LinReg_Stu.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Motivation\n",
    "The end-term paper for the Probability course, undertaken in the third semester, had a question about linear regression. The question established that there is some linear correlation between the marks a student scores in their assignment and their end-term papers.\\\n",
    "We were supposed to find this linear relation.\\\n",
    "Now, I want to explore the difference between the answers from two methods, one being the classical mathematics apporaoch taught to us and the other being the approach that uses machine learning model.\\\n",
    "Based on the outcome, we will be able to acertain the closeness of each method. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Methodology\n",
    "The question itself has a very small dataset, because the question was supposed to be done in an examination using only calsulators and matrix multiplication.\\\n",
    "That being said, I will convert the data given in the question into a .csv type file and then use Pandas to manipulate the dataframe and run the regression model. There will not be a test-train split, because I am not making a prediction model, I am interested in getting the parameters of the linear regression.\\\n",
    "On the flip side of the project, I will use tensors to condeuct matrix multiplication and get the answers.\\\n",
    "I will then compare both."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Question\n",
    "Students in a probability course claimed that doing the assignments\n",
    "had not helped prepare them for the end-term exam. The end-term exam score\n",
    "y and assignment score x (averaged up to the time of the end-term) for the\n",
    "n = 18 students in the class are in the table below as:\n",
    "\n",
    "x | 96 77 0 0 78 64 89 47 90 93 18 86 0 30 59 77 74 67\\\n",
    "y | 95 80 0 0 79 77 72 66 98 90 0 95 35 50 72 55 75 66"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing Necessary Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "# importing the libraries required"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning Approach\n",
    "I will now use Pandas and Scikit-Learn to get the Linear Regression model, and its metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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>Assignment_Scores</th>\n",
       "      <th>End-Term_Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>96</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>77</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>78</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Assignment_Scores  End-Term_Scores\n",
       "0                 96               95\n",
       "1                 77               80\n",
       "2                  0                0\n",
       "3                  0                0\n",
       "4                 78               79"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# making the dataframe using Pandas\n",
    "df = pd.read_csv(\"Student_Scores.csv\")\n",
    "\n",
    "# confirming the data is correctly indexed and labelled using df.head()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "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>Assignment_Scores</th>\n",
       "      <th>End-Term_Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>18.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>58.055556</td>\n",
       "      <td>61.388889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>33.895119</td>\n",
       "      <td>32.489164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>34.250000</td>\n",
       "      <td>51.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>70.500000</td>\n",
       "      <td>72.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>84.000000</td>\n",
       "      <td>79.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>96.000000</td>\n",
       "      <td>98.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Assignment_Scores  End-Term_Scores\n",
       "count          18.000000        18.000000\n",
       "mean           58.055556        61.388889\n",
       "std            33.895119        32.489164\n",
       "min             0.000000         0.000000\n",
       "25%            34.250000        51.250000\n",
       "50%            70.500000        72.000000\n",
       "75%            84.000000        79.750000\n",
       "max            96.000000        98.000000"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking the data and some of the usual statistics\n",
    "\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[96 77  0  0 78 64 89 47 90 93 18 86  0 30 59 77 74 67]\n",
      "[95 80  0  0 79 77 72 66 98 90  0 95 35 50 72 55 75 66]\n"
     ]
    }
   ],
   "source": [
    "# copying the data into arrays from the dataframe\n",
    "\n",
    "x = df['Assignment_Scores'].to_numpy()\n",
    "print(x)\n",
    "y = df['End-Term_Scores'].to_numpy()\n",
    "print(y)\n",
    "\n",
    "# converting the arrays into usabel arrays for the Linear Regression Model\n",
    "\n",
    "x_train = x.reshape(-1, 1)\n",
    "y_train = y.reshape(-1, 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'End-Term Scores')"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# just a scatter plot of the data\n",
    "\n",
    "plt.scatter(x, y, color = 'red')\n",
    "plt.xlabel('Assignment Scores')\n",
    "plt.ylabel('End-Term Scores')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</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 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 sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# importing the Linear Regression model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# getting the model and fitting it to the data\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Model Coeff (m) = [[0.87264654]]\n",
      "Linear Model Coeff (b) = [10.72690915]\n"
     ]
    }
   ],
   "source": [
    "# Getting Results\n",
    "# coefficients of the Linear Regression\n",
    "\n",
    "print('Linear Model Coeff (m) =' , model.coef_)\n",
    "print('Linear Model Coeff (b) =' , model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the output\n",
    "\n",
    "%matplotlib inline\n",
    "plt.scatter(x, y, color = 'blue', label = 'Scatter Plot')\n",
    "reg_lin = model.coef_ * x_train + model.intercept_\n",
    "plt.plot(x, reg_lin, color = 'orange', label = 'Regression Line') \n",
    "plt.xlabel('Assignment Marks')\n",
    "plt.ylabel('End-Term Marks')\n",
    "plt.title('Linear Regression done using Machine Algorithm')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Matrix Multiplication\n",
    "Now, I will use the matrix multiplication form and get the slope and intercept of the linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "# converting numpy arrays into matrices\n",
    "\n",
    "mat_x = np.column_stack((x_train, np.ones_like(x_train)))\n",
    "mat_y = y.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.87264654]\n",
      " [10.72690915]]\n"
     ]
    }
   ],
   "source": [
    "# doing the matrix multiplication to find the slope and the intercept\n",
    "# (b, m) = ((X^T * X)^-) * (X^T * Y)\n",
    "# mat_a = np.dot(mat_x.T, mat_x)\n",
    "# mat_b = np.dot(mat_x.T, mat_y)\n",
    "\n",
    "mat_fin = np.dot(np.linalg.inv(np.dot(mat_x.T, mat_x)), np.dot(mat_x.T, mat_y))\n",
    "print(mat_fin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8726465409592189 10.726909149867566\n"
     ]
    }
   ],
   "source": [
    "# checking the matrix \n",
    "\n",
    "print(mat_fin[0,0], mat_fin[1, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the output\n",
    "\n",
    "%matplotlib inline\n",
    "plt.scatter(x, y, color = 'blue', label = 'Scatter Plot')\n",
    "reg_line = mat_fin[0,0] * x_train + mat_fin[1,0]\n",
    "plt.plot(x, reg_line, color = 'green', label = 'Regression Line') \n",
    "plt.xlabel('Assignment Marks')\n",
    "plt.ylabel('End-Term Marks')\n",
    "plt.title('Linear Regression done using Matrix Multiplication')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison\n",
    "Looking at the plots, it is imperative that both methods yield coefficients that are very similiar to each other, correct to significant decimal values. Given below is a comparative graph of the data points and the regression lines drawn from the two methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the comparison\n",
    "\n",
    "plt.scatter(x, y, color = 'blue', label = 'Scatter Plot')\n",
    "reg_lin = model.coef_ * x_train + model.intercept_\n",
    "plt.plot(x, reg_lin, color = 'orange', label = 'ML Regression Line') \n",
    "reg_line = mat_fin[0,0] * x_train + mat_fin[1,0]\n",
    "plt.plot(x, reg_line, color = 'green', linestyle = 'dotted', label = 'Matrix Regression Line') \n",
    "plt.xlabel('Assignment Marks')\n",
    "plt.ylabel('End-Term Marks')\n",
    "plt.title('Machine Learning Algorithm v/s Matrix Multiplication Method')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In this case, it's interesting to note that the coefficients obtained from the matrix multiplication method match those obtained from the machine learning algorithm. This consistency is expected because both methods are essentially solving the same linear regression problem.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "In this study, we explored and compared two methods for linear regression: the traditional machine learning approach using scikit-learn and a novel method based on matrix multiplication. The objective was to predict end-term marks based on assignment marks.\n",
    "\n",
    "**Machine Learning Algorithm**\n",
    "Using the scikit-learn library, we trained a linear regression model on our dataset. The resulting coefficients for the linear model were found to be:\n",
    "\n",
    "Slope (m): 0.8726\\\n",
    "Y-intercept (b): 10.7269\\\n",
    "The regression equation,\\ \n",
    "End-Term Marks = 0.8726 × Assignment Marks + 10.7269\\\n",
    "End-Term Marks = 0.8726 × Assignment Marks + 10.7269, accurately captures the relationship between assignment marks and end-term marks as learned by the machine learning algorithm.\n",
    "\n",
    "**Matrix Multiplication Method**\n",
    "An alternative approach involved solving the linear regression problem through matrix multiplication. The resulting coefficients obtained were remarkably consistent with those from the machine learning algorithm:\n",
    "\n",
    "Slope (m): 0.8726\\\n",
    "Y-intercept (b): 10.7269\\\n",
    "This not only validates the accuracy of our machine learning model but also demonstrates the equivalence between the two methods in solving the linear regression problem.\\\n",
    "\n",
    "**Conclusion and Implications**\n",
    "The successful alignment of coefficients from both methods reinforces our confidence in the accuracy of the linear regression model. This study has practical implications, showcasing that the mathematical foundation of linear regression can be leveraged through matrix manipulation, providing an alternative avenue for those seeking a deeper understanding of the underlying principles.\n",
    "\n",
    "As we move forward, this exploration opens avenues for further investigation into the relationships between various machine learning algorithms and their mathematical counterparts. Additionally, it emphasizes the importance of understanding the fundamental operations that power these algorithms.\n",
    "\n",
    "In conclusion, our study highlights the synergy between traditional machine learning approaches and mathematical techniques, offering valuable insights for both practitioners and enthusiasts in the field."
   ]
  }
 ],
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