2. Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expedition to Data Science and Machine Learning\n",
    "## Module 4: Machine Learning with Python\n",
    "### Lecture 2: Supervised Learning: Linear Regression\n",
    "\n",
    "Instructor: Md Shahidullah Kawsar\n",
    "<br>Data Scientist, IDARE, Houston, TX, USA\n",
    "\n",
    "#### Objectives:\n",
    "- Supervised Learning: Linear Regression\n",
    "- train data, test data\n",
    "- Understanding the equation of a straight line\n",
    "- feature coefficient (slope, gradient, m)\n",
    "- bias coeffcient (y-interccept, c)\n",
    "- domain: x-axis, independent variable\n",
    "- range: y-axis, dependent variable\n",
    "- loss function, cost function, objective function, error function\n",
    "- bias-variance tradeoff, overfitting, underfitting\n",
    "- ordinary least square method\n",
    "- gradient descent method\n",
    "- residual, error, squared error, RMSE - Root Mean Squared Error\n",
    "\n",
    "#### References:\n",
    "[1] A Gentle Introduction to Machine Learning: https://www.youtube.com/watch?v=Gv9_4yMHFhI&list=PLblh5JKOoLUICTaGLRoHQDuF_7q2GfuJF&ab_channel=StatQuestwithJoshStarmer\n",
    "<br>[2] Linear Regression, Clearly Explained!!!: https://www.youtube.com/watch?v=nk2CQITm_eo&list=PLblh5JKOoLUICTaGLRoHQDuF_7q2GfuJF&index=10&ab_channel=StatQuestwithJoshStarmer\n",
    "<br>[3] Linear Regression scikit-learn: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\n",
    "<br>[4] Data Splitting: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html\n",
    "<br>[5] Mean Squared Error: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html\n",
    "<br>[6] RMSE calculation: https://www.youtube.com/watch?v=zMFdb__sUpw&ab_channel=KhanAcademy\n",
    "<br>[7] Regression coefficients: https://statisticsbyjim.com/glossary/regression-coefficient/\n",
    "<br>[8] Machine Learning Quiz 01: Linear Regression https://kawsar34.medium.com/machine-learning-quiz-01-a2fac2712a55\n",
    "<br>[9] Linear Regression Assumptions: https://www.statology.org/linear-regression-assumptions/\n",
    "<br>[10] Constant Variance: https://stats.stackexchange.com/questions/52089/what-does-having-constant-variance-in-a-linear-regression-model-mean\n",
    "<br>[11] Multiple Regression: https://www.youtube.com/watch?v=zITIFTsivN8&list=PLblh5JKOoLUICTaGLRoHQDuF_7q2GfuJF&index=11&ab_channel=StatQuestwithJoshStarmer\n",
    "<br>[12] Linear Regression Simplified - Ordinary Least Square vs Gradient Descent: https://towardsdatascience.com/linear-regression-simplified-ordinary-least-square-vs-gradient-descent-48145de2cf76"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Terminologies:\n",
    "\n",
    "- equation of a straight line: y=mx+c\n",
    "<br> Straight lines: https://github.com/SKawsar/Data_Visualization_with_Python/blob/main/Lecture_4.ipynb\n",
    "- feature coefficient (slope, gradient, m)\n",
    "- bias coeffcient (y-interccept, c)\n",
    "- domain: x-axis, independent variable\n",
    "- range: y-axis, dependent variable\n",
    "- loss function, cost function, objective function, error function\n",
    "- bias-variance tradeoff, overfitting, underfitting\n",
    "- ordinary least square method\n",
    "- gradient descent method\n",
    "- residual, error, squared error\n",
    "- train data, test data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import required Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>model</th>\n",
       "      <th>year</th>\n",
       "      <th>price</th>\n",
       "      <th>transmission</th>\n",
       "      <th>mileage</th>\n",
       "      <th>fuelType</th>\n",
       "      <th>mpg</th>\n",
       "      <th>engineSize</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>T-Roc</td>\n",
       "      <td>2019</td>\n",
       "      <td>25000</td>\n",
       "      <td>Automatic</td>\n",
       "      <td>13904</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>49.6</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>T-Roc</td>\n",
       "      <td>2019</td>\n",
       "      <td>26883</td>\n",
       "      <td>Automatic</td>\n",
       "      <td>4562</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>49.6</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>T-Roc</td>\n",
       "      <td>2019</td>\n",
       "      <td>20000</td>\n",
       "      <td>Manual</td>\n",
       "      <td>7414</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>50.4</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>T-Roc</td>\n",
       "      <td>2019</td>\n",
       "      <td>33492</td>\n",
       "      <td>Automatic</td>\n",
       "      <td>4825</td>\n",
       "      <td>Petrol</td>\n",
       "      <td>32.5</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>T-Roc</td>\n",
       "      <td>2019</td>\n",
       "      <td>22900</td>\n",
       "      <td>Semi-Auto</td>\n",
       "      <td>6500</td>\n",
       "      <td>Petrol</td>\n",
       "      <td>39.8</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    model  year  price transmission  mileage fuelType   mpg  engineSize\n",
       "0   T-Roc  2019  25000    Automatic    13904   Diesel  49.6         2.0\n",
       "1   T-Roc  2019  26883    Automatic     4562   Diesel  49.6         2.0\n",
       "2   T-Roc  2019  20000       Manual     7414   Diesel  50.4         2.0\n",
       "3   T-Roc  2019  33492    Automatic     4825   Petrol  32.5         2.0\n",
       "4   T-Roc  2019  22900    Semi-Auto     6500   Petrol  39.8         1.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(15157, 8)\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"vw.csv\")\n",
    "\n",
    "display(df.head())\n",
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 15157 entries, 0 to 15156\n",
      "Data columns (total 8 columns):\n",
      " #   Column        Non-Null Count  Dtype  \n",
      "---  ------        --------------  -----  \n",
      " 0   model         15157 non-null  object \n",
      " 1   year          15157 non-null  int64  \n",
      " 2   price         15157 non-null  int64  \n",
      " 3   transmission  15157 non-null  object \n",
      " 4   mileage       15157 non-null  int64  \n",
      " 5   fuelType      15157 non-null  object \n",
      " 6   mpg           15157 non-null  float64\n",
      " 7   engineSize    15157 non-null  float64\n",
      "dtypes: float64(2), int64(3), object(3)\n",
      "memory usage: 947.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        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>year</th>\n",
       "      <th>price</th>\n",
       "      <th>mileage</th>\n",
       "      <th>mpg</th>\n",
       "      <th>engineSize</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>15157.000000</td>\n",
       "      <td>15157.000000</td>\n",
       "      <td>15157.000000</td>\n",
       "      <td>15157.000000</td>\n",
       "      <td>15157.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2017.255789</td>\n",
       "      <td>16838.952365</td>\n",
       "      <td>22092.785644</td>\n",
       "      <td>53.753355</td>\n",
       "      <td>1.600693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.053059</td>\n",
       "      <td>7755.015206</td>\n",
       "      <td>21148.941635</td>\n",
       "      <td>13.642182</td>\n",
       "      <td>0.461695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2000.000000</td>\n",
       "      <td>899.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2016.000000</td>\n",
       "      <td>10990.000000</td>\n",
       "      <td>5962.000000</td>\n",
       "      <td>46.300000</td>\n",
       "      <td>1.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2017.000000</td>\n",
       "      <td>15497.000000</td>\n",
       "      <td>16393.000000</td>\n",
       "      <td>53.300000</td>\n",
       "      <td>1.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2019.000000</td>\n",
       "      <td>20998.000000</td>\n",
       "      <td>31824.000000</td>\n",
       "      <td>60.100000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2020.000000</td>\n",
       "      <td>69994.000000</td>\n",
       "      <td>212000.000000</td>\n",
       "      <td>188.300000</td>\n",
       "      <td>3.200000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               year         price        mileage           mpg    engineSize\n",
       "count  15157.000000  15157.000000   15157.000000  15157.000000  15157.000000\n",
       "mean    2017.255789  16838.952365   22092.785644     53.753355      1.600693\n",
       "std        2.053059   7755.015206   21148.941635     13.642182      0.461695\n",
       "min     2000.000000    899.000000       1.000000      0.300000      0.000000\n",
       "25%     2016.000000  10990.000000    5962.000000     46.300000      1.200000\n",
       "50%     2017.000000  15497.000000   16393.000000     53.300000      1.600000\n",
       "75%     2019.000000  20998.000000   31824.000000     60.100000      2.000000\n",
       "max     2020.000000  69994.000000  212000.000000    188.300000      3.200000"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-9600.0"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "120000*-0.08"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " Golf               4863\n",
       " Polo               3287\n",
       " Tiguan             1765\n",
       " Passat              915\n",
       " Up                  884\n",
       " T-Roc               733\n",
       " Touareg             363\n",
       " Touran              352\n",
       " T-Cross             300\n",
       " Golf SV             268\n",
       " Sharan              260\n",
       " Arteon              248\n",
       " Scirocco            242\n",
       " Amarok              111\n",
       " Caravelle           101\n",
       " CC                   95\n",
       " Tiguan Allspace      91\n",
       " Beetle               83\n",
       " Shuttle              61\n",
       " Caddy Maxi Life      59\n",
       " Jetta                32\n",
       " California           15\n",
       " Caddy Life            8\n",
       " Eos                   7\n",
       " Caddy                 6\n",
       " Caddy Maxi            4\n",
       " Fox                   4\n",
       "Name: model, dtype: int64"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"model\"].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['model', 'year', 'price', 'transmission', 'mileage', 'fuelType', 'mpg',\n",
       "       'engineSize'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Manual       9417\n",
       "Semi-Auto    3780\n",
       "Automatic    1960\n",
       "Name: transmission, dtype: int64"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"transmission\"].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Petrol    8553\n",
       "Diesel    6372\n",
       "Hybrid     145\n",
       "Other       87\n",
       "Name: fuelType, dtype: int64"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"fuelType\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Correlation plot: \n",
    "https://github.com/SKawsar/Data_Analysis_with_Python/blob/main/Lecture_8.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separating the features and target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of X =  (15157, 3)\n",
      "Shape of y =  (15157, 1)\n"
     ]
    }
   ],
   "source": [
    "features = ['year', 'mpg', 'engineSize']\n",
    "target = ['price']\n",
    "\n",
    "X = df[features]\n",
    "y = df[target]\n",
    "\n",
    "print(\"Shape of X = \", X.shape)\n",
    "print(\"Shape of y = \", y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create train and test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12125, 3) (3032, 3) (12125, 1) (3032, 1)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, \n",
    "                                                    y,\n",
    "                                                    test_size=0.2, \n",
    "                                                    random_state=42)\n",
    "\n",
    "print(X_train.shape, X_test.shape, y_train.shape, y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression()\n",
    "model = model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y = m1*x1 + m2*x2 + m3*x3 + m4*x4 + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2114.02170162 -106.30742038 8759.3771598 ]]\n"
     ]
    }
   ],
   "source": [
    "coefficients = model.coef_\n",
    "print(coefficients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4255990.43023728]\n"
     ]
    }
   ],
   "source": [
    "c = model.intercept_\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['year', 'mpg', 'engineSize'], dtype='object')"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>year</td>\n",
       "      <td>2114.021702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>mpg</td>\n",
       "      <td>-106.307420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>engineSize</td>\n",
       "      <td>8759.377160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     features  coefficients\n",
       "0        year   2114.021702\n",
       "1         mpg   -106.307420\n",
       "2  engineSize   8759.377160"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef_df = pd.DataFrame({\"features\": X.columns, \n",
    "                       \"coefficients\": np.squeeze(coefficients)})\n",
    "\n",
    "display(coef_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A positive sign indicates that as the feature variable increases, the target variable also increases.\n",
    "- A negative sign indicates that as the feature variable increases, the target variable decreases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[13304.86271129]\n",
      " [24646.01422239]\n",
      " [18355.60686375]\n",
      " ...\n",
      " [ 8375.19033353]\n",
      " [ 5771.45345778]\n",
      " [ 6261.1686319 ]]\n"
     ]
    }
   ],
   "source": [
    "y_pred = model.predict(X_test)\n",
    "print(y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       price\n",
      "7342   14450\n",
      "10328  23950\n",
      "14992  10495\n",
      "8466    9990\n",
      "10347  21998\n",
      "...      ...\n",
      "8211   17250\n",
      "8401   10450\n",
      "9810   10290\n",
      "7872    7499\n",
      "9399    7290\n",
      "\n",
      "[3032 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "print(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "# actual value - predicted value = +"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE =  2681.5051965262132\n",
      "MSE =  16459163.341451917\n",
      "RMSE =  4056.9894431033363\n",
      "r_squared =  0.7226377192887656\n"
     ]
    }
   ],
   "source": [
    "MAE = mean_absolute_error(y_test, y_pred)\n",
    "print(\"MAE = \", MAE)\n",
    "\n",
    "MSE = mean_squared_error(y_test, y_pred, squared=True)\n",
    "print(\"MSE = \", MSE)\n",
    "\n",
    "RMSE = mean_squared_error(y_test, y_pred, squared=False)\n",
    "print(\"RMSE = \", RMSE)\n",
    "\n",
    "r2 = r2_score(y_test, y_pred)\n",
    "print(\"r_squared = \", r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean_absolute_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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