON9WeTOceluvvf0+5uVcQ3gDSCiNwJCzRr4Cl0lS73+/XF77wBcIbQNphBI4pSeQrYDxABgDOI8AxZX6/f8Ig5gEyAHAeU+iYdslebQ0AMhEjcDiCfb0BwFkEOBwz2VQ7AODSMYUOAICBCHAAAAxEgAMAYCACHONycylUAMDECHBcVFNTo0KhJVq79h6FQkvU1PSM2yUBAM5DgONjUmkpVADAxRHg+Jip7joGAEg+Ahwfw1KoAJD6CHB8zHQthcpDcADgHFZiw0Vd7lKoqbAfOACkMwIc47rUpVDPfwju3Jai4fBWlZWVs7QqAEwTptAx7XgIDgCcR4Bj2vEQHAA4jwDHtGM/cABwHvfA4Qj2AwcAZxHgcAz7gQOAc5hCBwDAQAQ4AAAGIsABADAQAQ4AgIEIcAAADESAAwBgIAIcAAADEeAAABiIAAcAwEAEOAAABiLAAQAwEAEOAICBCHAAAAxEgAMAYCACHAAAAxHgAAAYiAAHAMBABDgAAAYiwAEAMBABDgCAgQhwAAAMRIADAGAgAhwAAANlbIBHo1G1tb2haDR6yecleg0AAKabowHe19enZcuW6Z133pEktba2qrq6WhUVFaqvr3fyoyfU1NSoUGiJ1q69R6HQEjU1PTPl8xK9BgAATnAswF9//XWtXLlSJ0+elCQNDAxoy5YteuSRR3Tw4EG1tbWppaXFqY8fVzQaVTi8TbHYgPr6+hSLDSgc3vqxUfRE5yV6DQAAnOJYgO/fv1/bt29XYWGhJOno0aMqLS1VSUmJvF6vqqur1dzc7NTHj6urq1M+n3fMMZ/Pq66uzoTPS/QaAAA4xTv5KZdm586dY16fOXNGgUBg9HVhYaG6u7ud+vhxFRUVKx4fGnMsHh9SUVHxlM5L5BoAADjFsQC/0MjIiDwez+hry7LGvE5UQUFeQucFAvnjHv/+9/fqgQcekM/nUzwe1969e/X//l/plM5L5BqpYLw+ZBr6YKMPNvpgow82U/uQtACfPXu2IpHI6OtIJDI6vT4VPT19GhmxJjwnEMhXJNI77vvXX/9lHTx4SF1dnSoqKpbf77/o+ROdl+g13DRZHzIFfbDRBxt9sNEHWyr3ISvLM+GgNWkBvmjRIrW3t6ujo0NXXXWVGhsbtWLFimR9/Mf4/X75/f7LOi/RawAAMN2SFuA5OTmqq6tTbW2tYrGYgsGgKisrk/XxAACkFccD/NChQ6N/Li8v19NPP+30RwIAkPYydiU2AABMRoADAGAgAhwAAAMR4AAAGIgABwDAQAQ4AAAGIsABADAQAQ4AgIEIcAAADESAAwBgIAIcAAADEeAAABgoabuRTZesLM+0npfu6IONPtjog40+2OiDLVX7MFldHsuyrCTVAgAApglT6AAAGIgABwDAQAQ4AAAGIsABADAQAQ4AgIEIcAAADESAAwBgIAIcAAADEeAAABiIAAcAwEBpF+BPPfWUqqqqVFVVpYceesjtcpKqr69Py5Yt0zvvvCNJam1tVXV1tSoqKlRfX+9ydclzYR/+7d/+TcuWLVN1dbX+7u/+ToODgy5XmBwX9uGcn/70p1q9erVLVSXfhX347W9/qzvuuENVVVXauHFjxv48HD58WH/xF3+hZcuWadOmTRnRh4cffng0H3bv3i3J8N+TVho5e/asde2111o9PT1WPB63br/9duvIkSNul5UUr732mrVs2TLr85//vHXq1Cmrv7/fCgaD1v/93/9Z8Xjcuvfee63//M//dLtMx13YhxMnTlhf+cpXrN7eXmtkZMTatGmT1dDQ4HaZjruwD+ccP37c+vM//3Nr1apVLlaXPBf2obe317r++uut3/3ud5ZlWdaGDRusxx9/3OUqnXexn4fFixdbv//97y3Lsqza2lpr//79bpbouCNHjlh33nmnFYvFrMHBQevuu++2fvGLXxj9ezKtRuDDw8MaGRlRf3+/hoaGNDQ0pJycHLfLSor9+/dr+/btKiwslCQdPXpUpaWlKikpkdfrVXV1tZqbm12u0nkX9mHGjBnavn278vLy5PF4NH/+fHV1dblcpfMu7IMkDQ4O6jvf+Y6+/e1vu1hZcl3YhyNHjugLX/iCrr76aknStm3b9JWvfMXNEpPiYj8Pw8PD6uvr0/DwsGKxWNr/rgwEAtq8ebNmzJghn8+nuXPn6uTJk0b/njRuO9GJ5OXlaf369QqFQsrNzdW1116rL37xi26XlRQ7d+4c8/rMmTMKBAKjrwsLC9Xd3Z3sspLuwj4UFxeruLhYkhSNRvX4449r165dbpSWVBf2QZL27t2rFStW6KqrrnKhIndc2IeOjg7NmjVLGzZs0IkTJ/TFL35Rmzdvdqm65LnYz0M4HNbq1auVl5enq666SpWVlS5Uljzz5s0b/fPJkyfV1NSkVatWGf17Mq1G4MeOHdPPf/5zPf/883rhhReUlZWlxx57zO2yXDEyMiKP5w97yVqWNeZ1punu7tbXvvY1rVixQmVlZW6Xk3RHjhzR6dOntWLFCrdLcdXw8LAOHz6sjRs36sCBA+rv79ejjz7qdllJF4lEtGfPHjU2Nurw4cNatGhRRvzDVpKOHz+ue++9V5s2bVJJSYnRvyfTKsAPHz6s8vJyFRQUaMaMGVq+fLlefvllt8tyxezZsxWJREZfRyKRMdNnmeTtt99WTU2NbrvtNq1bt87tclzR2Nio48eP65ZbbtG2bdvU1tamv/mbv3G7rKS78sortWjRIpWUlCg7O1uhUEhHjx51u6yke+WVVzR//nz98R//sbKysnTHHXdkxO/KV199VV//+tf1wAMP6LbbbjP+92RaBfjVV1+t1tZWnT17VpZl6dChQ1q4cKHbZbli0aJFam9vV0dHh4aHh9XY2KjFixe7XVbS9fX16Rvf+IbWr1+ve++91+1yXLNr1y41NTXpqaee0ve+9z0tWLBAP/jBD9wuK+luuOEG/c///I9Onz4tSXr++ef1+c9/3uWqkm/+/Pk6evSo3n33XUnSc889l/a/K0+fPq1169Zpz549qqqqkmT+78m0ugd+ww036M0339Ty5cvl8/m0cOFC/dVf/ZXbZbkiJydHdXV1qq2tVSwWUzAYTPt7XBfzxBNP6N1331VDQ4MaGhokSUuWLNH69etdrgxumDNnjnbs2KG1a9cqFovpc5/7nP72b//W7bKSbu7cuVq/fr3uvvtuZWdnq7S0VDt27HC7LEc99thjisViqqurGz1WU1Nj9O9Jj2VZlttFAACAqUmrKXQAADIFAQ4AgIEIcAAADESAAwBgIAIcAAADEeAAxvjhD3+of//3f7/oew8//LD+4z/+Q5K0efPmjF3pEEgFafU9cACXb6LvyL/00kv67Gc/m8RqAIyHAAcy2KOPPqonnnhCn/jEJ/SlL31Jzz33nK677jrNmzdP3/jGN7RgwQJ9+ctf1rFjx1RdXa22tjbt3r1b2dnZkuy9tWtqavTuu+9q3rx52rt3r2bNmuXy3wrIDEyhAxnqhRde0IEDB/TEE0/owIED+uijjz52Tjwe10033aRf/vKX+ta3vqUFCxZo06ZNo1twdnd3q6GhQb/85S/V3d2tZ599Ntl/DSBjEeBAhmppaVFlZaU++clPyuPx6C//8i8vet6XvvSlca9x8803Kzc3V9nZ2Zo3b56i0ahT5QK4AAEOZCiv16vzV1I+Ny1+oYmmxL3eP9yF83g8YmVmIHkIcCBDBYNBPfvss+rt7ZVkb/wymezsbA0NDTldGoAE8BAbkKHKy8t1xx136M4779TMmTM1b9485ebmTvjfLFmyRN///vcVj8eTVCWA8bAbGZCh3njjDf32t7/V3XffLUlqaGjQ66+/npH7hAMmIsCBDNXX16ctW7boxIkT8ng8mjNnjv7hH/5Bf/RHf+R2aQASQIADAGAgHmIDAMBABDgAAAYiwAEAMBABDgCAgQhwAAAM9P8BoyAmk2IN7ncAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_3b] Girth vs. volume (1 point)\n",
    "\n",
    "ax=df_timber.plot(kind='scatter', x='girth' , y='volume', c='k')\n",
    "ax.set_title(\"Girth vs. Volume\")\n",
    "ax.set_xlabel(\"Girth\")\n",
    "ax.set_ylabel(\"Volume\")\n",
    "\n",
    "#// END_TODO [HYP_3b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.c\n",
    "\n",
    "What order polynomial appears to be a good fit for a regression model with volume as dependent variable, and height and girth as independent variables?\n",
    "\n",
    "> a. A first order polynomial<br>\n",
    "> b. A second order polynomial<br>\n",
    "> c. A third order polynomial\n",
    "\n",
    "Assign your answer (`'a'`, `'b'`, or `'c'`) to `poly_order_timber`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3c] Polynomial order (1 point)\n",
    "\n",
    "poly_order_timber='a'\n",
    "\n",
    "#// END_TODO [HYP_3c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First Order Polynomial Model\n",
    "\n",
    "Regardless of your answer to the previous question, we will now fit a first order polynomial model and plot the normalized residuals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.d\n",
    "\n",
    "Construct the training set that will be used for fitting the first order polynomial model, with volume as the dependent variable and both girth and height as independent variables. Assign the data for the independent variables to the dataframe `X_timber` and the data for the dependent variable to the series `y_timber`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3d] Define the training dataset (1 point)\n",
    "\n",
    "X_timber=df_timber[ ['height', 'girth']] \n",
    "\n",
    "y_timber=df_timber['volume']\n",
    "\n",
    "#// END_TODO [HYP_3d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.e\n",
    "\n",
    "Fit the first order model, with volume as the dependent variable and both girth and height as independent variables. Assign the model to variable `lm_timber`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3e] Fit the first order polynomial model (1 point)\n",
    "\n",
    "lm_timber=LinearRegression() \n",
    "lm_timber.fit(X_timber ,y_timber);\n",
    "\n",
    "#// END_TODO [HYP_3e]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.f\n",
    "\n",
    "Compute the $R^2$ score of the `lm_timber` model on the training data. Assign the score to variable `r_timber`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9479500377816745"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_3f] Compute R2 score (1 point)\n",
    "\n",
    "r_timber=lm_timber.score(X_timber,y_timber)\n",
    "\n",
    "#// END_TODO [HYP_3f]\n",
    "\n",
    "r_timber"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.g\n",
    "\n",
    "Compute the normalized residuals for the training data. Assign them to the variable `residuals_timber`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3g] Model summary (1 point)\n",
    "\n",
    "residuals_timber=scale(y_timber-lm_timber.predict(X_timber))\n",
    "\n",
    "#// END_TODO [HYP_3g]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.h\n",
    "\n",
    "Plot the normalized residuals, with `'girth'` on the x-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Pp+c/g4noQwx9iKEPMfQhhj7EpGof4gr6RYsWSZLuvfdeVVVV6Z//+Z9VUVGhFStW9PgL29ra5HA42rej0WiH7QsuuEAvvvhi+/Z9992nioqKHgX9kSPNamuLdnuex9NfTU1H4/5cU9GHGPoQQx9i6EMMfYhJ5j5kZDi6vMCNa+g+EAjI5/PpjTfe0O23364lS5aooeHcpuocNGiQmpqa2rebmpqUl5fXvh0MBrV+/fr27Wg0qsxM3gIEAOBcxBX00WhUGRkZ2rlzp2644QZJUktLyzl94Y033qi3335boVBIx48f1+uvv65x48a1H8/OztaTTz6pAwcOKBqNas2aNbrlllvO6bsAAEh3cQX90KFDNX36dH3++ee6/vrr9dBDD+nb3/72OX3hwIEDNW/ePJWXl2vKlCkqLS3VVVddpenTp6u+vl5ut1vV1dV64IEHNHHiREWjUU2bNu2cvgsAgHTniEaj3d7M/uqrr/TGG2/oO9/5jgYPHqy1a9dqypQp6tu3rxU19hj36HuGPsTQhxj6EEMfYuhDTDL3obt79F3e/N67d2/7ny+99FJ9+eWX+vLLL3XVVVdp3759uvLKK3uvUgAA0Ou6DPpZs2ad9ZjD4dC2bdt6vSAAANB7ugz67du3W1UHAABIgLjeWwuFQvrtb3+rY8eOKRqNqq2tTZ999pmWL1+e6PoAAMB5iCvo586dq+zsbP35z3/WjTfeqLq6On3nO99JdG0AAOA8xfV6XTAY1AsvvKBx48bp7rvv1tq1a7Vv375E1wYAAM5TXEE/YMAASdIll1yiTz75RAMHDlRra2tCCwMAAOcvrqH73Nxc/cd//IcKCwu1YsUK5eTknPPMeAAAwDpxXdFXV1crKytLY8aM0ahRo/SLX/xCDz/8cKJrAwAA5ymumfFSDTPj9Uwy9SEUCikYbFB+foHcbrel351MfbATfYihDzH0ISaZ+3BeM+OdNGnSpE73v/LKK+dWFdAJv3+zfL4qOZ2ZikRa5fPVyOstsbssAEhpcQX9z372s/Y/RyIRbdmyRUOGDElYUUg/oVBIPl+VwuEWhcOxfT5fpYqKxlp+ZQ8AJokr6K+//voO2zfeeKPKysr0wAMPJKQopJ9gsEFOZ2Z7yEuS05mpYLCBoAeA8xDXw3in++KLL3To0KHergVpLD+/QJFIx1c2I5FW5ecX2FQRAJjhnO7RB4NBff/7309IQUhPbrdbPl+NfL7KDvfouZoHgPPT43v0DodDbrdbI0aMSFhRSE9eb4mKisba9tQ9AJioy6APBoOSpMGDB3d6LD8/PzFVIW253W4CPoXZ+XokgM51GfQlJSVyOByKRqNqaWnRBRdcoD59+uhvf/ubcnNztWPHDqvqBJDkeD0SSE5dBv37778vSVq0aJGKiopUUhL7P+22bdv0u9/9LvHVAUgJvB4JJK+4nroPBALtIS9JN998sz7++OOEFQX0llAopECgXqFQyO5SjHby9chTnXw9EoC94gr6trY2vfPOO+3b//u//yuHw5GwooDe4PdvltdbrBkzpsnrLZbfv8XukozF65FA8orrqfuqqirNnTtXTqdTbW1tkqSVK1cmtDDgfDCUbC1ejwSSV1xBP2bMGL355pv65JNPJEnf/va3lZkZ118FbMFMe9bj9UggOXWZ1i+++KKmT5+uRx99tNOh+qqqqoQVBpwPhpLtweuRQPLp8h59//79JUkXXXSRLrzwwjP+BySrk0PJLle2cnJy5HJlM5QMIC31eD36xsZGHThwQGPGjElUTeeN9eh7xuQ+9GQCF5P70BP0IYY+xNCHmGTuQ6+sR7927Vrt2rVLlZWVmjp1qnJycnTrrbfqoYce6rVCkZqSfSY0hpIBpLu4Xq/7n//5Hz3yyCPaunWriouLtWXLFu3cuTPRtSHJ8foaACS/uILe4XBowIABevvttzV27FhlZma2v2aH9HTq62vNzc0Kh1vk81UyMQ0AJJm4gj4rK0svvvii3n33Xf3TP/2TfvWrX6lv376Jrg1JjJnQACA1xBX0NTU12r9/v5544gn9wz/8g3bv3q3HHnss0bUhifH6GgCkhriCfvjw4frZz36miy++WNFoVI899hjr0ac5Xl8DgNQQ11P3f/zjH/WTn/xEmZmZ+vWvf63Jkyfrl7/8pa699tpE14ckxkxoAJD84rqiX7p0qV566SVdeOGFGjRokJYuXaqamppE14YU4Ha7NWrUaEIeAJJUXEHf0tKiSy+9tH17/PjxOnHiRMKKAgAAvSOuoM/MzNSXX37ZPt/9vn37EloUAADoHXHdo7///vt199136/Dhw3rwwQe1c+dOVVdXJ7o2AABwnuIK+l/84hdauXKlduzYoWg0qpkzZ/LUPWCgUCikhoa/qG/fi3juAjBEXEHft29fuVwu3XXXXYmuB4BN/P7N8vmqlJXl1NdfR+Tz1cjrLbG7LADnKa6gP378uG6++WYNGjRI/fr1a9//yiuvJKwwANY5dUrjcLhFkuTzVaqoaCxX9kCKiyvoKysre/VLX3nlFf3yl79Ua2ur7r333jNGCj766CNVVlbq2LFjGjNmjH7+858rMzOuUgGcg5NTGofD3+w7OaUxQQ+ktrjS8/rrr++1L2xsbNTTTz+tDRs2KCsrS2VlZSoqKurw+t78+fP12GOPqbCwUBUVFVq3bp1++MMf9loNADpiSmPAXHG9Xteb6urqdMMNN+jCCy9Uv379NGHCBG3durX9eENDg1paWlRYWChJmjp1aofjgBQbag4E6lktr5ecOqVx//79mdIYMIjl4+GHDh2Sx+Np387Ly9OePXvOetzj8aixsbFH35GbmxP3uR5P/x59tqlSqQ8bN27Uww8/LKfTqUgkouXLl2vKlCm98tmp1IfeVl5eppKSW3TgwAENGTJEubm5dpdku3T+93Aq+hCTqn2wPOjb2traJ96RpGg02mG7u+PxOHKkWW1t0W7P83j6q6npaI8+20Sp1IdQKKSHHnpY4XCLWlpiD409+OBDuuKKa8776jOV+pA4WSosLFRT09G07wX/HmLoQ0wy9yEjw9HlBa7lQ/eDBg1SU1NT+3ZTU5Py8vLOevzw4cMdjiO9nXxo7FQnHxoDAJzJ8qC/8cYb9fbbbysUCun48eN6/fXXNW7cuPbjBQUFcrlc2r17tySptra2w3GkNx4aA4CesTzoBw4cqHnz5qm8vFxTpkxRaWmprrrqKk2fPl319fWSpGXLlmnJkiWaOHGivvrqK5WXl1tdJpLUqQ+N5eTk8NAYAHTDEY1Gu7+ZnWK4R98zydqHUCh01rXuuzp2rpK1D1ajDzH0IYY+xCRzH7q7R88sNEhKJ6djdTozFYm0njEdq9vt5ioeAOJg+dA90J1Tp2Ntbm5WONwin6+Sd+YB4BwQ9Eg6PFkPAL2HoEfS4cl6AOg9BD2STjxP1jMFLgDEh4fxkJS83hIVFY3t9Mn67h7UAwB8g6BH0ursyfqO66bH9rFuOgCcHUP3sF1PhuF5UA8Aeoagh638/s3yeos1Y8Y0eb3F8vu3dHk+D+oBQM8Q9LDNubwvzxS4ANAz3KOHbU4Ow5+81y59MwzfVXB39aAeAKAjgh62OZ9heKbABYD4MHQP2zAMDwCJxxU9bMUwPAAkFkEP2zEMDwCJw9A9AAAGI+gBADAYQQ8AgMEIegAADEbQw3YsOQsAiUPQI2HiCfCeznUPAOgZgh4JEU+An8tc9wCAniHo0eviDXCWnAWAxCPo0eviDXCWnAWAxCPo0eviDXDmugeAxGMKXPS6kwHu81XK6cxUJNJ61gBnrnsASCyCHglxeoBLUiBQ32mYM9c9ACQOQ/dIGLfbrVGjRuudd+p4hQ4AbELQI6F4hQ4A7EXQI6F4hQ4A7EXQI6F4hQ4A7EXQI6F4hQ4A7MVT90g4XqEDAPsQ9LAEr9ABgD0YugcAwGAEPQAABiPoAQAwGEEPAIDBCHoAAAxG0AMAYDDLX68LBoOaP3++jhw5on/8x3/UsmXLdMEFF3Q4p6GhQaWlpRo6dKgkacCAAVq1apXVpQIAkPIsv6L/+c9/rh/+8IfaunWrRo0apeeee+6McwKBgCZNmqTa2lrV1tYS8gAAnCNLgz4Siei9997ThAkTJElTp07V1q1bzzivvr5en3zyiSZPnqzy8nL96U9/srJMAACMYenQ/RdffKGcnBxlZsa+1uPxqLGx8YzzXC6XbrvtNpWVlemtt97SzJkz9eqrryorKyuu78nNzYm7Jo+nf9znmow+xNCHGPoQQx9i6ENMqvYhYUHv9/u1ZMmSDvuGDRsmh8PRYd/p25I0a9as9j+PHz9ey5cv1759+3T55ZfH9d1HjjSrrS3a7XkeT381NR2N6zNNRh9i6EMMfYihDzH0ISaZ+5CR4ejyAjdhQe/1euX1ejvsi0QiKioq0okTJ9SnTx81NTUpLy/vjL/78ssvq7S0VBdddJEkKRqNto8CAACA+Fl6j97pdGrMmDF69dVXJUmbNm3SuHHjzjjvvffe0/r16yVJ7777rtra2jR8+HArSwUAwAiWP3W/ePFirVu3Tt/73ve0a9cuzZ07V5K0du1aPfvss5KkyspK1dXVqbS0VE888YSWL1+ujAxe+QcAoKcc0Wi0+5vZKYZ79D1DH2LoQwx9iKEPMfQhJpn70N09ei6TAQAwGEEPAIDBCHoAAAxG0APAOQqFQgoE6hUKhewuBTgrgh4AzoHfv1leb7FmzJgmr7dYfv8Wu0sCOkXQA0APhUIh+XxVCodb1NzcrHC4RT5fJVf2SEoEPQD0UDDYIKez42ydTmemgsEGmypKjFAopD/+8Y/8B0yKI+gBoIfy8wsUibR22BeJtCo/v8CminrfyVsTZWVl3JpIcQQ9APSQ2+2Wz1cjlytbOTk5crmy5fPVyO12211arzj11sTRo0e5NZHiWCkGAM6B11uioqKxCgYblJ9fYEzIS9/cmgiHv9l38taEST9nuiDoAeAcud1uI4MvHW5NpBOG7gEAHZx6a6J///7G3ZpIN1zRAwDOcPLWxPHjX6hv34sI+RRG0AMAOuV2u+XxDEvaVdsQH4buAQAwGEEPAIDBCHoAAAxG0AMAYDCCHgAAg/HUPQCgU6FQSA0Nf+H1uhTHFT0A4AwsamMOgh4A0AGL2piFoAcAdHByUZtTnVzUBqmHoAcAdMCiNmYh6AEAHbCojVl46h4AcAYWtTEHQQ8A6BSL2piBoXsAAAxG0AMAYDCCHgAAgxH0AAAYjKAHAMBgBD0AAAYj6AEAMBjv0QPAaVieFSbhih4ATsHyrDANQQ8Af8fyrDARQQ8Af8fyrDARQQ8Af8fyrDARQQ8Af8fyrDCRbU/dP/PMM+rTp49mzZp1xrGvv/5alZWVCgQCys7O1rJlyzRixAgbqgSQblieFaax/Ir+6NGjqqio0OrVq896zssvv6y+ffvK7/eroqJCjzzyiIUVAkh3brdbhYWFhDyMYHnQb9u2TZdccommTZt21nN+//vf67bbbpMkXXfddQqFQgoGg1aVCACAMSwfup8yZYokacWKFWc959ChQ/J4PO3bHo9H//d//6f8/Py4viM3Nyfuejye/nGfazL6EJMOfThy5IgOHDigIUOGKDc3t9Nz0qEP8aAPMfQhJlX7kLCg9/v9WrJkSYd9w4cP10svvdTt341Go3I4HB22MzLiH3w4cqRZbW3Rbs/zePqrqelo3J9rKvoQkw598Ps3y+erktOZqUikVT5fjbzekg7npEMf4kEfYuhDTDL3ISPD0eUFbsKC3uv1yuv1ntPfHThwoA4dOqShQ4dKkg4fPqy8vLzeLA9IO6dOBhMOx/b5fJUqKhrLvWjAYEn5et348eNVW1srSdq1a5dcLlfcw/YAOsdkMEB6SpqgX7t2rZ599llJ0j333KOvv/5aJSUlqqmp0dKlS22uDkh9TAYDpCdHNBrt/mZ2iuEefc/Qh5h06IPfv0U+XyX36ONAH2LoQ0wy98G2e/QAks/JyWCCwQbl5xdwbx5IAwQ9kGbcbjcBD6SRpLlHDwAAeh9BDwCAwQh6AAAMRtADAGAwgh4AAIMR9AAAGIygB9CtUCikQKBeoVDI7lIA9BBBD6BLfv9meb3FmjFjmrzeYvn9W+wuCUAPEPQAzurUFe+am5sVDrfI56vkyh5IIQQ9gLNixTsg9RH0AM6KFe+A1EfQAzgrt9stn69GLle2cnJy5HJly+erYa58IIWwqA2ALrHiHZDaCHoA3WLFOyB1MXQPAIDBCHoAAAxG0AMAYDCCHgAAgxH0AAAYjKAHAMBgvF4HKDane0PDX9S370W8RgbAKFzRI+2dXJ2trKyM1dkAGIegR1o7dXW2o0ePGrs6G+vJA+mLoEdaS4fV2VhPHkhvBD3Smumrs7GePACCHmnt1NXZ+vfvb9zqbOkwYgGgazx1j7R3cnW248e/MO6pe9NHLAB0jyt6QLEr+8LCQqNCXmI9eQBc0QPGYz15IL0R9EAaYD15IH0xdA8AgMEIegAADEbQAwBgMIIeAACDEfQAABiMoAcAwGAEPQAABiPoAQAwmG0T5jzzzDPq06ePZs2adcaxhoYGlZaWaujQoZKkAQMGaNWqVVaXCABAyrM86I8ePaolS5Zoy5Yt+vGPf9zpOYFAQJMmTVJ1dbXF1QEAYBbLh+63bdumSy65RNOmTTvrOfX19frkk080efJklZeX609/+pOFFQIAYA5HNBqN2vHFK1askKROh+5XrFih3NxclZWV6a233tKjjz6qV199VVlZWVaXCSTUkSNHdODAAQ0ZMkS5ubl2lwPAQAkbuvf7/VqyZEmHfcOHD9dLL73U7d89NfzHjx+v5cuXa9++fbr88svj+u4jR5rV1tb9f794PP3V1HQ0rs80GX2IsboPfv9m+XxVcjozFYm0yuerkddbYtn3nw3/HmLoQwx9iEnmPmRkOJSbm3PW4wkLeq/XK6/Xe05/9+WXX1ZpaakuuugiSVI0GlVmJgvtwRyhUEg+X5XC4RaFw7F9Pl+liorGssocgF6VlK/Xvffee1q/fr0k6d1331VbW5uGDx9uc1VA7wkGG+R0dvyPV6czU8Fgg00VATBV0lwmr127VocOHdKcOXNUWVmphQsXqra2Vi6XS8uXL1dGRlL+NwlwTvLzCxSJtHbYF4m0Kj+/wKaKAJjKtofxEol79D1DH2Ksv0e/RT5fJffokxR9iKEPMcncB9vu0QPomtdboqKisQoGG5SfX8C9eQAJQdADNnK73QQ8gITixjcAAAYj6AEAMBhBDwCAwQh6AAAMRtADAGAwgh4AAIMR9AAAGIygBwDAYAQ9AAAGI+gBADAYQQ8AgMEIegAADEbQAykmFAopEKhXKBSyuxQAKYCgB1KI379ZXm+xZsyYJq+3WH7/FrtLApDkCHogRYRCIfl8VQqHW9Tc3KxwuEU+XyVX9gC6RNADKSIYbJDTmdlhn9OZqWCwwaaKAKQCgh5IEfn5BYpEWjvsi0RalZ9fYFNFAFIBQQ+kCLfbLZ+vRi5XtnJycuRyZcvnq5Hb7ba7NABJLLP7UwAkC6+3REVFYxUMNig/v4CQB9Atgh5IMW63m4AHEDeG7gEAMBhBDwCAwQh6AAAMRtADAGAwgh4AAIMR9AAAGIygBwDAYAQ9AAAGI+gBADAYQQ8AgMEIegAADEbQAwBgMIIeAACDEfQAABjMyGVqMzIcCTnXZPQhhj7E0IcY+hBDH2KStQ/d1eWIRqNRi2oBAAAWY+geAACDEfQAABiMoAcAwGAEPQAABiPoAQAwGEEPAIDBCHoAAAxG0AMAYDCCHgAAg6Vl0NfW1qqkpEQlJSV64okn7C7Hcs3NzSotLdXnn38uSaqrq9OkSZN066236umnn7a5Ouuc3of//u//VmlpqSZNmqRHHnlEX3/9tc0VWuP0Ppz0X//1X7rnnntsqsp6p/fh/fff15133qmSkhI9+OCDafvvYceOHbrttttUWlqqBQsWpEUfVq5c2Z4RS5culZTavyfTLuiPHz+umpoavfzyy6qtrdWuXbtUV1dnd1mW+eCDD/SDH/xA+/fvlyS1tLSooqJCzz33nF599VUFAgH94Q9/sLdIC5zeh7/+9a9atWqVfv3rX+u3v/2t2tra9Ktf/creIi1weh9O+vOf/6wXXnjBnqJscHofmpubNWvWLFVXV2vLli2SpPXr19tYoTU6+/dQWVmpp59+Wps3b1ZLS4tqa2vtK9ACdXV12rFjhzZu3KhNmzZp79692rx5c0r/nky7oD9x4oTa2tp0/Phxtba2qrW1VS6Xy+6yLLNu3TotXrxYeXl5kqQ9e/Zo2LBhGjJkiDIzMzVp0iRt3brV5ioT7/Q+ZGVlafHixcrJyZHD4dBll12mYDBoc5WJd3ofJOnrr7/WokWLNHv2bBsrs9bpfdi5c6cKCwt1+eWXS5Kqqqp0yy232FmiJTr793DixAk1NzfrxIkTCofDxv++9Hg8WrhwobKysuR0OjVixAjt378/pX9PGrl6XVdycnI0Z84ceb1e9e3bV9ddd52uvfZau8uyTE1NTYftQ4cOyePxtG/n5eWpsbHR6rIsd3ofCgoKVFBQIEkKhUJas2aNlixZYkdpljq9D5K0fPly3XHHHRo8eLANFdnj9D589tln6tevn+bNm6d9+/bp2muv1cKFC22qzjqd/Xvw+Xy65557lJOTo8GDB2vixIk2VGadkSNHtv95//798vv9uvvuu1P692TaXdF//PHH+s1vfqM333xTb731ljIyMrRq1Sq7y7JNW1ubHI5vljiMRqMdttNNY2Oj7r33Xt1xxx0qKiqyuxzL7dy5UwcPHtQdd9xhdym2OnHihHbs2KEHH3xQGzZs0PHjx9PqVsZJTU1NWrZsmTZv3qwdO3bo6quvTov/AJakTz/9VPfdd58WLFigIUOGpPTvybQL+h07dmjs2LHKzc1VVlaWpk6dqnfffdfusmwzaNAgNTU1tW83NTV1GLZLJ3/5y19UVlam22+/XTNnzrS7HFts3rxZn376qSZPnqyqqioFAgHNnTvX7rIsN2DAAF199dUaMmSI+vTpI6/Xqz179thdluV27dqlyy67TEOHDlVGRobuvPPOtPh9uXv3bv3bv/2bHnroId1+++0p/3sy7YL+8ssvV11dnb766itFo1Ft375do0ePtrss21x99dX661//qs8++0wnTpzQ5s2bNW7cOLvLslxzc7N+9KMfac6cObrvvvvsLsc2S5Yskd/vV21trR577DGNGjVKzzzzjN1lWe673/2u9u7dq4MHD0qS3nzzTV155ZU2V2W9yy67THv27NHhw4clSdu2bTP+9+XBgwc1c+ZMLVu2TCUlJZJS//dk2t2j/+53v6sPP/xQU6dOldPp1OjRo/Xv//7vdpdlG5fLpccff1yzZs1SOBzW+PHjjb8H15n169fr8OHDWr16tVavXi1JKi4u1pw5c2yuDHa4+OKLVV1drRkzZigcDuuKK67QT3/6U7vLstyIESM0Z84clZeXq0+fPho2bJiqq6vtLiuhVq1apXA4rMcff7x9X1lZWUr/nnREo9Go3UUAAIDESLuhewAA0glBDwCAwQh6AAAMRtADAGAwgh4AAIMR9AB67Nlnn9WmTZs6PbZy5Ur97ne/kyQtXLgwrWeeBJJB2r1HD+D8dTW/wDvvvKNLL73UwmoAdIWgB9ClF154QevXr9cFF1ygMWPGaNu2bbr++us1cuRI/ehHP9KoUaN088036+OPP9akSZMUCAS0dOlS9enTR1JsXfeysjIdPnxYI0eO1PLly9WvXz+bfyogfTB0D+Cs3nrrLW3YsEHr16/Xhg0bdOzYsTPOiUQiuummm/Taa6/pJz/5iUaNGqUFCxa0L+va2Nio1atX67XXXlNjY6Nef/11q38MIK0R9ADO6g9/+IMmTpyob33rW3I4HLrrrrs6PW/MmDFn/Yx/+Zd/Ud++fdWnTx+NHDlSoVAoUeUC6ARBD+CsMjMzdeos2SeH40/X1VB8ZuY3dwgdDoeYdRuwFkEP4KzGjx+v119/XUePHpUUW/ynO3369FFra2uiSwMQJx7GA3BWY8eO1Z133qnvf//7ys7O1siRI9W3b98u/05xcbGeeuopRSIRi6oE0BVWrwNwVvX19Xr//fdVXl4uSVq9erU++OCDtFyjHkhVBD2As2publZFRYX27dsnh8Ohiy++WI8++qgGDhxod2kA4kTQAwBgMB7GAwDAYAQ9AAAGI+gBADAYQQ8AgMEIegAADEbQAwBgsP8HLCR7v34MVsAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_3h] Residual plot (1 point)\n",
    "\n",
    "df_plot=df_timber.copy() \n",
    "df_plot['residuals']= residuals_timber \n",
    "ax=df_plot.plot( kind='scatter', x='girth', y='residuals', c='k')\n",
    "#// END_TODO [HYP_3h]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the residual plot, how well does this first order polynomial model perform?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Better Model\n",
    "\n",
    "To help define a better fitting model we should look at the following:\n",
    "\n",
    "The tree girth can be viewed as its circumference. The radius $r$ of the tree can then be computed by \n",
    "\n",
    "$$r = \\mathsf{girth} / 2\\pi$$\n",
    "\n",
    "The volume of a cylinder of radius $r$ and height $h$ is equal to\n",
    "\n",
    "$$\\pi * r^2 * h$$\n",
    "\n",
    "Assuming the tree trunk extends to the top of the tree, we can use this formula to estimate the volume of the tree trunk.\n",
    "\n",
    "#### Exercise 3.i\n",
    "\n",
    "Add a column called `'volume_est'` to the dataframe `df_timber` with a volume estimate (in cubic feet) for the tree trunk based on the above statements. Use `math.pi` as approximation of $\\pi$.\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Remember that `df_timber['girth']` is in inches.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3i] Add volume estimates (1 point)\n",
    "\n",
    "df_timber['volume_est']=math. pi *((1/12)*( df_timber ['girth'])/ (2*math. pi)) **2*df_timber['height']\n",
    "\n",
    "#// END_TODO [HYP_3i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.j\n",
    "Fit a regression model with `volume` as the dependent and `volume_est` as the independent variable. Assign the data for the independent variables to dataframe `X_timber_est` and the model to `lm_timber_est`.\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Reuse the dependent variable `y_timber`.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3j] Fit the better model (1 point)\n",
    "\n",
    "X_timber_est=df_timber[['volume_est']]\n",
    "\n",
    "lm_timber_est=LinearRegression() \n",
    "lm_timber_est.fit(X_timber_est, y_timber);\n",
    "\n",
    "#// END_TODO [HYP_3j]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.k\n",
    "\n",
    "Compute the normalized residuals for the training data in the previous exercise. Assign them to the variable `residuals_timber_est`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3k] Residuals for the better model (1 point)\n",
    "\n",
    "residuals_timber_est=scale(y_timber-lm_timber_est.predict(X_timber_est))\n",
    "\n",
    "#// END_TODO [HYP_3k]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.l\n",
    "Plot the normalized residuals in `residuals_timber_est`, with `'volume_est'` on the x-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_3l] Normalized residuals vs volume estimate (1 point)\n",
    "\n",
    "df_plot = df_timber .copy()\n",
    "df_plot['residuals']=residuals_timber_est\n",
    "\n",
    "ax =df_plot.plot(kind='scatter',x='volume_est', y= 'volume',c='k')\n",
    "#// END_TODO [HYP_3l]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3.m\n",
    "Are there potential outliers?\n",
    "Assign your (boolean) answer to `outliers`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_3m] Potential outliers (1 point)\n",
    "\n",
    "outliers = False\n",
    "\n",
    "#// END_TODO [HYP_3m]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 4. Exercise: Hypothesis Testing\n",
    "\n",
    "Last week we applied data aggregation and sampling to extract features from the data you all collected in the mouse experiment. Now we will use that same data to verify Fitts's law and draw conclusions about perceived differences in this data.\n",
    "\n",
    "The Fitts's law describes the relation between the distance from a cursor to an object, the size of the object and the time it takes for a user to click the object. We have asked you all to record data in this experiment using two different input devices: trackpad and mouse. We use this recorded data to compare the two input methods. \n",
    "\n",
    "One can imagine that the use of an interface feels intuitive as long as finding and clicking specific buttons does not take too long. More specifically, it does not matter how long it takes to click a button as long as it does not take longer than 1 second. We would like to investigate if, for either of the input methods (trackpad vs. mouse), this limit is often exceeded.\n",
    "\n",
    "Let us first read the data into `df_fitts`, containing data from individual trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user</th>\n",
       "      <th>trial</th>\n",
       "      <th>delay</th>\n",
       "      <th>input_method</th>\n",
       "      <th>target_radius</th>\n",
       "      <th>target_x</th>\n",
       "      <th>target_y</th>\n",
       "      <th>total_time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1226</td>\n",
       "      <td>5</td>\n",
       "      <td>2.136719</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>-84</td>\n",
       "      <td>-84</td>\n",
       "      <td>3.607323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1226</td>\n",
       "      <td>6</td>\n",
       "      <td>3.540913</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>190</td>\n",
       "      <td>1.867664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1226</td>\n",
       "      <td>7</td>\n",
       "      <td>3.688381</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>-158</td>\n",
       "      <td>-158</td>\n",
       "      <td>1.645011</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user  trial     delay  input_method  target_radius  target_x  target_y  \\\n",
       "0  1226      5  2.136719             0              6       -84       -84   \n",
       "1  1226      6  3.540913             0              6         0       190   \n",
       "2  1226      7  3.688381             0              6      -158      -158   \n",
       "\n",
       "   total_time  \n",
       "0    3.607323  \n",
       "1    1.867664  \n",
       "2    1.645011  "
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_fitts = pd.read_csv(\"./datasets/user_trial_props.csv\")\n",
    "df_fitts.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and visualize the total time of a trial (in seconds) vs. the input method (0 for trackpad and 1 for mouse) using a strip plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Ben\\anaconda3\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.stripplot('input_method', 'total_time', data=df_fitts, jitter=True, s=1)\n",
    "ax.set_xlabel('Input method')\n",
    "ax.set_ylabel('Total time (s)')\n",
    "ax.set_ylim(0, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us extract the total time for the trials recorded using the mouse and trackpad into series `mouse` and `trackpad`, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "mouse = df_fitts[df_fitts['input_method'] == 1]['total_time']\n",
    "trackpad = df_fitts[df_fitts['input_method'] == 0]['total_time']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4.a\n",
    "\n",
    "Using the goal described above, define a quantitative question, with which you define what you plan to investigate. Use this question to guide your thinking in the next exercises."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assign `'a'`, `'b'` or `'c'` to the variable `question_fitts`\n",
    "\n",
    ">a. Is the proportion of trackpad trajectories that take longer than a second significantly larger than the proportion of  mouse trajectories that take longer than a second?<br>\n",
    "b. Is the proportion of trackpad trajectories that take longer than a second significantly different from the proportion of mouse trajectories that take longer than a second?<br>\n",
    "c. Is the proportion of trackpad trajectories that take longer than a second significantly smaller than the proportion of mouse trajectories that take longer than a second?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_4a] Formulate quantitative question (1 point)\n",
    "\n",
    "question_fitts = 'b'\n",
    "\n",
    "#// END_TODO [HYP_4a]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise <span class=\"exercise\">4.b</span>  \n",
    "Using the goal described above and the quantitative question you defined formulate the best fitting hypothesis. Think of the following:\n",
    "\n",
    "* one- or two-sample data\n",
    "* one- or two-sided test\n",
    "* equality of means or equality of proportions hypothesis\n",
    "\n",
    "Assign to the variable `data_fitts` the string `'one-sample'` if we are dealing with one-sample data and `'two-sample'` if we are dealing with two-sample data.\n",
    "\n",
    "Assign to the variable `test_fitts` the string `'one-sided'` if a one-sided test should be used and `'two-sided'` if a two-sided test should be used.\n",
    "\n",
    "Assign the hypotheses as string to variables `H_0_fitts` and `H_a_fitts`. Construct the strings in the following way: `'mu_mouse=mu_trackpad'` or `'p_mouse=p_trackpad'`. Use `mu` when comparing means and `p` when comparing proportions. Use `!=`, `>` or `<` for the alternative hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_4b] Formulate Hypothesis (1 point)\n",
    "\n",
    "H_0_fitts = 'p_mouse=p_trackpad'\n",
    "H_a_fitts = 'p_mouse!=p_trackpad'\n",
    "\n",
    "#// END_TODO [HYP_4b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise <span class=\"exercise\">4.c</span> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does the choice of hypothesis and the appropriate test for this hypothesis require you to test the normality assumptions? Assign boolean answer to `check_normal_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_4c] Is there a need to check assumptions? (1 point)\n",
    "\n",
    "check_normal_fitts = False\n",
    "\n",
    "#// END_TODO [HYP_4c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise <span class=\"exercise\">4.d</span> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you indicated the need to check normality assumptions in the previous question, please do so below. Assign boolean answer to `normal_fitts`: \n",
    "\n",
    "- `True` if the assumptions are met,\n",
    "- `False` if there is enough evidence to reject normality, or the intended test does not require you to test for normality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_4d] Check Assumptions (1 point)\n",
    "\n",
    "normal_fitts = False\n",
    "\n",
    "#// END_TODO [HYP_4d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise <span class=\"exercise\" >4.e</span>\n",
    "Apply the correct test, regardless of the results you found in the previous question.\n",
    "It is possible that more preprocessing is required. Add more code cells between the markers if you need them. Assign the p-value you found to `p_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'total_time'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32mc:\\Users\\Ben\\anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_loc\u001b[1;34m(self, key, method, tolerance)\u001b[0m\n\u001b[0;32m   3079\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3080\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcasted_key\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3081\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mpandas\\_libs\\index_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.index.Int64Engine._check_type\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 'total_time'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-79-c1307488e8a3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#// BEGIN_TODO [HYP_4e] Apply test (1 point)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mover1_mouse\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmouse\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmouse\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'total_time'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m>\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mover1_trackpad\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtrackpad\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mtrackpad\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'total_time'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m>\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mm_count\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmouse\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mt_count\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtrackpad\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\Ben\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m    851\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    852\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mkey_is_scalar\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 853\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    854\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    855\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mis_hashable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\Ben\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m_get_value\u001b[1;34m(self, label, takeable)\u001b[0m\n\u001b[0;32m    959\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    960\u001b[0m         \u001b[1;31m# Similar to Index.get_value, but we do not fall back to positional\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 961\u001b[1;33m         \u001b[0mloc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    962\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_values_for_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    963\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\Ben\\anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\base.py\u001b[0m in \u001b[0;36mget_loc\u001b[1;34m(self, key, method, tolerance)\u001b[0m\n\u001b[0;32m   3080\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcasted_key\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3081\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3082\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3083\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3084\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mtolerance\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 'total_time'"
     ]
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_4e] Apply test (1 point)\n",
    "over1_mouse = mouse[mouse['total_time']>1].count()[0]\n",
    "over1_trackpad = trackpad[trackpad['total_time']>1].count()[0]\n",
    "m_count = mouse.count()[0]\n",
    "t_count = trackpad.count()[0]\n",
    "p_fitts = sm.stats.proportions_ztest([over1_mouse,over1_trackpad],[m_count,t_count],alternative = \"two-sided\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// END_TODO [HYP_4e]\n",
    "\n",
    "p_fitts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise <span class=\"exercise\">4.f</span> \n",
    "Is there sufficient evidence to reject the null hypothesis (at significance level $\\alpha=0.05$)? Assign your (boolean) answer to `reject_null_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_4f] Decision (1 point)\n",
    "\n",
    "reject_null_fitts = True\n",
    "\n",
    "#// END_TODO [HYP_4f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 5. Exercise: Regression Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fitts's law describes the relation between the distance between a cursor and an object, the size of the object and the time it takes for a user to click the object. In particular, Fitts's law says that there is a linear relationship between trajectory's *total time* $T$ and its *Index of Difficulty* $I$:\n",
    "\n",
    "$$T = a * I + b$$\n",
    "\n",
    "where $I$ is given by\n",
    "\n",
    "$$I = \\log_2 \\left( \\frac{2D}{R} \\right)$$\n",
    "\n",
    "where $D$ is the *target distance* and $R$ is the *target radius*.\n",
    "\n",
    "In this exercise we will try to fit the Fitt's model to the trackpad data from the mouse experiment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Exercise 5.a\n",
    "\n",
    "Select the trackpad trajectories from `df_fitts`. Create a new dataframe `df_regression` with all the trackpad trajectories.\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Trackpad trajectories have an `input_method` equal to 0.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>6</td>\n",
       "      <td>-158</td>\n",
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       "      <th>3</th>\n",
       "      <td>1226</td>\n",
       "      <td>8</td>\n",
       "      <td>2.823134</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>81</td>\n",
       "      <td>-81</td>\n",
       "      <td>1.776010</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1226</td>\n",
       "      <td>9</td>\n",
       "      <td>3.690253</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>-157</td>\n",
       "      <td>157</td>\n",
       "      <td>1.567794</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user  trial     delay  input_method  target_radius  target_x  target_y  \\\n",
       "0  1226      5  2.136719             0              6       -84       -84   \n",
       "1  1226      6  3.540913             0              6         0       190   \n",
       "2  1226      7  3.688381             0              6      -158      -158   \n",
       "3  1226      8  2.823134             0              3        81       -81   \n",
       "4  1226      9  3.690253             0              9      -157       157   \n",
       "\n",
       "   total_time  \n",
       "0    3.607323  \n",
       "1    1.867664  \n",
       "2    1.645011  \n",
       "3    1.776010  \n",
       "4    1.567794  "
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5a] Create dataframe (1 point)\n",
    "\n",
    "df_regression = df_fitts[df_fitts['input_method']==0]\n",
    "#// END_TODO [HYP_5a]\n",
    "\n",
    "df_regression.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To apply the Fitt's law we will need to construct additional features first. We start with computing the *target distance*, which we will then use together with the *target radius* to compute the *Index of Difficulty*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.b\n",
    "\n",
    "Each trajectory starts at the coordinates (0,0). Use this information to calculate the distance of the target from the starting point using the `'target_x'` and `'target_y'` columns. Store the target distance in a new column `'target_distance'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-119-6f85e01b1a47>:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  df_regression['target_distance'] = np.sqrt(df_regression['target_x']**2+df_regression['target_y']**2)\n"
     ]
    },
    {
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1226</td>\n",
       "      <td>6</td>\n",
       "      <td>3.540913</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>190</td>\n",
       "      <td>1.867664</td>\n",
       "      <td>190.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1226</td>\n",
       "      <td>7</td>\n",
       "      <td>3.688381</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>-158</td>\n",
       "      <td>-158</td>\n",
       "      <td>1.645011</td>\n",
       "      <td>223.445743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1226</td>\n",
       "      <td>8</td>\n",
       "      <td>2.823134</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>81</td>\n",
       "      <td>-81</td>\n",
       "      <td>1.776010</td>\n",
       "      <td>114.551299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1226</td>\n",
       "      <td>9</td>\n",
       "      <td>3.690253</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>-157</td>\n",
       "      <td>157</td>\n",
       "      <td>1.567794</td>\n",
       "      <td>222.031529</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user  trial     delay  input_method  target_radius  target_x  target_y  \\\n",
       "0  1226      5  2.136719             0              6       -84       -84   \n",
       "1  1226      6  3.540913             0              6         0       190   \n",
       "2  1226      7  3.688381             0              6      -158      -158   \n",
       "3  1226      8  2.823134             0              3        81       -81   \n",
       "4  1226      9  3.690253             0              9      -157       157   \n",
       "\n",
       "   total_time  target_distance  \n",
       "0    3.607323       118.793939  \n",
       "1    1.867664       190.000000  \n",
       "2    1.645011       223.445743  \n",
       "3    1.776010       114.551299  \n",
       "4    1.567794       222.031529  "
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5b] Add distance column (1 point)\n",
    "\n",
    "df_regression['target_distance'] = np.sqrt(df_regression['target_x']**2+df_regression['target_y']**2)\n",
    "#// END_TODO [HYP_5b]\n",
    "df_regression.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.c\n",
    "\n",
    "Recall that the *Index of Difficulty* $I$ is given by:\n",
    "\n",
    "$$I = \\log_2 \\left( \\frac{2 D}{R} \\right)$$\n",
    "\n",
    "where $D$ is the *target distance* and $R$ is the *target radius*.\n",
    "\n",
    "Add a column `'ID'` to the data frame containing the Index of Difficulty.\n",
    "\n",
    "<span class=\"t\">Hint<span class=\"c\">:</span></span>\n",
    "<span class=\"h\">\n",
    "Use the function `np.log2()`.\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-120-d43a7cf68cfb>:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  df_regression['ID'] = np.log2(2*df_regression['target_distance']/df_regression['target_radius'])\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user</th>\n",
       "      <th>trial</th>\n",
       "      <th>delay</th>\n",
       "      <th>input_method</th>\n",
       "      <th>target_radius</th>\n",
       "      <th>target_x</th>\n",
       "      <th>target_y</th>\n",
       "      <th>total_time</th>\n",
       "      <th>target_distance</th>\n",
       "      <th>ID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1226</td>\n",
       "      <td>5</td>\n",
       "      <td>2.136719</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>-84</td>\n",
       "      <td>-84</td>\n",
       "      <td>3.607323</td>\n",
       "      <td>118.793939</td>\n",
       "      <td>5.307355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1226</td>\n",
       "      <td>6</td>\n",
       "      <td>3.540913</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>190</td>\n",
       "      <td>1.867664</td>\n",
       "      <td>190.000000</td>\n",
       "      <td>5.984893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1226</td>\n",
       "      <td>7</td>\n",
       "      <td>3.688381</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>-158</td>\n",
       "      <td>-158</td>\n",
       "      <td>1.645011</td>\n",
       "      <td>223.445743</td>\n",
       "      <td>6.218818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1226</td>\n",
       "      <td>8</td>\n",
       "      <td>2.823134</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>81</td>\n",
       "      <td>-81</td>\n",
       "      <td>1.776010</td>\n",
       "      <td>114.551299</td>\n",
       "      <td>6.254888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1226</td>\n",
       "      <td>9</td>\n",
       "      <td>3.690253</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>-157</td>\n",
       "      <td>157</td>\n",
       "      <td>1.567794</td>\n",
       "      <td>222.031529</td>\n",
       "      <td>5.624696</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user  trial     delay  input_method  target_radius  target_x  target_y  \\\n",
       "0  1226      5  2.136719             0              6       -84       -84   \n",
       "1  1226      6  3.540913             0              6         0       190   \n",
       "2  1226      7  3.688381             0              6      -158      -158   \n",
       "3  1226      8  2.823134             0              3        81       -81   \n",
       "4  1226      9  3.690253             0              9      -157       157   \n",
       "\n",
       "   total_time  target_distance        ID  \n",
       "0    3.607323       118.793939  5.307355  \n",
       "1    1.867664       190.000000  5.984893  \n",
       "2    1.645011       223.445743  6.218818  \n",
       "3    1.776010       114.551299  6.254888  \n",
       "4    1.567794       222.031529  5.624696  "
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5c] Add ID column (1 point)\n",
    "\n",
    "df_regression['ID'] = np.log2(2*df_regression['target_distance']/df_regression['target_radius'])\n",
    "#// END_TODO [HYP_5c]\n",
    "\n",
    "df_regression.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.d\n",
    "\n",
    "Plot a scatter diagram of the index of difficulty `'total_time'` vs. `'ID'`. Restrict the $y$-axis from $0$ to $5$ seconds and use a point size of `5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5d] Create scatter diagram (1 point)\n",
    "\n",
    "ax = df_regression.plot(kind = 'scatter', x = 'ID', y = 'total_time', s=5, c = 'b')\n",
    "ax.set_ylim(0,5);\n",
    "\n",
    "#// END_TODO [HYP_5d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.e\n",
    "\n",
    "Fit the appropriate regression model. Assign the data for the independent variables to the dataframe `X_fitts`, the data for the dependent variable to the series `y_fitts`, and the model to `lm_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'df_regression' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-80-bc4edf4125f4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#// BEGIN_TODO [HYP_5e] Fit model (1 point)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mX_fitts\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdf_regression\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'ID'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0my_fitts\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdf_regression\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'total_time'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'df_regression' is not defined"
     ]
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5e] Fit model (1 point)\n",
    "\n",
    "X_fitts=df_regression[['ID']].copy()\n",
    "y_fitts=df_regression['total_time'].copy()\n",
    "\n",
    "lm_fitts=LinearRegression() \n",
    "lm_fitts.fit(X_fitts, y_fitts);\n",
    "\n",
    "#// END_TODO [HYP_5e]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.f\n",
    "\n",
    "Plot the normalized residuals, with `'ID'` on the x-axis. Assign the normalized residuals to the variable `residuals_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'y_fitts' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-81-ddee001c187a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#// BEGIN_TODO [HYP_5f] Create scatter diagram of residuals (1 point)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mresiduals_fitts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mscale\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my_fitts\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mlm_fitts\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX_fitts\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mdf_regression\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'residuals'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mresiduals_fitts\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf_regression\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkind\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'scatter'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'ID'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'residuals'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'b'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'y_fitts' is not defined"
     ]
    }
   ],
   "source": [
    "#// BEGIN_TODO [HYP_5f] Create scatter diagram of residuals (1 point)\n",
    "\n",
    "residuals_fitts = scale(y_fitts-lm_fitts.predict(X_fitts))\n",
    "df_regression['residuals'] = residuals_fitts\n",
    "ax = df_regression.plot(kind='scatter',x='ID',y='residuals',c='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// END_TODO [HYP_5f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.g\n",
    "\n",
    "Are there any data points suspected to be outliers, because of a high normalized residual? Assign your (boolean) answer to `outlier_fitts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_TODO [HYP_5g] Are there suspicious points? (1 point)\n",
    "\n",
    "outlier_fitts = True\n",
    "\n",
    "#// END_TODO [HYP_5g]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feedback\n",
    "\n",
    "Please fill in this questionaire to help us improve this course for the next year. Your feedback will be anonymized and will not affect your grade in any way!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many hours did you spend on these Exercises?\n",
    "\n",
    "Assign a number to `feedback_time`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_FEEDBACK [Feedback_1] (0 point)\n",
    "feedback_time = 5\n",
    "#// END_FEEDBACK [Feedback_1] (0 point)\n",
    "\n",
    "import numbers\n",
    "assert isinstance(feedback_time, numbers.Number), \"Please assign a number to feedback_time\"\n",
    "feedback_time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How difficult did you find these Exercises?\n",
    "\n",
    "Assign an integer to `feedback_difficulty`, on a scale 0 - 10, with 0 being very easy, 5 being just right, and 10 being very difficult."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_FEEDBACK [Feedback_2] (0 point)\n",
    "feedback_difficulty = 7\n",
    "#// END_FEEDBACK [Feedback_2] (0 point)\n",
    "\n",
    "import numbers\n",
    "assert isinstance(feedback_difficulty, numbers.Number), \"Please assign a number to feedback_difficulty\"\n",
    "feedback_difficulty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Optional) What did you like?\n",
    "\n",
    "Assign a string to `feedback_like`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_FEEDBACK [Feedback_3] (0 point)\n",
    "\n",
    "#// END_FEEDBACK [Feedback_3] (0 point)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Optional) What can be improved?\n",
    "\n",
    "Assign a string to `feedback_improve`. Please be specific, so that we can act on your feedback. For example, mention the specific exercises and what was unclear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#// BEGIN_FEEDBACK [Feedback_4] (0 point)\n",
    "\n",
    "#// END_FEEDBACK [Feedback_4] (0 point)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "## How to Submit Your Work\n",
    "\n",
    "1. **Before submitting**, you must run your notebook by doing **Kernel > Restart & Run All**.  \n",
    "   Make sure that your notebook runs without errors **in linear order**.\n",
    "1. Remember to rename the notebook, replacing `...-template.ipynb` with `...-yourIDnr.ipynb`, where `yourIDnr` is your TU/e identification number.\n",
    "1. Submit the executed notebook with your work\n",
    "   for the appropriate assignment in **Canvas**.\n",
    "1. In the **Momotor** tab in Canvas,\n",
    "  you can select that assignment again to find some feedback on your submitted work.\n",
    "  If there are any problems reported by _Momotor_,\n",
    "  then you need to fix those,\n",
    "  and **resubmit the fixed notebook**.\n",
    "\n",
    "In case of a high workload on our server\n",
    "(because many students submit close to the deadline),\n",
    "it may take longer to receive the feedback.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# List all defined names\n",
    "%whos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# (End of Notebook) <span class=\"tocSkip\"></span>\n",
    "\n",
    "&copy; 2017-2023 - **TU/e** - Eindhoven University of Technology"
   ]
  }
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