salary.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "02783930-7bdc-4793-8334-3a3d1c6ea5cc",
   "metadata": {},
   "source": [
    "# Predicting Salary given Position"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6370665f-e136-4f93-950b-087ee747925d",
   "metadata": {},
   "source": [
    "# Introduction \n",
    "Have you ever wondered how much more you would be making if you were in a more senoir position? Wonder no more. In this project, I have taken data from the one and only [Position Salary Dataset](https://www.kaggle.com/datasets/mariospirito/position-salariescsv) and will walk you through my implementation of polynomial regression to help you derive a model. \n",
    "\n",
    "### Goal\n",
    "- Predict salary given experience in months\n",
    "\n",
    "### Sub-Goals\n",
    "- Understand how libraries like ```scikit-learn``` may implement regression\n",
    "- Understand how to use ```scikit-learn``` to implement regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77793e25-f20e-4bc9-9993-7c011b5ce8a4",
   "metadata": {},
   "source": [
    "## Tools\n",
    "In this project, I will make use of: \n",
    "- Pandas, a library for data manipulation\n",
    "- NumPy, a library for scientific computing\n",
    "- Matplotlib, a library for plotting data\n",
    "- scikit-learn, a library for Machine Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "24606871-dd2e-48cc-9493-5f7dc71e607c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import SGDRegressor #gradient descent with sckit-learn\n",
    "from sklearn.preprocessing import StandardScaler #z-score normalisation with sckit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e833c102-aebe-4aae-b58a-bcc2137a1a33",
   "metadata": {},
   "outputs": [],
   "source": [
    "#read data \n",
    "data = pd.read_csv('Position_Salaries.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2271b879-799e-43db-b05a-c21a106f59a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Position  Level   Salary\n",
      "0   Business Analyst      1    45000\n",
      "1  Junior Consultant      2    50000\n",
      "2  Senior Consultant      3    60000\n",
      "3            Manager      4    80000\n",
      "4    Country Manager      5   110000\n",
      "5     Region Manager      6   150000\n",
      "6            Partner      7   200000\n",
      "7     Senior Partner      8   300000\n",
      "8            C-level      9   500000\n",
      "9                CEO     10  1000000\n"
     ]
    }
   ],
   "source": [
    "# visualise data\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60d81db9-2fbb-40b3-a26d-a98d46ac50c4",
   "metadata": {},
   "source": [
    "We can see that as you take on more senior positions, your numerical level will increase and your salary will increase. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08e920fb-2706-4c46-9a39-215c83f5f0c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#convert data to numpy arrays\n",
    "data = data.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "eac639da-8d3c-46ab-b4fe-3052be6d7980",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = data[:,1] #Level\n",
    "y_train = data[:,2] #Salary\n",
    "y_train = y_train/1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4bd1c4b1-afc4-43b6-aacc-c2f1f363ea73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot data onto a scatter plot to visualise data\n",
    "plt.scatter(x_train, y_train, marker='x', c='r')\n",
    "plt.title(\"Level vs Salary\")\n",
    "plt.xlabel(\"Level\")\n",
    "plt.ylabel(\"Salary ('000s)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120faa84-2532-48a8-9f69-40839a3fb482",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "To get started, lets try and fit a linear function to the data set which can be represented as \n",
    "$$f_{w,b}(x) = wx + b$$\n",
    "where $w$ and $b$ are parameters we are trying to find. \n",
    "\n",
    "#### Cost Function \n",
    "A cost function is a function that is able to give us an indication of how well our model performs. There are many different types of cost function. For this project, I will be using the *sum of squared error* as given: \n",
    "\n",
    "$$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2$$ \n",
    "\n",
    "where $m$ represents the number of training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4e8d7992-2f6b-48fb-9e32-2084493450a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#function that calculates the cost given all the parameters\n",
    "\n",
    "def compute_cost(x, y, w, b):\n",
    "    #number of training examples\n",
    "    m = x.shape[0]\n",
    "\n",
    "    total_cost = 0\n",
    "\n",
    "    #getting the sum of squared errors\n",
    "    for i in range(m):\n",
    "        f_wb = w*x[i] + b\n",
    "        cost_i = (f_wb -y[i])**2\n",
    "        total_cost = total_cost + cost_i\n",
    "\n",
    "    #dividing the summation by 2m\n",
    "    total_cost = total_cost/(2*m)\n",
    "\n",
    "    return total_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0545f65-ebc9-4b4b-807a-508ac0c01076",
   "metadata": {},
   "source": [
    "#### Gradient Descent\n",
    "*Gradient Descent* is a method to **minimize** a cost function. \n",
    "<img align=\"right\" src=\"./gradient_descent.png\" style=\"width:200px;\"/>\n",
    "\n",
    "If you were to visualise how $J(w,b)$ looks like in relation to it's parameters $w$ and $b$, you get something like a bowl.\n",
    "\n",
    "*Gradient Descent* works by constantly updating the parameters $w$ and $b$ so that you reach the local minimum point of a cost function. \n",
    "\n",
    "[Here](https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/what-is-gradient-descent#:~:text=Gradient%20descent%20minimizes%20differentiable%20functions,direction%20of%20the%20negative%20gradient.) for a more detailed explanation of *Gradient Descent*. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ece73cc-05f8-4585-a28b-7091796bd81c",
   "metadata": {},
   "source": [
    "Formula for gradient descent is as follows: \n",
    "$$\\begin{align*}& \\text{repeat until convergence:} \\; \\lbrace \\newline \\; & \\phantom {0000} b := b -  \\alpha \\frac{\\partial J(w,b)}{\\partial b} \\newline       \\; & \\phantom {0000} w := w -  \\alpha \\frac{\\partial J(w,b)}{\\partial w} \\tag{1}  \\; & \n",
    "\\newline & \\rbrace\\end{align*}$$\n",
    "\n",
    "where, parameters $w, b$ are both updated simultaniously and where  \n",
    "$$\n",
    "\\frac{\\partial J(w,b)}{\\partial b}  = \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)}) \\tag{2}\n",
    "$$\n",
    "$$\n",
    "\\frac{\\partial J(w,b)}{\\partial w}  = \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) -y^{(i)})x^{(i)} \\tag{3}\n",
    "$$\n",
    "* m is the number of training examples in the dataset\n",
    "\n",
    "    \n",
    "*  $f_{w,b}(x^{(i)})$ is the model's prediction, while $y^{(i)}$, is the target value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93ea7ecb-0a1f-45a1-bffe-cbaf3fa5d7b0",
   "metadata": {},
   "source": [
    "> To get started, let's create a function that returns the derivative as shown in (2) and (3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a904a41f-f32d-458c-b3e2-12e10bf2bbb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient(x, y, w, b): \n",
    "    \n",
    "    # Number of training examples\n",
    "    m = x.shape[0]\n",
    "    \n",
    "    dj_dw = 0\n",
    "    dj_db = 0\n",
    "    \n",
    "    for i in range(m):\n",
    "        f_wb = w*x[i] + b\n",
    "        dj_db_i = f_wb - y[i]\n",
    "        dj_dw_i = (f_wb - y[i])*x[i]\n",
    "        dj_dw += dj_dw_i\n",
    "        dj_db += dj_db_i\n",
    "    dj_dw = dj_dw/m\n",
    "    dj_db = dj_db/m\n",
    "        \n",
    "    return dj_dw, dj_db"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362c5c37-5aea-4e00-a79a-4a72a306468e",
   "metadata": {},
   "source": [
    "> Now, let's create a function that does gradient descent using ```compute_cost``` and ```compute_gradient```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ed84d08f-6119-4799-a901-6b5ff8bf7110",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(x, y, w_in, b_in, alpha, num_iters): \n",
    "    \n",
    "    # number of training examples\n",
    "    m = len(x)\n",
    "    \n",
    "    # An array to store cost J and w's at each iteration — primarily for graphing later\n",
    "    J_history = []\n",
    "    w_history = []\n",
    "    w = w_in\n",
    "    b = b_in\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "\n",
    "        # Calculate the gradient and update the parameters\n",
    "        dj_dw, dj_db = compute_gradient(x, y, w, b )  \n",
    "\n",
    "        # Update Parameters using w, b, alpha and gradient\n",
    "        w = w - alpha * dj_dw               \n",
    "        b = b - alpha * dj_db              \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cdeb708-6eee-40d4-91a6-c2b9ffcdae4c",
   "metadata": {},
   "source": [
    "> Let's run the gradient descent algorithm above! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "25580c6f-5773-4d0d-833d-fe8dd5a684dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w,b found by gradient descent: 77.3121370287372 -170.50294366292795\n"
     ]
    }
   ],
   "source": [
    "# initialize fitting parameters. Recall that the shape of w is (n,)\n",
    "initial_w = 0.\n",
    "initial_b = 0.\n",
    "\n",
    "# some gradient descent settings\n",
    "iterations = 10000\n",
    "alpha = 0.001\n",
    "\n",
    "w_algo,b_algo = gradient_descent(x_train ,y_train, initial_w, initial_b, alpha, iterations)\n",
    "print(\"w,b found by gradient descent:\", w_algo, b_algo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a712a64-2e49-4a70-8bf9-55816bb58960",
   "metadata": {},
   "source": [
    "With our algorithm, $w = 77312.1370287372$ and $b = -170502.94366292786$. Let's try using ```Sckit-Learn```, a library that can do gradient descent for us!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2519fd53-91da-4813-8492-2a28af492910",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w,b found by Sckit-Learn: [69.82082655] [-108.30345066]\n",
      "w,b found by my algorithm 77.3121370287372 -170.50294366292795\n"
     ]
    }
   ],
   "source": [
    "sgdr = SGDRegressor(max_iter=10000000)\n",
    "\n",
    "x_train = x_train.reshape(-1, 1) #reformat x_train to have 1 column. rows is determined by number of training sets. \n",
    "sgdr.fit(x_train, y_train)\n",
    "\n",
    "w_sckit = sgdr.coef_\n",
    "b_sckit = sgdr.intercept_\n",
    "\n",
    "print(\"w,b found by Sckit-Learn:\", w_sckit, b_sckit)\n",
    "print(\"w,b found by my algorithm\", w_algo, b_algo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2a6e637-e096-4b5f-81d7-a71b2f518aec",
   "metadata": {},
   "source": [
    "> The parameters given by ```Sckit-Learn``` is quite different. Let's try and visualise it!  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2e73e934-3569-4333-b235-2e925bcf2bb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#convert x_train back to a 1-D Array\n",
    "x_train = x_train[:,0]\n",
    "\n",
    "#plotting\n",
    "plt.scatter(x_train, y_train, marker='x', c='r', label=\"data set\")\n",
    "plt.plot(x_train, x_train*w_algo + b_algo, c='b', label=\"my algo\")\n",
    "plt.plot(x_train, x_train*w_sckit +b_sckit, c='g', label=\"sckit-learn\")\n",
    "\n",
    "#labelling\n",
    "plt.legend(loc='upper left')\n",
    "plt.title(\"Level vs Salary\")\n",
    "plt.xlabel(\"Level\")\n",
    "plt.ylabel(\"Salary ('000s)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2acdc894-8cd5-4b72-ba5a-0697eb6557e1",
   "metadata": {},
   "source": [
    "> A linear model cannot accurately predict the data set which explains why both algorithms, even though using the same method, give very different parameters. Let's try **Polynomial Regression** instead!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c38a555b-ead6-4394-b37d-342451cfe25e",
   "metadata": {},
   "source": [
    "## Polynomial Regression \n",
    "#### Feature Engineering \n",
    "Suppose we use the following model for polynomial regression: \n",
    "$$y=w_0x_0 + w_1x_1^2 + w_2x_2^3+ ... + w_{15}x_{15}^{16} + b$$\n",
    "We would be adding new features to our equation. \n",
    "\n",
    "Rather than thinking that $x^2$ is the square of $x$, think of it as a new input variable that will ultimately have some effect on the salary. It can visualised with the following equation: \n",
    "\n",
    "$$ f_{\\mathbf{w},b}(\\mathbf{x}) =  w_0x_0+w_1x_1+w_2x_2 + ...+ w_{15}x_{15}+ b $$ \n",
    "where $\\mathbf{w}$ and $\\mathbf{x}$ are column vectors \n",
    "\n",
    "#### Z-Score Normalisation \n",
    "Assuming if $x_0 = 2,  x_{15}^{16} =65536 $. From this, we can expect $w_{15}$ to be alot smaller as compared to $w_{0}$ since a change in $w_{15}$ will induce a siginficant change to the whole equation. This will create a problem while doing gradient descent because we are trying to find all the values of $w$ simultaneously. \n",
    "\n",
    "To prevent this problem from happening, let's first do z-score normalisation on our features. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "030b7b0f-10a8-4a6e-88d7-79f6e89e44fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "#feature engineering\n",
    "x_train = x_train.reshape(-1, 1) #reformat x_train to have 1 column. rows is determined by number of training sets. \n",
    "x_train_poly = X = np.c_[x_train, x_train**2, x_train**3,x_train**4, x_train**5, x_train**6, x_train**7, \n",
    "x_train**8, x_train**9, x_train**10, x_train**11, x_train**12, x_train**13, x_train**14, x_train**15, x_train**16]\n",
    "\n",
    "#z-score normalise data with sklearn library\n",
    "scaler = StandardScaler()\n",
    "x_train_poly = scaler.fit_transform(x_train_poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c04d0e2-9176-4011-98cf-eaeb5a395dbd",
   "metadata": {},
   "source": [
    "#### Same same but different formulas \n",
    "$f(\\mathbf{w},b)$ can be simplified with vector dot product as:\n",
    "$$ f_{\\mathbf{w},b}(\\mathbf{x}) = \\mathbf{w} \\cdot \\mathbf{x} + b  \\tag{1} $$ \n",
    "Therefore, the new cost function is \n",
    "$$J(\\mathbf{w},b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})^2 \\tag{2}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fee9ae-af80-4952-a609-6cc585438050",
   "metadata": {},
   "source": [
    "> We will now implement the new cost function! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1476e5ad-0be9-4296-b8be-6a21b9f0b4f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#cost function as shown in (2)\n",
    "def poly_compute_cost(x,y,w,b):\n",
    "    #number of training sets\n",
    "    m = x.shape[0]\n",
    "    \n",
    "    cost = 0.0\n",
    "    \n",
    "    for i in range(m):                                \n",
    "        f_wb_i = np.dot(x[i], w) + b           \n",
    "        cost = cost + (f_wb_i - y[i])**2       \n",
    "    cost = cost / (2 * m)\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7a893a8-b609-4dcb-8d3f-d3197c8af397",
   "metadata": {},
   "source": [
    "#### Gradient Descent \n",
    "Gradient descent for multiple variables:\n",
    "\n",
    "$$\\begin{align*} \\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\\;\n",
    "& w_j = w_j -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} \\tag{3}  \\; & \\text{for j = 0..n-1}\\newline\n",
    "&b\\ \\ = b -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  \\newline \\rbrace\n",
    "\\end{align*}$$\n",
    "\n",
    "where, n is the number of features, parameters $w_j$,  $b$, are updated simultaneously and where  \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})x_{j}^{(i)} \\tag{4}  \\\\\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\tag{5}\n",
    "\\end{align}\n",
    "$$\n",
    "* m is the number of training examples in the data set\n",
    "\n",
    "    \n",
    "*  $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "421dce9d-6597-422d-ba9c-8b8f27cb4c10",
   "metadata": {},
   "source": [
    "> Let's create a function that calculates the gradient in (4) and (5)! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "417095c5-0534-496d-b923-33d38545eb9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_compute_gradient(x, y, w, b): \n",
    "\n",
    "    m,n = x.shape           #(number of examples, number of features)\n",
    "    dj_dw = np.zeros((n,))\n",
    "    dj_db = 0.\n",
    "\n",
    "    for i in range(m):                             \n",
    "        err = (np.dot(x[i], w) + b) - y[i]   \n",
    "        for j in range(n):                         \n",
    "            dj_dw[j] = dj_dw[j] + err * x[i, j]    \n",
    "        dj_db = dj_db + err                        \n",
    "    dj_dw = dj_dw / m                                \n",
    "    dj_db = dj_db / m                                \n",
    "        \n",
    "    return dj_db, dj_dw"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee72c1f0-bbac-4959-9f22-6226faa33233",
   "metadata": {},
   "source": [
    "> Function for gradient descent!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "824520f0-540a-484e-8bb5-7e727639ee96",
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_gradient_descent(x, y, w_in, b_in, alpha, num_iters): \n",
    "    \n",
    "    # An array to store cost J and w's at each iteration primarily for graphing later\n",
    "    J_history = []\n",
    "    w = w_in  #avoid modifying global w within function\n",
    "    b = b_in\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "\n",
    "        # Calculate the gradient and update the parameters\n",
    "        dj_db,dj_dw = poly_compute_gradient(x, y, w, b)   ##None\n",
    "\n",
    "        # Update Parameters using w, b, alpha and gradient\n",
    "        w = w - alpha * dj_dw               ##None\n",
    "        b = b - alpha * dj_db               ##None\n",
    "        \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9fb028f-5d98-4f9f-ab41-97efd9b882a5",
   "metadata": {},
   "source": [
    "> Let's test the implementation of Gradient Descent! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4e54a9e4-494b-451d-a89a-d3795b3418ac",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w, b found by gradient descent: [23.98971381 24.06654338 22.80716463 21.37950276 20.13566017 19.1302024\n",
      " 18.33387043 17.70296519 17.198735   16.79095952 16.45707929 16.18045807\n",
      " 15.94880248 15.75294627 15.58597039 15.44258055], 247.82\n"
     ]
    }
   ],
   "source": [
    "# initialize parameters\n",
    "initial_w = np.zeros_like(x_train_poly[0])\n",
    "initial_b = 0.\n",
    "\n",
    "# some gradient descent settings\n",
    "iterations = 10000\n",
    "alpha = 0.0005\n",
    "\n",
    "# run gradient descent \n",
    "w_algo_poly, b_algo_poly = poly_gradient_descent(x_train_poly, y_train, initial_w, initial_b,alpha, iterations)\n",
    "print(f\"w, b found by gradient descent: {w_algo_poly}, {b_algo_poly:0.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dacc32f-8cb4-4a97-a065-3f3c2e90c2e1",
   "metadata": {},
   "source": [
    "> let's do an implementation with ```sckit-learn```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6ff0e294-b060-4d90-8c87-ae6bdda50c4a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w,b found by Sckit-Learn: [24.39997028 24.77369039 23.07951681 21.17172292 19.61053267 18.46269212\n",
      " 17.6589371  17.11210279 16.74892051 16.51452471 16.36961831 16.28653937\n",
      " 16.24591885 16.23419273 16.24184196 16.26217202] [249.49580561]\n",
      "w,b found by my algorithm: [23.98971381 24.06654338 22.80716463 21.37950276 20.13566017 19.1302024\n",
      " 18.33387043 17.70296519 17.198735   16.79095952 16.45707929 16.18045807\n",
      " 15.94880248 15.75294627 15.58597039 15.44258055] 247.8209830079753\n"
     ]
    }
   ],
   "source": [
    "sgdr = SGDRegressor(max_iter=100000000)\n",
    " \n",
    "sgdr.fit(x_train_poly, y_train)\n",
    "\n",
    "w_sckit = sgdr.coef_\n",
    "b_sckit = sgdr.intercept_\n",
    "\n",
    "print(\"w,b found by Sckit-Learn:\", w_sckit, b_sckit)\n",
    "print(\"w,b found by my algorithm:\", w_algo_poly, b_algo_poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ea88903-bde9-482b-a6dc-5cb63d94a712",
   "metadata": {},
   "source": [
    "> The parameters are big and messy, let's plot our results on a graph to better visualise it!  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "60f69fd9-0f72-406d-8614-9e3b7ecbb286",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predicted_x(x, w, b):\n",
    "    m = x.shape[0]\n",
    "    predicted_x = []\n",
    "    for i in range(m):\n",
    "        predicted_x.append(np.dot(x[i],w) + b)\n",
    "    return predicted_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cb314398-c187-4065-b6de-181c2cf21370",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#convert x_train back to a 1-D Array\n",
    "poly_x_train_predicted = predicted_x(x_train_poly, w_algo_poly, b_algo_poly)\n",
    "poly_x_train_predicted_sckit = predicted_x(x_train_poly, w_sckit, b_sckit)\n",
    "\n",
    "#plotting\n",
    "plt.scatter(x_train, y_train, marker='x', c='r', label=\"data set\")\n",
    "plt.plot(x_train, poly_x_train_predicted, c='b', label=\"my algo\")\n",
    "plt.plot(x_train, poly_x_train_predicted_sckit, c='g', label=\"sckit-learn\")\n",
    "\n",
    "#labelling\n",
    "plt.legend(loc='upper left')\n",
    "plt.title(\"Level vs Salary\")\n",
    "plt.xlabel(\"Level\")\n",
    "plt.ylabel(\"Salary ('000s)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0bf9a2d-fd92-4cc6-b513-b77b0c2bd044",
   "metadata": {},
   "source": [
    "#### Hooray! \n",
    "Visually, we can see that our regression model closely matches the model derived using sckit-learn. More importantly, it seems to cut through most points on the dataset which implies that it can accurately predict your salary given your level in an organisation. \n",
    "\n",
    "Let's test our model out and see how much more you will be making in the future. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c894b26-3f72-498f-bc28-6101e565e2cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ensure that input is a float between 1 and 10\n"
     ]
    }
   ],
   "source": [
    "def f_wb(level): \n",
    "    x = level\n",
    "    x = np.array([x, x**2, x**3,x**4, x**5, x**6, x**7, x**8, x**9, x**10, x**11, x**12, x**13, x**14, x**15, x**16]) #reformat to fit feature engineered model\n",
    "    predicted_income = np.dot(x, w_algo_poly) + b_algo_poly\n",
    "    \n",
    "    return predicted_income\n",
    "    \n",
    "\n",
    "def predict_income_increase(curr_level, fut_level):\n",
    "    curr_inc = f_wb(curr_level)\n",
    "    fut_inc = f_wb(fut_level)\n",
    "\n",
    "    increase = (fut_inc - curr_inc)/curr_inc #calculate income increase in percentage\n",
    "    return round(increase) #round to nearest integer\n",
    "\n",
    "curr_level = 0.0 \n",
    "fut_level = 0.0 \n",
    "\n",
    "while (curr_level < 1 or curr_level > 10):\n",
    "    try:\n",
    "        curr_level = float(input(\"What is your current level in your organisation from a scale of 1 to 10?\"))\n",
    "    except:\n",
    "        print(\"Ensure that input is a float between 1 and 10\")\n",
    "        \n",
    "if int(curr_level) == 10:\n",
    "    print(\"You can't earn any more than this...\")\n",
    "else:\n",
    "    while (fut_level < curr_level or fut_level > 10):\n",
    "        try:\n",
    "            fut_level = float(input(\"Which level do you wish to be at?\"))\n",
    "        except:\n",
    "            print(\"Ensure that your input is a float above your curr_level and below 10\")\n",
    "    \n",
    "    income_increase = predict_income_increase(curr_level, fut_level)\n",
    "    print(f\"Work hard and you will see an income increase of {income_increase}%!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "29f554c8-613f-4190-98b9-775ef443d7eb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
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 },
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