machine learning multi linear from scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "      TV  Radio  Newspaper  Sales\n0  230.1   37.8       69.2   22.1\n1   44.5   39.3       45.1   10.4\n2   17.2   45.9       69.3   12.0\n3  151.5   41.3       58.5   16.5\n4  180.8   10.8       58.4   17.9",
      "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>TV</th>\n      <th>Radio</th>\n      <th>Newspaper</th>\n      <th>Sales</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>230.1</td>\n      <td>37.8</td>\n      <td>69.2</td>\n      <td>22.1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>44.5</td>\n      <td>39.3</td>\n      <td>45.1</td>\n      <td>10.4</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>17.2</td>\n      <td>45.9</td>\n      <td>69.3</td>\n      <td>12.0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>151.5</td>\n      <td>41.3</td>\n      <td>58.5</td>\n      <td>16.5</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>180.8</td>\n      <td>10.8</td>\n      <td>58.4</td>\n      <td>17.9</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# importing required packages\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split  # to split dataset\n",
    "from sklearn.linear_model import LinearRegression\n",
    "df  = pd.read_csv('advertising.csv')\n",
    "df.head()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape : (200, 4)\n",
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 200 entries, 0 to 199\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   TV         200 non-null    float64\n",
      " 1   Radio      200 non-null    float64\n",
      " 2   Newspaper  200 non-null    float64\n",
      " 3   Sales      200 non-null    float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 6.4 KB\n",
      "-------------=============================================------------------\n",
      "               TV       Radio   Newspaper       Sales\n",
      "count  200.000000  200.000000  200.000000  200.000000\n",
      "mean   147.042500   23.264000   30.554000   15.130500\n",
      "std     85.854236   14.846809   21.778621    5.283892\n",
      "min      0.700000    0.000000    0.300000    1.600000\n",
      "25%     74.375000    9.975000   12.750000   11.000000\n",
      "50%    149.750000   22.900000   25.750000   16.000000\n",
      "75%    218.825000   36.525000   45.100000   19.050000\n",
      "max    296.400000   49.600000  114.000000   27.000000\n"
     ]
    }
   ],
   "source": [
    "print(\"shape :\",df.shape)\n",
    "df.info()\n",
    "print('-------------=============================================------------------')\n",
    "print(df.describe())"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataplot = sns.heatmap(df.corr(), annot=True)\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 3) (200,)\n",
      "Size of Train set: 140\n",
      "Size of Test set: 60\n"
     ]
    }
   ],
   "source": [
    "x = df.drop('Sales',axis=1)\n",
    "y = df['Sales']\n",
    "# converting to numpy array\n",
    "x = np.array(x)\n",
    "y = np.array(y)\n",
    "\n",
    "# creating function for normalization of data\n",
    "def norm(x):\n",
    "    meanX = np.mean(x)\n",
    "    m = np.max(x)\n",
    "    n = np.min(x)\n",
    "    x= (x-meanX)/(m-n)\n",
    "    return x\n",
    "\n",
    "# creating function for Standardisation of data\n",
    "def stand(x):\n",
    "    x = (x-np.mean(x))/np.std(x)\n",
    "    return x\n",
    "\n",
    "x = stand(x)\n",
    "y = stand(y)\n",
    "print(x.shape,y.shape)\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, train_size=0.7, random_state=1)\n",
    "print(f\"Size of Train set: {y_train.shape[0]}\")\n",
    "print(f\"Size of Test set: {x_test.shape[0]}\")"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration:  0 current cost : 1.0281150585911458 current weight: [0.19573253 0.01904836 0.01492665] bias : -0.010725128810655725\n",
      "iteration:  1 current cost : 0.7140264811073166 current weight: [0.30908311 0.05630479 0.04453637] bias : -0.054340115127635334\n",
      "iteration:  2 current cost : 0.5616831526541691 current weight: [0.38692151 0.09668711 0.07619435] bias : -0.10451451252739635\n",
      "iteration:  3 current cost : 0.4577911376405934 current weight: [0.4470353  0.13516049 0.10573279] bias : -0.15237206974781464\n",
      "iteration:  4 current cost : 0.380721088842862 current weight: [0.49652883 0.17028848 0.13201004] bias : -0.19529841126211062\n",
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      "iteration:  561 current cost : 0.10330584465392811 current weight: [ 8.01928877e-01  1.42784312e+00 -9.95868629e-04] bias : -0.0325768986639464\n",
      "iteration:  562 current cost : 0.10330441229163546 current weight: [ 8.01925558e-01  1.42817455e+00 -1.10263102e-03] bias : -0.032432375734237205\n",
      "iteration:  563 current cost : 0.10330299451026773 current weight: [ 8.01922256e-01  1.42850429e+00 -1.20885044e-03] bias : -0.03228859136772939\n",
      "iteration:  564 current cost : 0.1033015911613963 current weight: [ 8.01918972e-01  1.42883234e+00 -1.31452962e-03] bias : -0.03214554178234739\n",
      "iteration:  565 current cost : 0.10330020209810346 current weight: [ 8.01915703e-01  1.42915872e+00 -1.41967132e-03] bias : -0.032003223215477966\n",
      "iteration:  566 current cost : 0.10329882717496704 current weight: [ 0.80191245  1.42948344 -0.00152428] bias : -0.03186163192386884\n",
      "iteration:  567 current cost : 0.10329746624804524 current weight: [ 0.80190922  1.4298065  -0.00162835] bias : -0.031720764183527976\n",
      "iteration:  568 current cost : 0.1032961191748616 current weight: [ 0.801906    1.43012791 -0.0017319 ] bias : -0.0315806162896234\n",
      "iteration:  569 current cost : 0.10329478581438993 current weight: [ 0.8019028   1.43044767 -0.00183492] bias : -0.031441184556383436\n",
      "iteration:  570 current cost : 0.10329346602703972 current weight: [ 0.80189961  1.43076581 -0.00193741] bias : -0.03130246531699757\n",
      "iteration:  571 current cost : 0.10329215967464139 current weight: [ 0.80189644  1.43108232 -0.00203939] bias : -0.03116445492351779\n",
      "iteration:  572 current cost : 0.10329086662043194 current weight: [ 0.80189329  1.43139722 -0.00214084] bias : -0.031027149746760543\n",
      "iteration:  573 current cost : 0.10328958672904044 current weight: [ 0.80189016  1.43171051 -0.00224178] bias : -0.030890546176209063\n",
      "iteration:  574 current cost : 0.10328831986647419 current weight: [ 0.80188704  1.43202221 -0.0023422 ] bias : -0.030754640619916385\n",
      "iteration:  575 current cost : 0.10328706590010435 current weight: [ 0.80188393  1.43233231 -0.00244212] bias : -0.03061942950440874\n",
      "iteration:  576 current cost : 0.10328582469865225 current weight: [ 0.80188084  1.43264083 -0.00254152] bias : -0.030484909274589633\n",
      "iteration:  577 current cost : 0.10328459613217551 current weight: [ 0.80187777  1.43294777 -0.00264042] bias : -0.030351076393644143\n",
      "iteration:  578 current cost : 0.10328338007205466 current weight: [ 0.80187471  1.43325315 -0.00273882] bias : -0.030217927342944057\n",
      "iteration:  579 current cost : 0.10328217639097947 current weight: [ 0.80187167  1.43355697 -0.00283672] bias : -0.030085458621953352\n",
      "iteration:  580 current cost : 0.10328098496293564 current weight: [ 0.80186865  1.43385924 -0.00293412] bias : -0.029953666748134152\n",
      "iteration:  581 current cost : 0.1032798056631917 current weight: [ 0.80186564  1.43415997 -0.00303102] bias : -0.029822548256853213\n",
      "iteration:  582 current cost : 0.1032786383682859 current weight: [ 0.80186264  1.43445916 -0.00312743] bias : -0.02969209970128896\n",
      "iteration:  583 current cost : 0.10327748295601327 current weight: [ 0.80185966  1.43475683 -0.00322335] bias : -0.029562317652338962\n",
      "iteration:  584 current cost : 0.1032763393054129 current weight: [ 0.8018567   1.43505297 -0.00331878] bias : -0.02943319869852795\n",
      "iteration:  585 current cost : 0.10327520729675516 current weight: [ 0.80185375  1.43534761 -0.00341372] bias : -0.02930473944591621\n",
      "iteration:  586 current cost : 0.10327408681152923 current weight: [ 0.80185082  1.43564074 -0.00350819] bias : -0.02917693651800861\n",
      "iteration:  587 current cost : 0.10327297773243076 current weight: [ 0.8018479   1.43593238 -0.00360217] bias : -0.029049786555664012\n",
      "iteration:  588 current cost : 0.10327187994334941 current weight: [ 0.80184499  1.43622252 -0.00369567] bias : -0.028923286217005198\n",
      "iteration:  589 current cost : 0.10327079332935689 current weight: [ 0.80184211  1.43651119 -0.0037887 ] bias : -0.028797432177329274\n",
      "iteration:  590 current cost : 0.10326971777669484 current weight: [ 0.80183923  1.43679838 -0.00388125] bias : -0.028672221129018554\n",
      "iteration:  591 current cost : 0.10326865317276285 current weight: [ 0.80183637  1.43708411 -0.00397334] bias : -0.028547649781451915\n",
      "iteration:  592 current cost : 0.10326759940610682 current weight: [ 0.80183353  1.43736838 -0.00406495] bias : -0.028423714860916605\n",
      "iteration:  593 current cost : 0.10326655636640716 current weight: [ 0.8018307  1.4376512 -0.0041561] bias : -0.028300413110520506\n",
      "iteration:  594 current cost : 0.10326552394446738 current weight: [ 0.80182788  1.43793258 -0.00424678] bias : -0.028177741290104915\n",
      "iteration:  595 current cost : 0.10326450203220242 current weight: [ 0.80182508  1.43821252 -0.00433701] bias : -0.028055696176157795\n",
      "iteration:  596 current cost : 0.10326349052262761 current weight: [ 0.80182229  1.43849103 -0.00442677] bias : -0.02793427456172742\n",
      "iteration:  597 current cost : 0.10326248930984736 current weight: [ 0.80181952  1.43876812 -0.00451608] bias : -0.02781347325633645\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# creating linearRegression Function\n",
    "def linearRegression(x,y,iterations  = 1000 ,learning_rate = 0.001,stopping = 1e-6):\n",
    "    # giving initial values to weight and bias\n",
    "    m = np.zeros(x.shape[1])   #weight\n",
    "    c = 0                      #bias\n",
    "\n",
    "    n = float(len(x))\n",
    "    costs = []\n",
    "    weights  = []\n",
    "    bias =[]\n",
    "    previous_cost  = 0\n",
    "    for i in range(iterations):\n",
    "        # calculating y\n",
    "        Yp = np.dot(x , m) + c\n",
    "        # calculating cost\n",
    "        cost = (np.square(np.subtract(y,Yp)).mean())\n",
    "        costs.append(cost)\n",
    "\n",
    "        weights.append(m)\n",
    "        bias.append(c)\n",
    "        if i > 0:\n",
    "            if np.abs(cost - previous_cost) < stopping:\n",
    "                break\n",
    "\n",
    "        # calculating derivative\n",
    "        weight_derivative = (2/n) *np.dot(x.T , (Yp-y))\n",
    "        bias_derivative = (2/n) * sum(Yp-y)\n",
    "        # modifying weight and bias\n",
    "        m = m - (learning_rate * weight_derivative)\n",
    "        c = c - (learning_rate * bias_derivative)\n",
    "        previous_cost = cost\n",
    "        print('iteration: ',i,'current cost :',cost,'current weight:',m,'bias :',c)\n",
    "    plt.plot(costs)\n",
    "    plt.xlabel('Iteration')\n",
    "    plt.ylabel('Cost')\n",
    "    plt.show()\n",
    "    # returning last weight and bias\n",
    "    return m,c\n",
    "\n",
    "m,c = linearRegression(x_train,y_train,learning_rate = 0.1,iterations = 1000)\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mse:      0.22877358969346784\n",
      "r2_score: 0.9062394305298411\n"
     ]
    }
   ],
   "source": [
    "y_pred = np.dot(m,x_test.T) + c\n",
    "\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "m = mean_absolute_error(y_test, y_pred)\n",
    "from sklearn.metrics import r2_score\n",
    "r = r2_score(y_test, y_pred)\n",
    "print(\"mse:     \",m)\n",
    "print(\"r2_score:\",r)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mse:      0.2266775623001647\n",
      "r2_score: 0.9071151423684273\n",
      "intercept: -0.004272190875330539\n",
      "slope: [ 0.80127987  1.49279121 -0.02194706]\n"
     ]
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(x_train, y_train)\n",
    "model.score(x_train, y_train)\n",
    "model.score(x_test, y_test)\n",
    "y_pred = model.predict(x_test)\n",
    "m = mean_absolute_error(y_test, y_pred)\n",
    "r = r2_score(y_test, y_pred)\n",
    "print(\"mse:     \",m)\n",
    "print(\"r2_score:\",r)\n",
    "print('intercept:', model.intercept_)\n",
    "print('slope:', model.coef_)"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}