04-Regression-and-Prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <div class=\"alert alert-info\" style=\"text-align: center;\" markdown=\"1\">Regression and Prediction</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Simple Regression Equation`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y = b_0 + b_1x$\n",
    "\n",
    "- where:\n",
    "    - $y$ is the dependent variable\n",
    "    - $b_0$ is the intercept\n",
    "    - $b_1$ is the coefficients\n",
    "    - $x$ is the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>PEFR</th>\n",
       "      <th>Exposure</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>390</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>410</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>430</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>460</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>420</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PEFR  Exposure\n",
       "0   390         0\n",
       "1   410         0\n",
       "2   430         0\n",
       "3   460         0\n",
       "4   420         1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_lung = pd.read_csv(\"data/LungDisease.csv\")\n",
    "df_lung.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors = df_lung[\"Exposure\"]\n",
    "target = df_lung[\"PEFR\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.18457649] 424.582806573957\n"
     ]
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(predictors.values.reshape(-1,1), target)\n",
    "\n",
    "print(model.coef_, model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Regression line\n",
    "\n",
    "plt.scatter(predictors, target)\n",
    "plt.plot(predictors, model.predict(predictors.values.reshape(-1,1)), color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      -34.582807\n",
       "1      -14.582807\n",
       "2        5.417193\n",
       "3       35.417193\n",
       "4       -0.398230\n",
       "          ...    \n",
       "117    117.477876\n",
       "118    157.477876\n",
       "119    167.477876\n",
       "120     41.662453\n",
       "121     61.662453\n",
       "Name: PEFR, Length: 122, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted = model.predict(predictors.values.reshape(-1,1))\n",
    "residuals = target - fitted\n",
    "residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares\n",
    "\n",
    "- Sum of squared residuals.\n",
    "\n",
    "$SSR = \\sum_{i=1}^{n} (y_i - \\hat{y_i})^2$\n",
    "\n",
    "- where:\n",
    "    - $y_i$ is the actual value\n",
    "    - $\\hat{y_i}$ is the predicted value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Multiple Regression Equation`\n",
    "\n",
    "$y = b_0 + b_1x_1 + b_2x_2 + ... + b_nx_n$\n",
    "\n",
    "- where:\n",
    "    - $y$ is the dependent variable\n",
    "    - $b_0$ is the intercept\n",
    "    - $b_1, b_2, ..., b_n$ are the coefficients\n",
    "    - $x_1, x_2, ..., x_n$ are the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>DocumentDate</th>\n",
       "      <th>SalePrice</th>\n",
       "      <th>PropertyID</th>\n",
       "      <th>PropertyType</th>\n",
       "      <th>ym</th>\n",
       "      <th>zhvi_px</th>\n",
       "      <th>zhvi_idx</th>\n",
       "      <th>AdjSalePrice</th>\n",
       "      <th>NbrLivingUnits</th>\n",
       "      <th>SqFtLot</th>\n",
       "      <th>...</th>\n",
       "      <th>Bathrooms</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>BldgGrade</th>\n",
       "      <th>YrBuilt</th>\n",
       "      <th>YrRenovated</th>\n",
       "      <th>TrafficNoise</th>\n",
       "      <th>LandVal</th>\n",
       "      <th>ImpsVal</th>\n",
       "      <th>ZipCode</th>\n",
       "      <th>NewConstruction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-09-16</td>\n",
       "      <td>280000</td>\n",
       "      <td>1000102</td>\n",
       "      <td>Multiplex</td>\n",
       "      <td>2014-09-01</td>\n",
       "      <td>405100</td>\n",
       "      <td>0.930836</td>\n",
       "      <td>300805.0</td>\n",
       "      <td>2</td>\n",
       "      <td>9373</td>\n",
       "      <td>...</td>\n",
       "      <td>3.00</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1991</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>70000</td>\n",
       "      <td>229000</td>\n",
       "      <td>98002</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2006-06-16</td>\n",
       "      <td>1000000</td>\n",
       "      <td>1200013</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2006-06-01</td>\n",
       "      <td>404400</td>\n",
       "      <td>0.929228</td>\n",
       "      <td>1076162.0</td>\n",
       "      <td>1</td>\n",
       "      <td>20156</td>\n",
       "      <td>...</td>\n",
       "      <td>3.75</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>2005</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>203000</td>\n",
       "      <td>590000</td>\n",
       "      <td>98166</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2007-01-29</td>\n",
       "      <td>745000</td>\n",
       "      <td>1200019</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2007-01-01</td>\n",
       "      <td>425600</td>\n",
       "      <td>0.977941</td>\n",
       "      <td>761805.0</td>\n",
       "      <td>1</td>\n",
       "      <td>26036</td>\n",
       "      <td>...</td>\n",
       "      <td>1.75</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>1947</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>183000</td>\n",
       "      <td>275000</td>\n",
       "      <td>98166</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2008-02-25</td>\n",
       "      <td>425000</td>\n",
       "      <td>2800016</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2008-02-01</td>\n",
       "      <td>418400</td>\n",
       "      <td>0.961397</td>\n",
       "      <td>442065.0</td>\n",
       "      <td>1</td>\n",
       "      <td>8618</td>\n",
       "      <td>...</td>\n",
       "      <td>3.75</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1966</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>104000</td>\n",
       "      <td>229000</td>\n",
       "      <td>98168</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2013-03-29</td>\n",
       "      <td>240000</td>\n",
       "      <td>2800024</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2013-03-01</td>\n",
       "      <td>351600</td>\n",
       "      <td>0.807904</td>\n",
       "      <td>297065.0</td>\n",
       "      <td>1</td>\n",
       "      <td>8620</td>\n",
       "      <td>...</td>\n",
       "      <td>1.75</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>1948</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>104000</td>\n",
       "      <td>205000</td>\n",
       "      <td>98168</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  DocumentDate  SalePrice  PropertyID   PropertyType          ym  zhvi_px  \\\n",
       "1   2014-09-16     280000     1000102      Multiplex  2014-09-01   405100   \n",
       "2   2006-06-16    1000000     1200013  Single Family  2006-06-01   404400   \n",
       "3   2007-01-29     745000     1200019  Single Family  2007-01-01   425600   \n",
       "4   2008-02-25     425000     2800016  Single Family  2008-02-01   418400   \n",
       "5   2013-03-29     240000     2800024  Single Family  2013-03-01   351600   \n",
       "\n",
       "   zhvi_idx  AdjSalePrice  NbrLivingUnits  SqFtLot  ...  Bathrooms  Bedrooms  \\\n",
       "1  0.930836      300805.0               2     9373  ...       3.00         6   \n",
       "2  0.929228     1076162.0               1    20156  ...       3.75         4   \n",
       "3  0.977941      761805.0               1    26036  ...       1.75         4   \n",
       "4  0.961397      442065.0               1     8618  ...       3.75         5   \n",
       "5  0.807904      297065.0               1     8620  ...       1.75         4   \n",
       "\n",
       "   BldgGrade  YrBuilt  YrRenovated  TrafficNoise  LandVal  ImpsVal  ZipCode  \\\n",
       "1          7     1991            0             0    70000   229000    98002   \n",
       "2         10     2005            0             0   203000   590000    98166   \n",
       "3          8     1947            0             0   183000   275000    98166   \n",
       "4          7     1966            0             0   104000   229000    98168   \n",
       "5          7     1948            0             0   104000   205000    98168   \n",
       "\n",
       "   NewConstruction  \n",
       "1            False  \n",
       "2             True  \n",
       "3            False  \n",
       "4            False  \n",
       "5            False  \n",
       "\n",
       "[5 rows x 22 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_house = pd.read_csv(\"data/house_sales.csv\", sep=\"\\t\")\n",
    "df_house.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors = [\"SqFtTotLiving\", \"SqFtLot\", \"Bathrooms\", \"Bedrooms\", \"BldgGrade\"]\n",
    "target = df_house[\"AdjSalePrice\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(df_house[predictors], target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.28830604e+02 -6.04668207e-02 -1.94428404e+04 -4.77699552e+04\n",
      "  1.06106963e+05] -521871.36818828376\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(model.coef_, model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Assesing the Model\n",
    "\n",
    "- RMSE (Root Mean Squared Error)\n",
    "\n",
    "$RMSE = \\sqrt{\\frac{1}{n} \\sum_{i=1}^{n} (y_i - \\hat{y_i})^2}$\n",
    "\n",
    "- where:\n",
    "    - $y_i$ is the actual value\n",
    "    - $\\hat{y_i}$ is the predicted value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "261220.19743696266\n"
     ]
    }
   ],
   "source": [
    "fitted = model.predict(df_house[predictors])\n",
    "residuals = target - fitted\n",
    "\n",
    "RMSE = np.sqrt(np.mean(residuals**2))\n",
    "print(RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "261220.19743696266\n",
      "0.5405875253381902\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "print(np.sqrt(mean_squared_error(target, fitted)))\n",
    "print(r2_score(target, fitted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Validation\n",
    "\n",
    "- Cross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample.\n",
    "\n",
    "- #### K-Fold Cross Validation\n",
    "\n",
    "    - The data set is divided into k subsets, and the holdout method is repeated k times. Each time, one of the k subsets is used as the test set and the other k-1 subsets are put together to form a training set.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weighted Regression\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_house[\"weights\"] = df_house[\"DocumentDate\"].str[:4].astype(int) - 2005"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(df_house[predictors], target, sample_weight=df_house[\"weights\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "261908.05510888086\n",
      "0.5381648454281938\n"
     ]
    }
   ],
   "source": [
    "fitted = model.predict(df_house[predictors])\n",
    "residuals = target - fitted\n",
    "\n",
    "print(np.sqrt(mean_squared_error(target, fitted)))\n",
    "print(r2_score(target, fitted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Categorical Variables in Regression`\n",
    "\n",
    "### Dummy Variables (One-Hot Encoding)\n",
    "\n",
    "- Dummy variables are used to include categorical data in a regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1        Multiplex\n",
       "2    Single Family\n",
       "3    Single Family\n",
       "4    Single Family\n",
       "5    Single Family\n",
       "Name: PropertyType, dtype: object"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_house.PropertyType.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- To use this variable in a regression model, we need to convert it into a set of binary variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>Multiplex</th>\n",
       "      <th>Single Family</th>\n",
       "      <th>Townhouse</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Multiplex  Single Family  Townhouse\n",
       "1          1              0          0\n",
       "2          0              1          0\n",
       "3          0              1          0\n",
       "4          0              1          0\n",
       "5          0              1          0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.get_dummies(df_house.PropertyType).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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>Single Family</th>\n",
       "      <th>Townhouse</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Single Family  Townhouse\n",
       "1              0          0\n",
       "2              1          0\n",
       "3              1          0\n",
       "4              1          0\n",
       "5              1          0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To avoid multicollinearity, we drop the first column\n",
    "pd.get_dummies(df_house.PropertyType, drop_first=True).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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>SqFtTotLiving</th>\n",
       "      <th>SqFtLot</th>\n",
       "      <th>Bathrooms</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>BldgGrade</th>\n",
       "      <th>PropertyType_Single Family</th>\n",
       "      <th>PropertyType_Townhouse</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2400</td>\n",
       "      <td>9373</td>\n",
       "      <td>3.00</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3764</td>\n",
       "      <td>20156</td>\n",
       "      <td>3.75</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2060</td>\n",
       "      <td>26036</td>\n",
       "      <td>1.75</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3200</td>\n",
       "      <td>8618</td>\n",
       "      <td>3.75</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1720</td>\n",
       "      <td>8620</td>\n",
       "      <td>1.75</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SqFtTotLiving  SqFtLot  Bathrooms  Bedrooms  BldgGrade  \\\n",
       "1           2400     9373       3.00         6          7   \n",
       "2           3764    20156       3.75         4         10   \n",
       "3           2060    26036       1.75         4          8   \n",
       "4           3200     8618       3.75         5          7   \n",
       "5           1720     8620       1.75         4          7   \n",
       "\n",
       "   PropertyType_Single Family  PropertyType_Townhouse  \n",
       "1                           0                       0  \n",
       "2                           1                       0  \n",
       "3                           1                       0  \n",
       "4                           1                       0  \n",
       "5                           1                       0  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors = [\"SqFtTotLiving\", \"SqFtLot\", \"Bathrooms\", \"Bedrooms\", \"BldgGrade\", \"PropertyType\"]\n",
    "target = df_house[\"AdjSalePrice\"]\n",
    "X = pd.get_dummies(df_house[predictors], drop_first=True)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X, target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: -446841.366311674\n",
      "Coefficients: [ 2.23373629e+02 -7.03679814e-02 -1.59790135e+04 -5.08897322e+04\n",
      "  1.09416305e+05 -8.46782163e+04 -1.15121979e+05]\n"
     ]
    }
   ],
   "source": [
    "print(\"Intercept:\", model.intercept_)\n",
    "print(\"Coefficients:\", model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "260971.6799933774\n",
      "0.5414612533643957\n"
     ]
    }
   ],
   "source": [
    "fitted = model.predict(X)\n",
    "residuals = target - fitted\n",
    "\n",
    "print(np.sqrt(mean_squared_error(target, fitted)))\n",
    "print(r2_score(target, fitted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Categorical Variables with Many Levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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>98038</th>\n",
       "      <th>98103</th>\n",
       "      <th>98042</th>\n",
       "      <th>98115</th>\n",
       "      <th>98117</th>\n",
       "      <th>98052</th>\n",
       "      <th>98034</th>\n",
       "      <th>98033</th>\n",
       "      <th>98059</th>\n",
       "      <th>98074</th>\n",
       "      <th>...</th>\n",
       "      <th>98051</th>\n",
       "      <th>98024</th>\n",
       "      <th>98354</th>\n",
       "      <th>98050</th>\n",
       "      <th>98057</th>\n",
       "      <th>98288</th>\n",
       "      <th>98224</th>\n",
       "      <th>98068</th>\n",
       "      <th>98113</th>\n",
       "      <th>98043</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ZipCode</th>\n",
       "      <td>788</td>\n",
       "      <td>671</td>\n",
       "      <td>641</td>\n",
       "      <td>620</td>\n",
       "      <td>619</td>\n",
       "      <td>614</td>\n",
       "      <td>575</td>\n",
       "      <td>517</td>\n",
       "      <td>513</td>\n",
       "      <td>502</td>\n",
       "      <td>...</td>\n",
       "      <td>32</td>\n",
       "      <td>31</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 80 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         98038  98103  98042  98115  98117  98052  98034  98033  98059  98074  \\\n",
       "ZipCode    788    671    641    620    619    614    575    517    513    502   \n",
       "\n",
       "         ...  98051  98024  98354  98050  98057  98288  98224  98068  98113  \\\n",
       "ZipCode  ...     32     31      9      7      4      4      3      1      1   \n",
       "\n",
       "         98043  \n",
       "ZipCode      1  \n",
       "\n",
       "[1 rows x 80 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(df_house.ZipCode.value_counts()).transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "zip_groups = pd.DataFrame([\n",
    "    *pd.DataFrame({\n",
    "        \"ZipCode\": df_house.ZipCode,\n",
    "        'residuals': residuals\n",
    "    })\n",
    "    .groupby([\"ZipCode\"])\n",
    "    .apply(lambda x: {\n",
    "        'ZipCode': x.iloc[0,0],\n",
    "        'count': len(x),\n",
    "        'median_residual': x.residuals.median()\n",
    "    })\n",
    "]).sort_values(\"median_residual\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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>ZipCode</th>\n",
       "      <th>count</th>\n",
       "      <th>median_residual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>98057</td>\n",
       "      <td>4</td>\n",
       "      <td>-538938.746571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>98043</td>\n",
       "      <td>1</td>\n",
       "      <td>-304848.132844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>98092</td>\n",
       "      <td>289</td>\n",
       "      <td>-195063.801799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>98038</td>\n",
       "      <td>788</td>\n",
       "      <td>-148401.858065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>98051</td>\n",
       "      <td>32</td>\n",
       "      <td>-142571.462708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ZipCode  count  median_residual\n",
       "36    98057      4   -538938.746571\n",
       "27    98043      1   -304848.132844\n",
       "46    98092    289   -195063.801799\n",
       "23    98038    788   -148401.858065\n",
       "31    98051     32   -142571.462708"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zip_groups.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "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>ZipCode</th>\n",
       "      <th>count</th>\n",
       "      <th>median_residual</th>\n",
       "      <th>cumulative_count</th>\n",
       "      <th>ZipGroup</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>98057</td>\n",
       "      <td>4</td>\n",
       "      <td>-538938.746571</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>98043</td>\n",
       "      <td>1</td>\n",
       "      <td>-304848.132844</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>98092</td>\n",
       "      <td>289</td>\n",
       "      <td>-195063.801799</td>\n",
       "      <td>294</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>98038</td>\n",
       "      <td>788</td>\n",
       "      <td>-148401.858065</td>\n",
       "      <td>1082</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>98051</td>\n",
       "      <td>32</td>\n",
       "      <td>-142571.462708</td>\n",
       "      <td>1114</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ZipCode  count  median_residual  cumulative_count ZipGroup\n",
       "36    98057      4   -538938.746571                 4        0\n",
       "27    98043      1   -304848.132844                 5        0\n",
       "46    98092    289   -195063.801799               294        0\n",
       "23    98038    788   -148401.858065              1082        0\n",
       "31    98051     32   -142571.462708              1114        0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zip_groups[\"cumulative_count\"] = zip_groups[\"count\"].cumsum()\n",
    "zip_groups[\"ZipGroup\"] = pd.cut(zip_groups[\"cumulative_count\"], bins=5, labels=range(5))\n",
    "zip_groups.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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>DocumentDate</th>\n",
       "      <th>SalePrice</th>\n",
       "      <th>PropertyID</th>\n",
       "      <th>PropertyType</th>\n",
       "      <th>ym</th>\n",
       "      <th>zhvi_px</th>\n",
       "      <th>zhvi_idx</th>\n",
       "      <th>AdjSalePrice</th>\n",
       "      <th>NbrLivingUnits</th>\n",
       "      <th>SqFtLot</th>\n",
       "      <th>...</th>\n",
       "      <th>BldgGrade</th>\n",
       "      <th>YrBuilt</th>\n",
       "      <th>YrRenovated</th>\n",
       "      <th>TrafficNoise</th>\n",
       "      <th>LandVal</th>\n",
       "      <th>ImpsVal</th>\n",
       "      <th>ZipCode</th>\n",
       "      <th>NewConstruction</th>\n",
       "      <th>weights</th>\n",
       "      <th>ZipGroup</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-09-16</td>\n",
       "      <td>280000</td>\n",
       "      <td>1000102</td>\n",
       "      <td>Multiplex</td>\n",
       "      <td>2014-09-01</td>\n",
       "      <td>405100</td>\n",
       "      <td>0.930836</td>\n",
       "      <td>300805.0</td>\n",
       "      <td>2</td>\n",
       "      <td>9373</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1991</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>70000</td>\n",
       "      <td>229000</td>\n",
       "      <td>98002</td>\n",
       "      <td>False</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2006-06-16</td>\n",
       "      <td>1000000</td>\n",
       "      <td>1200013</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2006-06-01</td>\n",
       "      <td>404400</td>\n",
       "      <td>0.929228</td>\n",
       "      <td>1076162.0</td>\n",
       "      <td>1</td>\n",
       "      <td>20156</td>\n",
       "      <td>...</td>\n",
       "      <td>10</td>\n",
       "      <td>2005</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>203000</td>\n",
       "      <td>590000</td>\n",
       "      <td>98166</td>\n",
       "      <td>True</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2007-01-29</td>\n",
       "      <td>745000</td>\n",
       "      <td>1200019</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2007-01-01</td>\n",
       "      <td>425600</td>\n",
       "      <td>0.977941</td>\n",
       "      <td>761805.0</td>\n",
       "      <td>1</td>\n",
       "      <td>26036</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1947</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>183000</td>\n",
       "      <td>275000</td>\n",
       "      <td>98166</td>\n",
       "      <td>False</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2008-02-25</td>\n",
       "      <td>425000</td>\n",
       "      <td>2800016</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2008-02-01</td>\n",
       "      <td>418400</td>\n",
       "      <td>0.961397</td>\n",
       "      <td>442065.0</td>\n",
       "      <td>1</td>\n",
       "      <td>8618</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1966</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>104000</td>\n",
       "      <td>229000</td>\n",
       "      <td>98168</td>\n",
       "      <td>False</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2013-03-29</td>\n",
       "      <td>240000</td>\n",
       "      <td>2800024</td>\n",
       "      <td>Single Family</td>\n",
       "      <td>2013-03-01</td>\n",
       "      <td>351600</td>\n",
       "      <td>0.807904</td>\n",
       "      <td>297065.0</td>\n",
       "      <td>1</td>\n",
       "      <td>8620</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1948</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>104000</td>\n",
       "      <td>205000</td>\n",
       "      <td>98168</td>\n",
       "      <td>False</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  DocumentDate  SalePrice  PropertyID   PropertyType          ym  zhvi_px  \\\n",
       "1   2014-09-16     280000     1000102      Multiplex  2014-09-01   405100   \n",
       "2   2006-06-16    1000000     1200013  Single Family  2006-06-01   404400   \n",
       "3   2007-01-29     745000     1200019  Single Family  2007-01-01   425600   \n",
       "4   2008-02-25     425000     2800016  Single Family  2008-02-01   418400   \n",
       "5   2013-03-29     240000     2800024  Single Family  2013-03-01   351600   \n",
       "\n",
       "   zhvi_idx  AdjSalePrice  NbrLivingUnits  SqFtLot  ...  BldgGrade  YrBuilt  \\\n",
       "1  0.930836      300805.0               2     9373  ...          7     1991   \n",
       "2  0.929228     1076162.0               1    20156  ...         10     2005   \n",
       "3  0.977941      761805.0               1    26036  ...          8     1947   \n",
       "4  0.961397      442065.0               1     8618  ...          7     1966   \n",
       "5  0.807904      297065.0               1     8620  ...          7     1948   \n",
       "\n",
       "   YrRenovated  TrafficNoise  LandVal  ImpsVal  ZipCode  NewConstruction  \\\n",
       "1            0             0    70000   229000    98002            False   \n",
       "2            0             0   203000   590000    98166             True   \n",
       "3            0             0   183000   275000    98166            False   \n",
       "4            0             0   104000   229000    98168            False   \n",
       "5            0             0   104000   205000    98168            False   \n",
       "\n",
       "   weights  ZipGroup  \n",
       "1        9         1  \n",
       "2        1         2  \n",
       "3        2         2  \n",
       "4        3         2  \n",
       "5        8         2  \n",
       "\n",
       "[5 rows x 24 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_join = zip_groups[[\"ZipCode\", \"ZipGroup\"]].set_index(\"ZipCode\")\n",
    "df_house = df_house.join(to_join, on=\"ZipCode\")\n",
    "df_house[\"ZipGroup\"] = df_house[\"ZipGroup\"].astype(\"category\")\n",
    "df_house.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordinal Categorical Variables\n",
    "\n",
    "- Ordinal variables are categorical variables that have a clear ordering.\n",
    "- We can convert these variables into numerical values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Interpreting the Regression Equation`\n",
    "\n",
    "### Correlated Predictors\n",
    "\n",
    "- When predictors are correlated, the estimated coefficients can be unreliable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: -446841.366311674\n",
      "Coefficients:\n",
      "SqFtTotLiving 223.37362892503828\n",
      "SqFtLot -0.07036798136813083\n",
      "Bathrooms -15979.013473415205\n",
      "Bedrooms -50889.73218483025\n",
      "BldgGrade 109416.30516146179\n",
      "PropertyType_Single Family -84678.21629549257\n",
      "PropertyType_Townhouse -115121.97921609184\n"
     ]
    }
   ],
   "source": [
    "print(\"Intercept:\", model.intercept_)\n",
    "print(\"Coefficients:\")\n",
    "\n",
    "for name, coef in zip(X.columns, model.coef_):\n",
    "    print(name, coef)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors = [\"Bedrooms\", \"BldgGrade\", \"PropertyType\", \"YrBuilt\"]\n",
    "target = df_house[\"AdjSalePrice\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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>Bedrooms</th>\n",
       "      <th>BldgGrade</th>\n",
       "      <th>YrBuilt</th>\n",
       "      <th>PropertyType_Single Family</th>\n",
       "      <th>PropertyType_Townhouse</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1991</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>2005</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>1947</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1966</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>1948</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Bedrooms  BldgGrade  YrBuilt  PropertyType_Single Family  \\\n",
       "1         6          7     1991                           0   \n",
       "2         4         10     2005                           1   \n",
       "3         4          8     1947                           1   \n",
       "4         5          7     1966                           1   \n",
       "5         4          7     1948                           1   \n",
       "\n",
       "   PropertyType_Townhouse  \n",
       "1                       0  \n",
       "2                       0  \n",
       "3                       0  \n",
       "4                       0  \n",
       "5                       0  "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = pd.get_dummies(df_house[predictors], drop_first=True)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-4 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-4 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-4 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-4 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-4 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-4 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X, target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "268113.92781191465\n",
      "0.5160193182911705\n"
     ]
    }
   ],
   "source": [
    "fitted = model.predict(X)\n",
    "residuals = target - fitted\n",
    "\n",
    "print(np.sqrt(mean_squared_error(target, fitted)))\n",
    "print(r2_score(target, fitted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multi-Collinearity\n",
    "\n",
    "- An extreme case of correlation is multi-collinearity, where two or more predictors are highly correlated.\n",
    "- Perfect multi-collinearity occurs when one predictor can be expressed as a linear combination of the others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confounding Variables\n",
    "\n",
    "- With confounding variables, the problem is one of omitted variable: an important variable is left out of the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interaction an Main Effects\n",
    "\n",
    "- Main effects are often reffered to as the predictor variables in a regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Interaction between **SqFtTotLiving:ZipGroup2** and **SqFtToLiving:ZipGroup3**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>AdjSalePrice</td>   <th>  R-squared:         </th>  <td>   0.686</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.686</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>   3298.</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 25 Jul 2024</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:17:51</td>     <th>  Log-Likelihood:    </th> <td>-3.1086e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 22687</td>      <th>  AIC:               </th>  <td>6.218e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 22671</td>      <th>  BIC:               </th>  <td>6.219e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    15</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                <td></td>                   <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                     <td>-4.748e+05</td> <td> 2.05e+04</td> <td>  -23.172</td> <td> 0.000</td> <td>-5.15e+05</td> <td>-4.35e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZipGroup[T.1]</th>                 <td> -3.31e+04</td> <td> 1.28e+04</td> <td>   -2.593</td> <td> 0.010</td> <td>-5.81e+04</td> <td>-8082.649</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZipGroup[T.2]</th>                 <td> 1.243e+04</td> <td>  1.2e+04</td> <td>    1.036</td> <td> 0.300</td> <td>-1.11e+04</td> <td>  3.6e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZipGroup[T.3]</th>                 <td>-7651.7537</td> <td> 1.24e+04</td> <td>   -0.617</td> <td> 0.537</td> <td> -3.2e+04</td> <td> 1.67e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZipGroup[T.4]</th>                 <td>-1.759e+05</td> <td> 1.17e+04</td> <td>  -15.045</td> <td> 0.000</td> <td>-1.99e+05</td> <td>-1.53e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PropertyType[T.Single Family]</th> <td> 1.586e+04</td> <td> 1.38e+04</td> <td>    1.146</td> <td> 0.252</td> <td>-1.13e+04</td> <td>  4.3e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PropertyType[T.Townhouse]</th>     <td>-5.654e+04</td> <td> 1.51e+04</td> <td>   -3.756</td> <td> 0.000</td> <td>-8.61e+04</td> <td> -2.7e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving</th>                 <td>  104.1395</td> <td>    5.039</td> <td>   20.667</td> <td> 0.000</td> <td>   94.263</td> <td>  114.016</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving:ZipGroup[T.1]</th>   <td>   46.9400</td> <td>    5.459</td> <td>    8.599</td> <td> 0.000</td> <td>   36.241</td> <td>   57.639</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving:ZipGroup[T.2]</th>   <td>   48.2843</td> <td>    5.405</td> <td>    8.934</td> <td> 0.000</td> <td>   37.691</td> <td>   58.878</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving:ZipGroup[T.3]</th>   <td>   95.3545</td> <td>    5.727</td> <td>   16.649</td> <td> 0.000</td> <td>   84.128</td> <td>  106.581</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving:ZipGroup[T.4]</th>   <td>  244.3591</td> <td>    5.051</td> <td>   48.383</td> <td> 0.000</td> <td>  234.460</td> <td>  254.258</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtLot</th>                       <td>    0.6730</td> <td>    0.051</td> <td>   13.110</td> <td> 0.000</td> <td>    0.572</td> <td>    0.774</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bathrooms</th>                     <td>-5005.0008</td> <td> 3182.321</td> <td>   -1.573</td> <td> 0.116</td> <td>-1.12e+04</td> <td> 1232.566</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bedrooms</th>                      <td>-4.033e+04</td> <td> 2108.863</td> <td>  -19.124</td> <td> 0.000</td> <td>-4.45e+04</td> <td>-3.62e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BldgGrade</th>                     <td> 1.051e+05</td> <td> 2052.634</td> <td>   51.214</td> <td> 0.000</td> <td> 1.01e+05</td> <td> 1.09e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>30682.932</td> <th>  Durbin-Watson:     </th>   <td>   1.589</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>33564128.499</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 7.166</td>   <th>  Prob(JB):          </th>   <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>190.886</td>  <th>  Cond. No.          </th>   <td>5.85e+05</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 5.85e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}                &   AdjSalePrice   & \\textbf{  R-squared:         } &      0.686    \\\\\n",
       "\\textbf{Model:}                        &       OLS        & \\textbf{  Adj. R-squared:    } &      0.686    \\\\\n",
       "\\textbf{Method:}                       &  Least Squares   & \\textbf{  F-statistic:       } &      3298.    \\\\\n",
       "\\textbf{Date:}                         & Thu, 25 Jul 2024 & \\textbf{  Prob (F-statistic):} &      0.00     \\\\\n",
       "\\textbf{Time:}                         &     21:17:51     & \\textbf{  Log-Likelihood:    } & -3.1086e+05   \\\\\n",
       "\\textbf{No. Observations:}             &       22687      & \\textbf{  AIC:               } &  6.218e+05    \\\\\n",
       "\\textbf{Df Residuals:}                 &       22671      & \\textbf{  BIC:               } &  6.219e+05    \\\\\n",
       "\\textbf{Df Model:}                     &          15      & \\textbf{                     } &               \\\\\n",
       "\\textbf{Covariance Type:}              &    nonrobust     & \\textbf{                     } &               \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                                       & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}                     &   -4.748e+05  &     2.05e+04     &   -23.172  &         0.000        &    -5.15e+05    &    -4.35e+05     \\\\\n",
       "\\textbf{ZipGroup[T.1]}                 &    -3.31e+04  &     1.28e+04     &    -2.593  &         0.010        &    -5.81e+04    &    -8082.649     \\\\\n",
       "\\textbf{ZipGroup[T.2]}                 &    1.243e+04  &      1.2e+04     &     1.036  &         0.300        &    -1.11e+04    &      3.6e+04     \\\\\n",
       "\\textbf{ZipGroup[T.3]}                 &   -7651.7537  &     1.24e+04     &    -0.617  &         0.537        &     -3.2e+04    &     1.67e+04     \\\\\n",
       "\\textbf{ZipGroup[T.4]}                 &   -1.759e+05  &     1.17e+04     &   -15.045  &         0.000        &    -1.99e+05    &    -1.53e+05     \\\\\n",
       "\\textbf{PropertyType[T.Single Family]} &    1.586e+04  &     1.38e+04     &     1.146  &         0.252        &    -1.13e+04    &      4.3e+04     \\\\\n",
       "\\textbf{PropertyType[T.Townhouse]}     &   -5.654e+04  &     1.51e+04     &    -3.756  &         0.000        &    -8.61e+04    &     -2.7e+04     \\\\\n",
       "\\textbf{SqFtTotLiving}                 &     104.1395  &        5.039     &    20.667  &         0.000        &       94.263    &      114.016     \\\\\n",
       "\\textbf{SqFtTotLiving:ZipGroup[T.1]}   &      46.9400  &        5.459     &     8.599  &         0.000        &       36.241    &       57.639     \\\\\n",
       "\\textbf{SqFtTotLiving:ZipGroup[T.2]}   &      48.2843  &        5.405     &     8.934  &         0.000        &       37.691    &       58.878     \\\\\n",
       "\\textbf{SqFtTotLiving:ZipGroup[T.3]}   &      95.3545  &        5.727     &    16.649  &         0.000        &       84.128    &      106.581     \\\\\n",
       "\\textbf{SqFtTotLiving:ZipGroup[T.4]}   &     244.3591  &        5.051     &    48.383  &         0.000        &      234.460    &      254.258     \\\\\n",
       "\\textbf{SqFtLot}                       &       0.6730  &        0.051     &    13.110  &         0.000        &        0.572    &        0.774     \\\\\n",
       "\\textbf{Bathrooms}                     &   -5005.0008  &     3182.321     &    -1.573  &         0.116        &    -1.12e+04    &     1232.566     \\\\\n",
       "\\textbf{Bedrooms}                      &   -4.033e+04  &     2108.863     &   -19.124  &         0.000        &    -4.45e+04    &    -3.62e+04     \\\\\n",
       "\\textbf{BldgGrade}                     &    1.051e+05  &     2052.634     &    51.214  &         0.000        &     1.01e+05    &     1.09e+05     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 30682.932 & \\textbf{  Durbin-Watson:     } &      1.589    \\\\\n",
       "\\textbf{Prob(Omnibus):} &    0.000  & \\textbf{  Jarque-Bera (JB):  } & 33564128.499  \\\\\n",
       "\\textbf{Skew:}          &    7.166  & \\textbf{  Prob(JB):          } &       0.00    \\\\\n",
       "\\textbf{Kurtosis:}      &  190.886  & \\textbf{  Cond. No.          } &   5.85e+05    \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 5.85e+05. This might indicate that there are \\newline\n",
       " strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           AdjSalePrice   R-squared:                       0.686\n",
       "Model:                            OLS   Adj. R-squared:                  0.686\n",
       "Method:                 Least Squares   F-statistic:                     3298.\n",
       "Date:                Thu, 25 Jul 2024   Prob (F-statistic):               0.00\n",
       "Time:                        21:17:51   Log-Likelihood:            -3.1086e+05\n",
       "No. Observations:               22687   AIC:                         6.218e+05\n",
       "Df Residuals:                   22671   BIC:                         6.219e+05\n",
       "Df Model:                          15                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=================================================================================================\n",
       "                                    coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------------------------\n",
       "Intercept                     -4.748e+05   2.05e+04    -23.172      0.000   -5.15e+05   -4.35e+05\n",
       "ZipGroup[T.1]                  -3.31e+04   1.28e+04     -2.593      0.010   -5.81e+04   -8082.649\n",
       "ZipGroup[T.2]                  1.243e+04    1.2e+04      1.036      0.300   -1.11e+04     3.6e+04\n",
       "ZipGroup[T.3]                 -7651.7537   1.24e+04     -0.617      0.537    -3.2e+04    1.67e+04\n",
       "ZipGroup[T.4]                 -1.759e+05   1.17e+04    -15.045      0.000   -1.99e+05   -1.53e+05\n",
       "PropertyType[T.Single Family]  1.586e+04   1.38e+04      1.146      0.252   -1.13e+04     4.3e+04\n",
       "PropertyType[T.Townhouse]     -5.654e+04   1.51e+04     -3.756      0.000   -8.61e+04    -2.7e+04\n",
       "SqFtTotLiving                   104.1395      5.039     20.667      0.000      94.263     114.016\n",
       "SqFtTotLiving:ZipGroup[T.1]      46.9400      5.459      8.599      0.000      36.241      57.639\n",
       "SqFtTotLiving:ZipGroup[T.2]      48.2843      5.405      8.934      0.000      37.691      58.878\n",
       "SqFtTotLiving:ZipGroup[T.3]      95.3545      5.727     16.649      0.000      84.128     106.581\n",
       "SqFtTotLiving:ZipGroup[T.4]     244.3591      5.051     48.383      0.000     234.460     254.258\n",
       "SqFtLot                           0.6730      0.051     13.110      0.000       0.572       0.774\n",
       "Bathrooms                     -5005.0008   3182.321     -1.573      0.116   -1.12e+04    1232.566\n",
       "Bedrooms                      -4.033e+04   2108.863    -19.124      0.000   -4.45e+04   -3.62e+04\n",
       "BldgGrade                      1.051e+05   2052.634     51.214      0.000    1.01e+05    1.09e+05\n",
       "==============================================================================\n",
       "Omnibus:                    30682.932   Durbin-Watson:                   1.589\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):         33564128.499\n",
       "Skew:                           7.166   Prob(JB):                         0.00\n",
       "Kurtosis:                     190.886   Cond. No.                     5.85e+05\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 5.85e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "\n",
    "model = smf.ols(formula='AdjSalePrice ~ SqFtTotLiving * ZipGroup  + SqFtLot + ' + ' Bathrooms + Bedrooms + BldgGrade + PropertyType', data=df_house)\n",
    "result = model.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Reggression Diagnostic`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outliers\n",
    "\n",
    "- In regression outliers is a record whose actual value is far from the predicted value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "house_98105 = df_house[df_house.ZipCode == 98105]\n",
    "predictors = [\"SqFtTotLiving\", \"SqFtLot\", \"Bathrooms\", \"Bedrooms\", \"BldgGrade\"]\n",
    "target = house_98105[\"AdjSalePrice\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>AdjSalePrice</td>   <th>  R-squared:         </th> <td>   0.795</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.792</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   238.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 25 Jul 2024</td> <th>  Prob (F-statistic):</th> <td>1.69e-103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:00:16</td>     <th>  Log-Likelihood:    </th> <td> -4226.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   8464.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   307</td>      <th>  BIC:               </th> <td>   8486.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving</th> <td>  209.6023</td> <td>   24.408</td> <td>    8.587</td> <td> 0.000</td> <td>  161.574</td> <td>  257.631</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtLot</th>       <td>   38.9333</td> <td>    5.330</td> <td>    7.305</td> <td> 0.000</td> <td>   28.445</td> <td>   49.421</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bathrooms</th>     <td> 2282.2641</td> <td>    2e+04</td> <td>    0.114</td> <td> 0.909</td> <td> -3.7e+04</td> <td> 4.16e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bedrooms</th>      <td>-2.632e+04</td> <td> 1.29e+04</td> <td>   -2.043</td> <td> 0.042</td> <td>-5.17e+04</td> <td> -973.867</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BldgGrade</th>     <td>   1.3e+05</td> <td> 1.52e+04</td> <td>    8.533</td> <td> 0.000</td> <td>    1e+05</td> <td>  1.6e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>         <td>-7.725e+05</td> <td> 9.83e+04</td> <td>   -7.861</td> <td> 0.000</td> <td>-9.66e+05</td> <td>-5.79e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>82.127</td> <th>  Durbin-Watson:     </th> <td>   1.508</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 586.561</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.859</td> <th>  Prob(JB):          </th> <td>4.26e-128</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.483</td> <th>  Cond. No.          </th> <td>5.63e+04</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 5.63e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &   AdjSalePrice   & \\textbf{  R-squared:         } &     0.795   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared:    } &     0.792   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       } &     238.7   \\\\\n",
       "\\textbf{Date:}             & Thu, 25 Jul 2024 & \\textbf{  Prob (F-statistic):} & 1.69e-103   \\\\\n",
       "\\textbf{Time:}             &     20:00:16     & \\textbf{  Log-Likelihood:    } &   -4226.0   \\\\\n",
       "\\textbf{No. Observations:} &         313      & \\textbf{  AIC:               } &     8464.   \\\\\n",
       "\\textbf{Df Residuals:}     &         307      & \\textbf{  BIC:               } &     8486.   \\\\\n",
       "\\textbf{Df Model:}         &           5      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                       & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{SqFtTotLiving} &     209.6023  &       24.408     &     8.587  &         0.000        &      161.574    &      257.631     \\\\\n",
       "\\textbf{SqFtLot}       &      38.9333  &        5.330     &     7.305  &         0.000        &       28.445    &       49.421     \\\\\n",
       "\\textbf{Bathrooms}     &    2282.2641  &        2e+04     &     0.114  &         0.909        &     -3.7e+04    &     4.16e+04     \\\\\n",
       "\\textbf{Bedrooms}      &   -2.632e+04  &     1.29e+04     &    -2.043  &         0.042        &    -5.17e+04    &     -973.867     \\\\\n",
       "\\textbf{BldgGrade}     &      1.3e+05  &     1.52e+04     &     8.533  &         0.000        &        1e+05    &      1.6e+05     \\\\\n",
       "\\textbf{const}         &   -7.725e+05  &     9.83e+04     &    -7.861  &         0.000        &    -9.66e+05    &    -5.79e+05     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 82.127 & \\textbf{  Durbin-Watson:     } &     1.508  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.000 & \\textbf{  Jarque-Bera (JB):  } &   586.561  \\\\\n",
       "\\textbf{Skew:}          &  0.859 & \\textbf{  Prob(JB):          } & 4.26e-128  \\\\\n",
       "\\textbf{Kurtosis:}      &  9.483 & \\textbf{  Cond. No.          } &  5.63e+04  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 5.63e+04. This might indicate that there are \\newline\n",
       " strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           AdjSalePrice   R-squared:                       0.795\n",
       "Model:                            OLS   Adj. R-squared:                  0.792\n",
       "Method:                 Least Squares   F-statistic:                     238.7\n",
       "Date:                Thu, 25 Jul 2024   Prob (F-statistic):          1.69e-103\n",
       "Time:                        20:00:16   Log-Likelihood:                -4226.0\n",
       "No. Observations:                 313   AIC:                             8464.\n",
       "Df Residuals:                     307   BIC:                             8486.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=================================================================================\n",
       "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "SqFtTotLiving   209.6023     24.408      8.587      0.000     161.574     257.631\n",
       "SqFtLot          38.9333      5.330      7.305      0.000      28.445      49.421\n",
       "Bathrooms      2282.2641      2e+04      0.114      0.909    -3.7e+04    4.16e+04\n",
       "Bedrooms      -2.632e+04   1.29e+04     -2.043      0.042   -5.17e+04    -973.867\n",
       "BldgGrade        1.3e+05   1.52e+04      8.533      0.000       1e+05     1.6e+05\n",
       "const         -7.725e+05   9.83e+04     -7.861      0.000   -9.66e+05   -5.79e+05\n",
       "==============================================================================\n",
       "Omnibus:                       82.127   Durbin-Watson:                   1.508\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              586.561\n",
       "Skew:                           0.859   Prob(JB):                    4.26e-128\n",
       "Kurtosis:                       9.483   Cond. No.                     5.63e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 5.63e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "model_outliers = sm.OLS(target, house_98105[predictors].assign(const=1))\n",
    "result_outliers = model_outliers.fit()\n",
    "result_outliers.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dfb_SqFtTotLiving</th>\n",
       "      <th>dfb_SqFtLot</th>\n",
       "      <th>dfb_Bathrooms</th>\n",
       "      <th>dfb_Bedrooms</th>\n",
       "      <th>dfb_BldgGrade</th>\n",
       "      <th>dfb_const</th>\n",
       "      <th>cooks_d</th>\n",
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       "      <th>student_resid</th>\n",
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       "      <th>1036</th>\n",
       "      <td>-0.125290</td>\n",
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       "      <td>-0.022508</td>\n",
       "      <td>0.001138</td>\n",
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       "      <td>-0.035540</td>\n",
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       "      <td>-0.007731</td>\n",
       "      <td>-0.000894</td>\n",
       "      <td>0.011657</td>\n",
       "      <td>0.004167</td>\n",
       "      <td>0.001010</td>\n",
       "      <td>-0.563783</td>\n",
       "      <td>0.018706</td>\n",
       "      <td>-0.077839</td>\n",
       "      <td>-0.563156</td>\n",
       "      <td>-0.077752</td>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26628</th>\n",
       "      <td>0.002754</td>\n",
       "      <td>-0.004252</td>\n",
       "      <td>-0.006529</td>\n",
       "      <td>0.003311</td>\n",
       "      <td>0.003276</td>\n",
       "      <td>-0.002359</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>0.085499</td>\n",
       "      <td>0.011676</td>\n",
       "      <td>0.009293</td>\n",
       "      <td>0.085361</td>\n",
       "      <td>0.009278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26629</th>\n",
       "      <td>-0.009418</td>\n",
       "      <td>0.005211</td>\n",
       "      <td>0.004278</td>\n",
       "      <td>0.006629</td>\n",
       "      <td>0.015610</td>\n",
       "      <td>-0.022984</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>-0.544324</td>\n",
       "      <td>0.004909</td>\n",
       "      <td>-0.038233</td>\n",
       "      <td>-0.543699</td>\n",
       "      <td>-0.038189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26630</th>\n",
       "      <td>0.004713</td>\n",
       "      <td>0.021502</td>\n",
       "      <td>0.004005</td>\n",
       "      <td>-0.033168</td>\n",
       "      <td>-0.008856</td>\n",
       "      <td>0.013503</td>\n",
       "      <td>0.000355</td>\n",
       "      <td>-0.355351</td>\n",
       "      <td>0.016586</td>\n",
       "      <td>-0.046149</td>\n",
       "      <td>-0.354844</td>\n",
       "      <td>-0.046083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26631</th>\n",
       "      <td>-0.001692</td>\n",
       "      <td>0.000563</td>\n",
       "      <td>0.001825</td>\n",
       "      <td>0.005071</td>\n",
       "      <td>-0.000341</td>\n",
       "      <td>-0.002197</td>\n",
       "      <td>0.000008</td>\n",
       "      <td>-0.049035</td>\n",
       "      <td>0.020766</td>\n",
       "      <td>-0.007141</td>\n",
       "      <td>-0.048956</td>\n",
       "      <td>-0.007129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26632</th>\n",
       "      <td>-0.168910</td>\n",
       "      <td>0.055985</td>\n",
       "      <td>0.140792</td>\n",
       "      <td>0.129420</td>\n",
       "      <td>0.044977</td>\n",
       "      <td>-0.108051</td>\n",
       "      <td>0.008970</td>\n",
       "      <td>-1.480952</td>\n",
       "      <td>0.023952</td>\n",
       "      <td>-0.231995</td>\n",
       "      <td>-1.483848</td>\n",
       "      <td>-0.232449</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>313 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       dfb_SqFtTotLiving  dfb_SqFtLot  dfb_Bathrooms  dfb_Bedrooms  \\\n",
       "1036           -0.125290    -0.000515      -0.333379     -0.079473   \n",
       "1769            0.055249    -0.055857       0.033285     -0.060896   \n",
       "1770           -0.001648    -0.022508       0.001138      0.007058   \n",
       "1771           -0.061826    -0.054655       0.027716      0.049985   \n",
       "1783           -0.028669    -0.011060      -0.007731     -0.000894   \n",
       "...                  ...          ...            ...           ...   \n",
       "26628           0.002754    -0.004252      -0.006529      0.003311   \n",
       "26629          -0.009418     0.005211       0.004278      0.006629   \n",
       "26630           0.004713     0.021502       0.004005     -0.033168   \n",
       "26631          -0.001692     0.000563       0.001825      0.005071   \n",
       "26632          -0.168910     0.055985       0.140792      0.129420   \n",
       "\n",
       "       dfb_BldgGrade  dfb_const   cooks_d  standard_resid  hat_diag  \\\n",
       "1036        0.355775  -0.193888  0.061440       -2.622626  0.050869   \n",
       "1769       -0.047651   0.049793  0.001938       -0.892439  0.014388   \n",
       "1770        0.015993  -0.018091  0.000211       -0.354599  0.009945   \n",
       "1771        0.074387  -0.082970  0.002906       -1.054669  0.015435   \n",
       "1783        0.011657   0.004167  0.001010       -0.563783  0.018706   \n",
       "...              ...        ...       ...             ...       ...   \n",
       "26628       0.003276  -0.002359  0.000014        0.085499  0.011676   \n",
       "26629       0.015610  -0.022984  0.000244       -0.544324  0.004909   \n",
       "26630      -0.008856   0.013503  0.000355       -0.355351  0.016586   \n",
       "26631      -0.000341  -0.002197  0.000008       -0.049035  0.020766   \n",
       "26632       0.044977  -0.108051  0.008970       -1.480952  0.023952   \n",
       "\n",
       "       dffits_internal  student_resid    dffits  \n",
       "1036         -0.607155      -2.648185 -0.613072  \n",
       "1769         -0.107828      -0.892142 -0.107792  \n",
       "1770         -0.035540      -0.354093 -0.035490  \n",
       "1771         -0.132053      -1.054863 -0.132078  \n",
       "1783         -0.077839      -0.563156 -0.077752  \n",
       "...                ...            ...       ...  \n",
       "26628         0.009293       0.085361  0.009278  \n",
       "26629        -0.038233      -0.543699 -0.038189  \n",
       "26630        -0.046149      -0.354844 -0.046083  \n",
       "26631        -0.007141      -0.048956 -0.007129  \n",
       "26632        -0.231995      -1.483848 -0.232449  \n",
       "\n",
       "[313 rows x 12 columns]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.outliers_influence import OLSInfluence\n",
    "influence = OLSInfluence(result_outliers)\n",
    "influence.summary_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24333, 14392)"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sresisiduals = influence.resid_studentized_internal\n",
    "sresisiduals.idxmin(), sresisiduals.idxmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdjSalePrice: 119748.0\n",
      "SqFtTotLiving    2900\n",
      "SqFtLot          7276\n",
      "Bathrooms         3.0\n",
      "Bedrooms            6\n",
      "BldgGrade           7\n",
      "Name: 24333, dtype: object\n"
     ]
    }
   ],
   "source": [
    "outlier = house_98105.loc[sresisiduals.idxmin(), :]\n",
    "print('AdjSalePrice:', outlier.AdjSalePrice)\n",
    "print(outlier[predictors])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influential Values\n",
    "\n",
    "- Influential values are records that have a large effect on the regression model.\n",
    "- High influence values are those whose **Cook's distance is greater than > 0.08.**\n",
    "\n",
    "#### Cook's Distance\n",
    "\n",
    "- Cook's distance is a measure of the influence of each individual observation on the regression coefficients.\n",
    "\n",
    "$D_i = \\frac{\\sum_{j=1}^{n} (\\hat{y_j} - \\hat{y_{j(i)}})^2}{p \\times MSE}$\n",
    "\n",
    "- where:\n",
    "    - $D_i$ is the Cook's distance\n",
    "    - $\\hat{y_j}$ is the predicted value\n",
    "    - $\\hat{y_{j(i)}}$ is the predicted value without the ith observation\n",
    "    - $p$ is the number of predictors\n",
    "    - $MSE$ is the mean squared error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> #### Influence Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "ax.axhline(-2.5, linestyle='--', color='C1')\n",
    "ax.axhline(2.5, linestyle='--', color='C1')\n",
    "ax.scatter(influence.hat_matrix_diag, influence.resid_studentized_internal, s=1000*np.sqrt(influence.cooks_distance[0]), alpha=0.5)\n",
    "ax.set_xlabel('Hat values')\n",
    "ax.set_ylabel('Studentized residuals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Heteroscedasticity\n",
    "\n",
    "- Heteroscedasticity is a problem in regression analysis where the variance of the residuals is not constant. Errors are greater for some portion of the range than for others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "sns.regplot(x=result_outliers.fittedvalues, y=np.abs(result_outliers.resid), scatter_kws={'alpha':0.25}, line_kws={'color':'C1'}, lowess=True, ax=ax)\n",
    "ax.set_xlabel('Predicted values')\n",
    "ax.set_ylabel('Absolute residuals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normality of Residuals\n",
    "\n",
    "- The residuals should be normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "sns.histplot(result_outliers.resid_pearson, kde=True, ax=ax)\n",
    "ax.set_xlabel('Standardized residuals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We can see the plot exibits mild skewness towards the larger residuals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation of Residuals\n",
    "\n",
    "- The residuals should not be correlated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Residual Plots and Nonlinearity\n",
    "\n",
    "- Partial residual plots are a way to visualize how well the estimated fit explains the relationship between the target and the predictor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "sm.graphics.regressionplots.plot_ccpr(result_outliers, 'SqFtTotLiving', ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Polynomial and Spline Regression`\n",
    "\n",
    "### Polynomial Regression\n",
    "\n",
    "- Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial.\n",
    "\n",
    "\n",
    "$y = b_0 + b_1x + b_2x^2 + ... + b_nx^n$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>AdjSalePrice</td>   <th>  R-squared:         </th> <td>   0.806</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.802</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   211.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 25 Jul 2024</td> <th>  Prob (F-statistic):</th> <td>9.95e-106</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:19:46</td>     <th>  Log-Likelihood:    </th> <td> -4217.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   8450.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   306</td>      <th>  BIC:               </th> <td>   8476.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td>-6.159e+05</td> <td> 1.03e+05</td> <td>   -5.953</td> <td> 0.000</td> <td>-8.19e+05</td> <td>-4.12e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtTotLiving</th>         <td>    7.4521</td> <td>   55.418</td> <td>    0.134</td> <td> 0.893</td> <td> -101.597</td> <td>  116.501</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I(SqFtTotLiving ** 2)</th> <td>    0.0388</td> <td>    0.010</td> <td>    4.040</td> <td> 0.000</td> <td>    0.020</td> <td>    0.058</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtLot</th>               <td>   32.5594</td> <td>    5.436</td> <td>    5.990</td> <td> 0.000</td> <td>   21.863</td> <td>   43.256</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bathrooms</th>             <td>-1435.1231</td> <td> 1.95e+04</td> <td>   -0.074</td> <td> 0.941</td> <td>-3.99e+04</td> <td>  3.7e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bedrooms</th>              <td>-9191.9441</td> <td> 1.33e+04</td> <td>   -0.693</td> <td> 0.489</td> <td>-3.53e+04</td> <td> 1.69e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BldgGrade</th>             <td> 1.357e+05</td> <td> 1.49e+04</td> <td>    9.087</td> <td> 0.000</td> <td> 1.06e+05</td> <td> 1.65e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>75.161</td> <th>  Durbin-Watson:     </th> <td>   1.625</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 637.978</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.699</td> <th>  Prob(JB):          </th> <td>2.92e-139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.853</td> <th>  Cond. No.          </th> <td>7.37e+07</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 7.37e+07. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}        &   AdjSalePrice   & \\textbf{  R-squared:         } &     0.806   \\\\\n",
       "\\textbf{Model:}                &       OLS        & \\textbf{  Adj. R-squared:    } &     0.802   \\\\\n",
       "\\textbf{Method:}               &  Least Squares   & \\textbf{  F-statistic:       } &     211.6   \\\\\n",
       "\\textbf{Date:}                 & Thu, 25 Jul 2024 & \\textbf{  Prob (F-statistic):} & 9.95e-106   \\\\\n",
       "\\textbf{Time:}                 &     21:19:46     & \\textbf{  Log-Likelihood:    } &   -4217.9   \\\\\n",
       "\\textbf{No. Observations:}     &         313      & \\textbf{  AIC:               } &     8450.   \\\\\n",
       "\\textbf{Df Residuals:}         &         306      & \\textbf{  BIC:               } &     8476.   \\\\\n",
       "\\textbf{Df Model:}             &           6      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}      &    nonrobust     & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                               & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}             &   -6.159e+05  &     1.03e+05     &    -5.953  &         0.000        &    -8.19e+05    &    -4.12e+05     \\\\\n",
       "\\textbf{SqFtTotLiving}         &       7.4521  &       55.418     &     0.134  &         0.893        &     -101.597    &      116.501     \\\\\n",
       "\\textbf{I(SqFtTotLiving ** 2)} &       0.0388  &        0.010     &     4.040  &         0.000        &        0.020    &        0.058     \\\\\n",
       "\\textbf{SqFtLot}               &      32.5594  &        5.436     &     5.990  &         0.000        &       21.863    &       43.256     \\\\\n",
       "\\textbf{Bathrooms}             &   -1435.1231  &     1.95e+04     &    -0.074  &         0.941        &    -3.99e+04    &      3.7e+04     \\\\\n",
       "\\textbf{Bedrooms}              &   -9191.9441  &     1.33e+04     &    -0.693  &         0.489        &    -3.53e+04    &     1.69e+04     \\\\\n",
       "\\textbf{BldgGrade}             &    1.357e+05  &     1.49e+04     &     9.087  &         0.000        &     1.06e+05    &     1.65e+05     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 75.161 & \\textbf{  Durbin-Watson:     } &     1.625  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.000 & \\textbf{  Jarque-Bera (JB):  } &   637.978  \\\\\n",
       "\\textbf{Skew:}          &  0.699 & \\textbf{  Prob(JB):          } & 2.92e-139  \\\\\n",
       "\\textbf{Kurtosis:}      &  9.853 & \\textbf{  Cond. No.          } &  7.37e+07  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 7.37e+07. This might indicate that there are \\newline\n",
       " strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           AdjSalePrice   R-squared:                       0.806\n",
       "Model:                            OLS   Adj. R-squared:                  0.802\n",
       "Method:                 Least Squares   F-statistic:                     211.6\n",
       "Date:                Thu, 25 Jul 2024   Prob (F-statistic):          9.95e-106\n",
       "Time:                        21:19:46   Log-Likelihood:                -4217.9\n",
       "No. Observations:                 313   AIC:                             8450.\n",
       "Df Residuals:                     306   BIC:                             8476.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept             -6.159e+05   1.03e+05     -5.953      0.000   -8.19e+05   -4.12e+05\n",
       "SqFtTotLiving             7.4521     55.418      0.134      0.893    -101.597     116.501\n",
       "I(SqFtTotLiving ** 2)     0.0388      0.010      4.040      0.000       0.020       0.058\n",
       "SqFtLot                  32.5594      5.436      5.990      0.000      21.863      43.256\n",
       "Bathrooms             -1435.1231   1.95e+04     -0.074      0.941   -3.99e+04     3.7e+04\n",
       "Bedrooms              -9191.9441   1.33e+04     -0.693      0.489   -3.53e+04    1.69e+04\n",
       "BldgGrade              1.357e+05   1.49e+04      9.087      0.000    1.06e+05    1.65e+05\n",
       "==============================================================================\n",
       "Omnibus:                       75.161   Durbin-Watson:                   1.625\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              637.978\n",
       "Skew:                           0.699   Prob(JB):                    2.92e-139\n",
       "Kurtosis:                       9.853   Cond. No.                     7.37e+07\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 7.37e+07. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_poly = smf.ols(formula='AdjSalePrice ~ SqFtTotLiving + I(SqFtTotLiving**2) + SqFtLot + Bathrooms + Bedrooms + BldgGrade', data=house_98105)\n",
    "result_poly = model_poly.fit()\n",
    "result_poly.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "sm.graphics.regressionplots.plot_ccpr(result_poly, 'I(SqFtTotLiving ** 2)', ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spline Regression\n",
    "\n",
    "- Spline regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as a piecewise polynomial.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>AdjSalePrice</td>   <th>  R-squared:         </th> <td>   0.814</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.807</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   131.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 26 Jul 2024</td> <th>  Prob (F-statistic):</th> <td>7.10e-104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:35:50</td>     <th>  Log-Likelihood:    </th> <td> -4211.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   8445.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   302</td>      <th>  BIC:               </th> <td>   8486.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    10</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                    <td></td>                      <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                            <td>-4.142e+05</td> <td> 1.43e+05</td> <td>   -2.899</td> <td> 0.004</td> <td>-6.95e+05</td> <td>-1.33e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[0]</th> <td>-1.995e+05</td> <td> 1.86e+05</td> <td>   -1.076</td> <td> 0.283</td> <td>-5.65e+05</td> <td> 1.66e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[1]</th> <td>-1.206e+05</td> <td> 1.23e+05</td> <td>   -0.983</td> <td> 0.326</td> <td>-3.62e+05</td> <td> 1.21e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[2]</th> <td>-7.164e+04</td> <td> 1.36e+05</td> <td>   -0.525</td> <td> 0.600</td> <td> -3.4e+05</td> <td> 1.97e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[3]</th> <td> 1.957e+05</td> <td> 1.62e+05</td> <td>    1.212</td> <td> 0.227</td> <td>-1.22e+05</td> <td> 5.14e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[4]</th> <td> 8.452e+05</td> <td> 2.18e+05</td> <td>    3.878</td> <td> 0.000</td> <td> 4.16e+05</td> <td> 1.27e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bs(SqFtTotLiving, df=6, degree=3)[5]</th> <td> 6.955e+05</td> <td> 2.14e+05</td> <td>    3.255</td> <td> 0.001</td> <td> 2.75e+05</td> <td> 1.12e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SqFtLot</th>                              <td>   33.3258</td> <td>    5.454</td> <td>    6.110</td> <td> 0.000</td> <td>   22.592</td> <td>   44.059</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bathrooms</th>                            <td>-4778.2080</td> <td> 1.94e+04</td> <td>   -0.246</td> <td> 0.806</td> <td> -4.3e+04</td> <td> 3.34e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Bedrooms</th>                             <td>-5778.7045</td> <td> 1.32e+04</td> <td>   -0.437</td> <td> 0.663</td> <td>-3.18e+04</td> <td> 2.03e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BldgGrade</th>                            <td> 1.345e+05</td> <td> 1.52e+04</td> <td>    8.842</td> <td> 0.000</td> <td> 1.05e+05</td> <td> 1.64e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>58.816</td> <th>  Durbin-Watson:     </th> <td>   1.633</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 622.021</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.330</td> <th>  Prob(JB):          </th> <td>8.51e-136</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.874</td> <th>  Cond. No.          </th> <td>1.97e+05</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.97e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}                       &   AdjSalePrice   & \\textbf{  R-squared:         } &     0.814   \\\\\n",
       "\\textbf{Model:}                               &       OLS        & \\textbf{  Adj. R-squared:    } &     0.807   \\\\\n",
       "\\textbf{Method:}                              &  Least Squares   & \\textbf{  F-statistic:       } &     131.8   \\\\\n",
       "\\textbf{Date:}                                & Fri, 26 Jul 2024 & \\textbf{  Prob (F-statistic):} & 7.10e-104   \\\\\n",
       "\\textbf{Time:}                                &     18:35:50     & \\textbf{  Log-Likelihood:    } &   -4211.4   \\\\\n",
       "\\textbf{No. Observations:}                    &         313      & \\textbf{  AIC:               } &     8445.   \\\\\n",
       "\\textbf{Df Residuals:}                        &         302      & \\textbf{  BIC:               } &     8486.   \\\\\n",
       "\\textbf{Df Model:}                            &          10      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}                     &    nonrobust     & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                                              & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}                            &   -4.142e+05  &     1.43e+05     &    -2.899  &         0.004        &    -6.95e+05    &    -1.33e+05     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[0]} &   -1.995e+05  &     1.86e+05     &    -1.076  &         0.283        &    -5.65e+05    &     1.66e+05     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[1]} &   -1.206e+05  &     1.23e+05     &    -0.983  &         0.326        &    -3.62e+05    &     1.21e+05     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[2]} &   -7.164e+04  &     1.36e+05     &    -0.525  &         0.600        &     -3.4e+05    &     1.97e+05     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[3]} &    1.957e+05  &     1.62e+05     &     1.212  &         0.227        &    -1.22e+05    &     5.14e+05     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[4]} &    8.452e+05  &     2.18e+05     &     3.878  &         0.000        &     4.16e+05    &     1.27e+06     \\\\\n",
       "\\textbf{bs(SqFtTotLiving, df=6, degree=3)[5]} &    6.955e+05  &     2.14e+05     &     3.255  &         0.001        &     2.75e+05    &     1.12e+06     \\\\\n",
       "\\textbf{SqFtLot}                              &      33.3258  &        5.454     &     6.110  &         0.000        &       22.592    &       44.059     \\\\\n",
       "\\textbf{Bathrooms}                            &   -4778.2080  &     1.94e+04     &    -0.246  &         0.806        &     -4.3e+04    &     3.34e+04     \\\\\n",
       "\\textbf{Bedrooms}                             &   -5778.7045  &     1.32e+04     &    -0.437  &         0.663        &    -3.18e+04    &     2.03e+04     \\\\\n",
       "\\textbf{BldgGrade}                            &    1.345e+05  &     1.52e+04     &     8.842  &         0.000        &     1.05e+05    &     1.64e+05     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 58.816 & \\textbf{  Durbin-Watson:     } &     1.633  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.000 & \\textbf{  Jarque-Bera (JB):  } &   622.021  \\\\\n",
       "\\textbf{Skew:}          &  0.330 & \\textbf{  Prob(JB):          } & 8.51e-136  \\\\\n",
       "\\textbf{Kurtosis:}      &  9.874 & \\textbf{  Cond. No.          } &  1.97e+05  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 1.97e+05. This might indicate that there are \\newline\n",
       " strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           AdjSalePrice   R-squared:                       0.814\n",
       "Model:                            OLS   Adj. R-squared:                  0.807\n",
       "Method:                 Least Squares   F-statistic:                     131.8\n",
       "Date:                Fri, 26 Jul 2024   Prob (F-statistic):          7.10e-104\n",
       "Time:                        18:35:50   Log-Likelihood:                -4211.4\n",
       "No. Observations:                 313   AIC:                             8445.\n",
       "Df Residuals:                     302   BIC:                             8486.\n",
       "Df Model:                          10                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "========================================================================================================\n",
       "                                           coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------------------------\n",
       "Intercept                            -4.142e+05   1.43e+05     -2.899      0.004   -6.95e+05   -1.33e+05\n",
       "bs(SqFtTotLiving, df=6, degree=3)[0] -1.995e+05   1.86e+05     -1.076      0.283   -5.65e+05    1.66e+05\n",
       "bs(SqFtTotLiving, df=6, degree=3)[1] -1.206e+05   1.23e+05     -0.983      0.326   -3.62e+05    1.21e+05\n",
       "bs(SqFtTotLiving, df=6, degree=3)[2] -7.164e+04   1.36e+05     -0.525      0.600    -3.4e+05    1.97e+05\n",
       "bs(SqFtTotLiving, df=6, degree=3)[3]  1.957e+05   1.62e+05      1.212      0.227   -1.22e+05    5.14e+05\n",
       "bs(SqFtTotLiving, df=6, degree=3)[4]  8.452e+05   2.18e+05      3.878      0.000    4.16e+05    1.27e+06\n",
       "bs(SqFtTotLiving, df=6, degree=3)[5]  6.955e+05   2.14e+05      3.255      0.001    2.75e+05    1.12e+06\n",
       "SqFtLot                                 33.3258      5.454      6.110      0.000      22.592      44.059\n",
       "Bathrooms                            -4778.2080   1.94e+04     -0.246      0.806    -4.3e+04    3.34e+04\n",
       "Bedrooms                             -5778.7045   1.32e+04     -0.437      0.663   -3.18e+04    2.03e+04\n",
       "BldgGrade                             1.345e+05   1.52e+04      8.842      0.000    1.05e+05    1.64e+05\n",
       "==============================================================================\n",
       "Omnibus:                       58.816   Durbin-Watson:                   1.633\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              622.021\n",
       "Skew:                           0.330   Prob(JB):                    8.51e-136\n",
       "Kurtosis:                       9.874   Cond. No.                     1.97e+05\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.97e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'AdjSalePrice ~ bs(SqFtTotLiving, df=6, degree=3) + SqFtLot + Bathrooms + Bedrooms + BldgGrade'\n",
    "model_spline = smf.ols(formula=formula, data=house_98105)\n",
    "result_spline = model_spline.fit()\n",
    "result_spline.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalized Additive Models (GAM)\n",
    "\n",
    "- Generalized additive models can be used to automatically fit spline regression models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygam import LinearGAM, s, l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors = [\"SqFtTotLiving\", \"SqFtLot\", \"Bathrooms\", \"Bedrooms\", \"BldgGrade\"]\n",
    "target = house_98105[\"AdjSalePrice\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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      " 27% (3 of 11) |######                   | Elapsed Time: 0:00:00 ETA:   0:00:00\n",
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      "100% (11 of 11) |########################| Elapsed Time: 0:00:00 Time:  0:00:00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearGAM(callbacks=[Deviance(), Diffs()], fit_intercept=True, \n",
       "   max_iter=100, scale=None, \n",
       "   terms=s(0) + l(1) + l(2) + l(3) + l(4) + intercept, tol=0.0001, \n",
       "   verbose=False)"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_gam = LinearGAM(s(0, n_splines=12) + l(1) + l(2) + l(3) + l(4))\n",
    "model_gam.gridsearch(house_98105[predictors].values, target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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