univariate_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "358bb147",
   "metadata": {},
   "source": [
    "# Univariate Linear Regression\n",
    "\n",
    "We shall work with a dataset taken from Kaggle (https://www.kaggle.com/datasets/krishnaraj30/salary-prediction-data-simple-linear-regression)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "65d88291",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# render plots in the notebook.\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ef84b45",
   "metadata": {},
   "source": [
    "Let us explore the dataset by creating a Pandas DataFrame from the CSV data file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ee876be5",
   "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>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.1</td>\n",
       "      <td>39343.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.3</td>\n",
       "      <td>46205.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>37731.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>43525.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.2</td>\n",
       "      <td>39891.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   YearsExperience   Salary\n",
       "0              1.1  39343.0\n",
       "1              1.3  46205.0\n",
       "2              1.5  37731.0\n",
       "3              2.0  43525.0\n",
       "4              2.2  39891.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"data/Salary_Data.csv\")\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f0036333",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 30 entries, 0 to 29\n",
      "Data columns (total 2 columns):\n",
      " #   Column           Non-Null Count  Dtype  \n",
      "---  ------           --------------  -----  \n",
      " 0   YearsExperience  30 non-null     float64\n",
      " 1   Salary           30 non-null     float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 608.0 bytes\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c3727de",
   "metadata": {},
   "source": [
    "There are 30 rows and 2 columns in the dataset, with no missing values. The values in the dataset are of numeric type (`float64`). We shall visualise the relationship between the 2 columns using a scatter plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2a9c5402",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(data[\"YearsExperience\"], data[\"Salary\"]/1000, c=\"#636EFA\")\n",
    "\n",
    "ax.set(title=\"Salary vs Experience\",\n",
    "       xlabel=\"Experience (Years)\", xticks=np.arange(1, 12), xlim=(0.5, 11.5),\n",
    "       ylabel=\"Salary (in thousands of dollars)\", yticks=np.arange(30, 131, 10), ylim=(25, 135));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24612b9a",
   "metadata": {},
   "source": [
    "From the plot above, we can conclude that a linear relationship exists between the `YearsExperience` and `Salary` columns. Thus, we can construct a simple linear regression model that fits the data. The feature variable is the experience in years and the target variable is salary. Thus, we have a univariate linear regression problem at hand."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45a08696",
   "metadata": {},
   "source": [
    "## Modelling\n",
    "\n",
    "Let $x_i$ be the value of the feature variable corresponding to the $i^{\\mathrm{th}}$ row. The true value of the target variable is denoted by $y_i$. Since we are constructing a univariate linear regression model $f$, the predicted value for the target variable is given by:\n",
    "\n",
    "$$\n",
    "\\hat{y}_i=f(x_i)=mx_i+c\n",
    "$$\n",
    "\n",
    "where $m$ and $c$ are parameters of the model. They represent the slope and $y$-intercept of the regression line. Optimal values of the parameters should minimise the error between the true and the predicted values of the target variable. Let us try to minimise the Mean Squared Error (MSE) by using the following cost function $J(m,c)$:\n",
    "\n",
    "$$\n",
    "J(m,c)=\\frac{1}{2n}\\sum_{i=1}^n (\\hat{y}_i-y_i)^2=\\frac{1}{2n}\\sum_{i=1}^n (mx_i+c-y_i)^2\n",
    "$$\n",
    "\n",
    "where $n$ is the total number of rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6119f78b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the model f.\n",
    "def f(m, c, x):\n",
    "    return m*x + c\n",
    "\n",
    "# Define the cost function J.\n",
    "def J(m, c, x, y, n):\n",
    "    return np.sum(np.square(f(m, c, x) - y)) / (2*n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9ecbb1f",
   "metadata": {},
   "source": [
    "We shall find the best values for the parameters by using the `gradient descent` algorithm. After providing initial values for $m$ and $c$, we keep updating their values till the corresponding cost function reaches a local minimum. This is done through the following transformation:\n",
    "\n",
    "$$\n",
    "m = m - \\alpha \\cdot \\partial_m J\n",
    "$$\n",
    "\n",
    "$$\n",
    "c = c - \\alpha \\cdot \\partial_c J\n",
    "$$\n",
    "\n",
    "where $\\partial_m J$ and $\\partial_c J$ are the partial derivatives of $J$. The `learning rate` $\\alpha$ controls the step size of the update in the values of the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f3cc5b3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Partial derivative of J with respect to m.\n",
    "def dJ_dm(m, c, x, y, n):\n",
    "    return np.sum((f(m, c, x) - y) * x) / n\n",
    "\n",
    "# Partial derivative of J with respect to c.\n",
    "def dJ_dc(m, c, x, y, n):\n",
    "    return np.sum(f(m, c, x) - y) / n\n",
    "\n",
    "def gradiant_descent(m, c, x, y, alpha, iter_num):\n",
    "    \"\"\"\n",
    "    Employ gradiant descent to find the optimal values for m and c.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    m : scalar\n",
    "        initial value for slope of the regression line\n",
    "    \n",
    "    c : scalar\n",
    "        initial value for y-intercept of the regression line\n",
    "    \n",
    "    x : array_like\n",
    "        values of the feature variable\n",
    "      \n",
    "    y : array_like\n",
    "        values of the target variable\n",
    "      \n",
    "    alpha : scalar\n",
    "        value for the learning rate\n",
    "      \n",
    "    iter_num : scalar\n",
    "        number of updates to be performed\n",
    "      \n",
    "     Returns\n",
    "     -------\n",
    "     tuple\n",
    "        the pair of optimal values (m,c)\n",
    "    \"\"\"\n",
    "    \n",
    "    print(\"Gradiant Descent\", 16 * \"*\", sep=\"\\n\")\n",
    "    \n",
    "    # number of rows in the dataset.\n",
    "    n = x.shape[0]\n",
    "    \n",
    "    for i in range(1, iter_num+1):\n",
    "        m -= alpha * dJ_dm(m, c, x, y, n)\n",
    "        c -= alpha * dJ_dc(m, c, x, y, n)\n",
    "        if i % 1000 == 0:\n",
    "            print(f\"i: {i:5}\\tJ(m,c): {J(m, c, x, y, n)}\")\n",
    "    return m, c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fb2254d",
   "metadata": {},
   "source": [
    "To execute gradiant descent, let us specify the values for the learning rate and the number of times to perform the update (`iter_num`), along with initial values for $m$ and $c$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "78dad101",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial values for m and c.\n",
    "m_init = 0\n",
    "c_init = 0\n",
    "\n",
    "# feature values. \n",
    "x = data[\"YearsExperience\"]\n",
    "\n",
    "# target values.\n",
    "y = data[\"Salary\"]\n",
    "\n",
    "# value for learning rate.\n",
    "alpha = 2e-2\n",
    "\n",
    "# number of times to perform the update.\n",
    "iter_num = 15000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "55d46ca1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradiant Descent\n",
      "****************\n",
      "i:  1000\tJ(m,c): 15648005.835395116\n",
      "i:  2000\tJ(m,c): 15635478.140312457\n",
      "i:  3000\tJ(m,c): 15635475.861555051\n",
      "i:  4000\tJ(m,c): 15635475.861140553\n",
      "i:  5000\tJ(m,c): 15635475.861140486\n",
      "i:  6000\tJ(m,c): 15635475.861140493\n",
      "i:  7000\tJ(m,c): 15635475.861140484\n",
      "i:  8000\tJ(m,c): 15635475.86114047\n",
      "i:  9000\tJ(m,c): 15635475.86114047\n",
      "i: 10000\tJ(m,c): 15635475.86114047\n",
      "i: 11000\tJ(m,c): 15635475.86114047\n",
      "i: 12000\tJ(m,c): 15635475.86114047\n",
      "i: 13000\tJ(m,c): 15635475.86114047\n",
      "i: 14000\tJ(m,c): 15635475.86114047\n",
      "i: 15000\tJ(m,c): 15635475.86114047\n"
     ]
    }
   ],
   "source": [
    "m, c = gradiant_descent(m_init, c_init, x, y, alpha, iter_num)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8adb8a19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal values of m and c are 9449.9623 and 25792.2002 respectively.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The optimal values of m and c are {m:.4f} and {c:.4f} respectively.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9080dbaa",
   "metadata": {},
   "source": [
    "## Result\n",
    "\n",
    "The predicted values for the target variable can be obtained from the model $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f90c558f",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = f(m, c, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44bedb6e",
   "metadata": {},
   "source": [
    "Let us plot the regression line associated with the optimal values of $m$ and $c$. The true values of the target variable are also shown in the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8ffcf546",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(data[\"YearsExperience\"], data[\"Salary\"]/1000, c=\"#636EFA\")\n",
    "\n",
    "ax.plot(x, y_pred/1000, color=\"crimson\", linestyle=\"--\")\n",
    "\n",
    "ax.set(title=\"Salary vs Experience\",\n",
    "       xlabel=\"Experience (Years)\", xticks=np.arange(1, 12), xlim=(0.5, 11.5),\n",
    "       ylabel=\"Salary (in thousands of dollars)\", yticks=np.arange(30, 131, 10), ylim=(25, 135));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0321408",
   "metadata": {},
   "source": [
    "Using the simple linear regression model, the salary corresponding to a certain level of experience (measured in years) can be predicted in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f085326f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Salary corresponding to 3.5 years of experience is 58,867.07 dollars.\n"
     ]
    }
   ],
   "source": [
    "# experience in years.\n",
    "experience = 3.5\n",
    "\n",
    "print(f\"Salary corresponding to {experience} years of experience is {f(m, c, experience):,.2f} dollars.\")"
   ]
  }
 ],
 "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": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}