3. Linear Regression using Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7e3c88c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "61f5ed28",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris=pd.read_csv('iris.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7c886676",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 150 entries, 0 to 149\n",
      "Data columns (total 6 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   Id             150 non-null    int64  \n",
      " 1   SepalLengthCm  150 non-null    float64\n",
      " 2   SepalWidthCm   150 non-null    float64\n",
      " 3   PetalLengthCm  150 non-null    float64\n",
      " 4   PetalWidthCm   150 non-null    float64\n",
      " 5   Species        150 non-null    object \n",
      "dtypes: float64(4), int64(1), object(1)\n",
      "memory usage: 7.2+ KB\n"
     ]
    }
   ],
   "source": [
    "iris.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d32ec21e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>75.500000</td>\n",
       "      <td>5.843333</td>\n",
       "      <td>3.054000</td>\n",
       "      <td>3.758667</td>\n",
       "      <td>1.198667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>43.445368</td>\n",
       "      <td>0.828066</td>\n",
       "      <td>0.433594</td>\n",
       "      <td>1.764420</td>\n",
       "      <td>0.763161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.300000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>38.250000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>75.500000</td>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>1.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>112.750000</td>\n",
       "      <td>6.400000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>1.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>7.900000</td>\n",
       "      <td>4.400000</td>\n",
       "      <td>6.900000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm\n",
       "count  150.000000     150.000000    150.000000     150.000000    150.000000\n",
       "mean    75.500000       5.843333      3.054000       3.758667      1.198667\n",
       "std     43.445368       0.828066      0.433594       1.764420      0.763161\n",
       "min      1.000000       4.300000      2.000000       1.000000      0.100000\n",
       "25%     38.250000       5.100000      2.800000       1.600000      0.300000\n",
       "50%     75.500000       5.800000      3.000000       4.350000      1.300000\n",
       "75%    112.750000       6.400000      3.300000       5.100000      1.800000\n",
       "max    150.000000       7.900000      4.400000       6.900000      2.500000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5351a8c5",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>92</td>\n",
       "      <td>6.1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>Iris-versicolor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "      <td>5.4</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>145</td>\n",
       "      <td>6.7</td>\n",
       "      <td>3.3</td>\n",
       "      <td>5.7</td>\n",
       "      <td>2.5</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>93</td>\n",
       "      <td>5.8</td>\n",
       "      <td>2.6</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>Iris-versicolor</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
       "91    92            6.1           3.0            4.6           1.4   \n",
       "20    21            5.4           3.4            1.7           0.2   \n",
       "144  145            6.7           3.3            5.7           2.5   \n",
       "92    93            5.8           2.6            4.0           1.2   \n",
       "\n",
       "             Species  \n",
       "91   Iris-versicolor  \n",
       "20       Iris-setosa  \n",
       "144   Iris-virginica  \n",
       "92   Iris-versicolor  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.sample(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "286df36c",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
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       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  Species\n",
       "0    False          False         False          False         False    False\n",
       "1    False          False         False          False         False    False\n",
       "2    False          False         False          False         False    False\n",
       "3    False          False         False          False         False    False\n",
       "4    False          False         False          False         False    False\n",
       "..     ...            ...           ...            ...           ...      ...\n",
       "145  False          False         False          False         False    False\n",
       "146  False          False         False          False         False    False\n",
       "147  False          False         False          False         False    False\n",
       "148  False          False         False          False         False    False\n",
       "149  False          False         False          False         False    False\n",
       "\n",
       "[150 rows x 6 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.isnull()==True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "740f07f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.isnull().values.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9029ca17",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 0\n",
    "c = 0\n",
    "alpha = 0.01\n",
    "# learninig rate: alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66feec99",
   "metadata": {},
   "source": [
    "The algorithm starts with some value of m and c (usually starts with m=0, c=0). We calculate MSE - Mean Squared Error (cost) at point m=0, c=0. Let say the MSE (cost) at m=0, c=0 is 100. Then we reduce the value of m and c by some amount (Learning Step). We will notice a decrease in MSE (cost). We will continue doing the same until our loss function is a very small value or ideally 0 (which means 0 error or 100% accuracy)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3fd219c",
   "metadata": {},
   "source": [
    "1. Let m = 0 and c = 0. Let L be our learning rate. It could be a small value like 0.01 for good accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f334b511",
   "metadata": {},
   "source": [
    "Learning rate gives the rate of speed where the gradient moves during gradient descent. Setting it too high would make your path instable, too low would make convergence slow. Put it to zero means your model isn’t learning anything from the gradients."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "193cd2c4",
   "metadata": {},
   "source": [
    "2. Calculate the partial derivative of the Cost function with respect to m. Let partial derivative of the Cost function with respect to m be Dm (With little change in m how much Cost function changes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4b5ed000",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris['SepalLengthCm'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a6a13128",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.1, 4.9, 4.7, 4.6, 5. , 5.4, 4.6, 5. , 4.4, 4.9, 5.4, 4.8, 4.8,\n",
       "       4.3, 5.8, 5.7, 5.4, 5.1, 5.7, 5.1, 5.4, 5.1, 4.6, 5.1, 4.8, 5. ,\n",
       "       5. , 5.2, 5.2, 4.7, 4.8, 5.4, 5.2, 5.5, 4.9, 5. , 5.5, 4.9, 4.4,\n",
       "       5.1, 5. , 4.5, 4.4, 5. , 5.1, 4.8, 5.1, 4.6, 5.3, 5. , 7. , 6.4,\n",
       "       6.9, 5.5, 6.5, 5.7, 6.3, 4.9, 6.6, 5.2, 5. , 5.9, 6. , 6.1, 5.6,\n",
       "       6.7, 5.6, 5.8, 6.2, 5.6, 5.9, 6.1, 6.3, 6.1, 6.4, 6.6, 6.8, 6.7,\n",
       "       6. , 5.7, 5.5, 5.5, 5.8, 6. , 5.4, 6. , 6.7, 6.3, 5.6, 5.5, 5.5,\n",
       "       6.1, 5.8, 5. , 5.6, 5.7, 5.7, 6.2, 5.1, 5.7, 6.3, 5.8, 7.1, 6.3,\n",
       "       6.5, 7.6, 4.9, 7.3, 6.7, 7.2, 6.5, 6.4, 6.8, 5.7, 5.8, 6.4, 6.5,\n",
       "       7.7, 7.7, 6. , 6.9, 5.6, 7.7, 6.3, 6.7, 7.2, 6.2, 6.1, 6.4, 7.2,\n",
       "       7.4, 7.9, 6.4, 6.3, 6.1, 7.7, 6.3, 6.4, 6. , 6.9, 6.7, 6.9, 5.8,\n",
       "       6.8, 6.7, 6.7, 6.3, 6.5, 6.2, 5.9])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3e544ef0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = iris['PetalLengthCm'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4e4e0fae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.4, 1.4, 1.3, 1.5, 1.4, 1.7, 1.4, 1.5, 1.4, 1.5, 1.5, 1.6, 1.4,\n",
       "       1.1, 1.2, 1.5, 1.3, 1.4, 1.7, 1.5, 1.7, 1.5, 1. , 1.7, 1.9, 1.6,\n",
       "       1.6, 1.5, 1.4, 1.6, 1.6, 1.5, 1.5, 1.4, 1.5, 1.2, 1.3, 1.5, 1.3,\n",
       "       1.5, 1.3, 1.3, 1.3, 1.6, 1.9, 1.4, 1.6, 1.4, 1.5, 1.4, 4.7, 4.5,\n",
       "       4.9, 4. , 4.6, 4.5, 4.7, 3.3, 4.6, 3.9, 3.5, 4.2, 4. , 4.7, 3.6,\n",
       "       4.4, 4.5, 4.1, 4.5, 3.9, 4.8, 4. , 4.9, 4.7, 4.3, 4.4, 4.8, 5. ,\n",
       "       4.5, 3.5, 3.8, 3.7, 3.9, 5.1, 4.5, 4.5, 4.7, 4.4, 4.1, 4. , 4.4,\n",
       "       4.6, 4. , 3.3, 4.2, 4.2, 4.2, 4.3, 3. , 4.1, 6. , 5.1, 5.9, 5.6,\n",
       "       5.8, 6.6, 4.5, 6.3, 5.8, 6.1, 5.1, 5.3, 5.5, 5. , 5.1, 5.3, 5.5,\n",
       "       6.7, 6.9, 5. , 5.7, 4.9, 6.7, 4.9, 5.7, 6. , 4.8, 4.9, 5.6, 5.8,\n",
       "       6.1, 6.4, 5.6, 5.1, 5.6, 6.1, 5.6, 5.5, 4.8, 5.4, 5.6, 5.1, 5.1,\n",
       "       5.9, 5.7, 5.2, 5. , 5.2, 5.4, 5.1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
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   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6c86a74f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "150"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cc827c2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2937359d",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def Gradient_Descent(X, Y, m, c, alpha, iters):\n",
    "    \n",
    "    dm = 0\n",
    "    dc = 0\n",
    "    \n",
    "    n = len(X)\n",
    "    \n",
    "    for j in range(iters):\n",
    "        \n",
    "        for i in range(n):\n",
    "            y_pred_i = m*X[i] + c\n",
    "            \n",
    "             # dj = (1/2*n)*(y_pred - Y[i])**2\n",
    "            \n",
    "            dm = dm + (Y[i] - y_pred_i)*X[i]\n",
    "            dc = dc + (Y[i] - y_pred_i)\n",
    "            \n",
    "        dm = (-1*2/n)*dm\n",
    "        dc = (-1*2/n)*dc\n",
    "        \n",
    "        m = m - alpha*dm\n",
    "        c = c - alpha*dc\n",
    "    \n",
    "    return m, c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8e6434ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final M:1.829210537829152 and Final C:-6.926813707832797\n"
     ]
    }
   ],
   "source": [
    "m = 0\n",
    "c = 0\n",
    "\n",
    "alpha = 0.01\n",
    "\n",
    "iters = 10000\n",
    "\n",
    "m_final, c_final =  Gradient_Descent(X, Y, m, c, alpha, iters)\n",
    "\n",
    "print(f\"Final M:{m_final} and Final C:{c_final}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8c3f4cbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y)\n",
    "\n",
    "y_pred = m_final*X + c_final\n",
    "plt.plot(X, y_pred)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a1f2e5f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c4c4613",
   "metadata": {},
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