Polynomial Regression/Polynomial Regression ( From Scratch ).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.646079</td>\n",
       "      <td>15.377223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.600236</td>\n",
       "      <td>0.253358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.468107</td>\n",
       "      <td>0.892842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.361340</td>\n",
       "      <td>28.497259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.801337</td>\n",
       "      <td>17.295326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-1.465917</td>\n",
       "      <td>-1.023191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.425133</td>\n",
       "      <td>2.559774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.227036</td>\n",
       "      <td>-5.590461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.154828</td>\n",
       "      <td>-2.076532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.615898</td>\n",
       "      <td>-1.025788</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "          x          y\n",
       "0  2.646079  15.377223\n",
       "1  0.600236   0.253358\n",
       "2  1.468107   0.892842\n",
       "3  3.361340  28.497259\n",
       "4  2.801337  17.295326\n",
       "5 -1.465917  -1.023191\n",
       "6  1.425133   2.559774\n",
       "7 -0.227036  -5.590461\n",
       "8 -0.154828  -2.076532\n",
       "9  0.615898  -1.025788"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generating some random data where x is input variable and y is target variable\n",
    "np.random.seed(0)  # it used to stop the randomness if we run this code again and again\n",
    "x = np.random.normal(0,1.5,1000)\n",
    "y =  (x ** 2) + 0.5 * (x ** 3) + np.random.normal(-2, 2, 1000)\n",
    "raw_data = pd.DataFrame([x,y]).T\n",
    "raw_data.columns = ['x','y']\n",
    "raw_data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data Preprocessing \n",
    "train_data = raw_data.iloc[:750,:]\n",
    "train_data_x = raw_data.iloc[:750,0]\n",
    "train_data_y = raw_data.iloc[:750,1]\n",
    "\n",
    "test_data  = raw_data.iloc[750:,:]\n",
    "test_data_x = raw_data.iloc[750:,0]\n",
    "test_data_y =raw_data.iloc[750:,1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train_data['x'] , train_data['y'] , s = 10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This function create more features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>x</th>\n",
       "      <th>xx</th>\n",
       "      <th>xxx</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.646079</td>\n",
       "      <td>7.001732</td>\n",
       "      <td>18.527131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.600236</td>\n",
       "      <td>0.360283</td>\n",
       "      <td>0.216255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.468107</td>\n",
       "      <td>2.155338</td>\n",
       "      <td>3.164267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.361340</td>\n",
       "      <td>11.298605</td>\n",
       "      <td>37.978451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.801337</td>\n",
       "      <td>7.847489</td>\n",
       "      <td>21.983461</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         xx        xxx\n",
       "0  2.646079   7.001732  18.527131\n",
       "1  0.600236   0.360283   0.216255\n",
       "2  1.468107   2.155338   3.164267\n",
       "3  3.361340  11.298605  37.978451\n",
       "4  2.801337   7.847489  21.983461"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def poly_Feature(degree , data):\n",
    "    ''' Pass data as DataFrame '''\n",
    "    new_data = data.copy()\n",
    "    p = pd.DataFrame()\n",
    "    from itertools import combinations_with_replacement \n",
    "    z = []\n",
    "    for i in range(1,degree + 1):\n",
    "        t = list(combinations_with_replacement(new_data.columns , i ))\n",
    "        for j in t:\n",
    "            x = 1\n",
    "            st = ''\n",
    "            for k in j:\n",
    "                st+=k\n",
    "                x *= new_data[k]\n",
    "            p[st] = x\n",
    "    return p\n",
    "\n",
    "poly_Feature(3,pd.DataFrame(train_data_x) ).head()  # we are passing our data for increase features with degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "h_{\\theta}(x)=\\theta_{0}+\\theta_{1} x_{1}+\\theta_{2} x_{2}\n",
    "$$\n",
    "\n",
    "$$\n",
    "h(x)=\\sum_{i=0}^{n} \\theta_{i} x_{i}=\\theta^{T} x\n",
    "$$\n",
    "\n",
    "**The Cost function is:** \n",
    "$$\n",
    "J(\\theta)=\\frac{1}{2} \\sum_{i=1}^{m}\\left(h_{\\theta}\\left(x^{(i)}\\right)-y^{(i)}\\right)^{2}\n",
    "$$\n",
    "\n",
    "Now we have to minimize this cost function\n",
    "\n",
    "for gradient decent we have a formula :\n",
    "\n",
    "$$\n",
    "\\theta_{j} :=\\theta_{j}-\\alpha \\frac{\\partial}{\\partial \\theta_{j}} J(\\theta)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{aligned} \\frac{\\partial}{\\partial \\theta_{j}} J(\\theta) &=\\frac{\\partial}{\\partial \\theta_{j}} \\frac{1}{2}\\left(h_{\\theta}(x)-y\\right)^{2} \\\\ &=2 \\cdot \\frac{1}{2}\\left(h_{\\theta}(x)-y\\right) \\cdot \\frac{\\partial}{\\partial \\theta_{j}}\\left(h_{\\theta}(x)-y\\right) \\\\ &=\\left(h_{\\theta}(x)-y\\right) \\cdot \\frac{\\partial}{\\partial \\theta_{j}}\\left(\\sum_{i=0}^{n} \\theta_{i} x_{i}-y\\right) \\\\ &=\\left(h_{\\theta}(x)-y\\right) x_{j} \\end{aligned}\n",
    "$$\n",
    "\n",
    "# Matrix calculation\n",
    "\n",
    "The polynomial regression model\n",
    "\n",
    "$$\n",
    "y_{i}=\\beta_{0}+\\beta_{1} x_{i}+\\beta_{2} x_{i}^{2}+\\cdots+\\beta_{m} x_{i}^{m}+\\varepsilon_{i}(i=1,2, \\ldots, n)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\left[ \\begin{array}{c}{y_{1}} \\\\ {y_{2}} \\\\ {y_{3}} \\\\ {\\vdots} \\\\ {y_{n}}\\end{array}\\right]=\\left[ \\begin{array}{ccccc}{1} & {x_{1}} & {x_{1}^{2}} & {\\ldots} & {x_{1}^{m}} \\\\ {1} & {x_{2}} & {x_{2}^{2}} & {\\ldots} & {x_{2}^{m}} \\\\ {1} & {x_{3}} & {x_{3}^{2}} & {\\ldots} & {x_{3}^{m}} \\\\ {\\vdots} & {\\vdots} & {\\vdots} & {\\ddots} & {\\vdots} \\\\ {1} & {x_{n}} & {x_{n}^{2}} & {\\ldots} & {x_{n}^{m}}\\end{array}\\right] \\left[ \\begin{array}{c}{\\beta_{0}} \\\\ {\\beta_{1}} \\\\ {\\beta_{2}} \\\\ {\\vdots} \\\\ {\\beta_{m}}\\end{array}\\right]+\\left[ \\begin{array}{c}{\\varepsilon_{1}} \\\\ {\\varepsilon_{2}} \\\\ {\\varepsilon_{3}} \\\\ {\\vdots} \\\\ {\\varepsilon_{n}}\\end{array}\\right]\n",
    "$$\n",
    "\n",
    "which when using pure matrix notation is written as\n",
    "\n",
    "$$\n",
    "\\vec{y}=\\mathbf{X} \\vec{\\beta}+\\vec{\\varepsilon}\n",
    "$$\n",
    "\n",
    "The vector of estimated polynomial regression coefficients (using ordinary least squares estimation) is\n",
    "\n",
    "$$\n",
    "\\widehat{\\vec{\\beta}}=\\left(\\mathbf{X}^{\\top} \\mathbf{X}\\right)^{-1} \\mathbf{X}^{\\top} \\vec{y}\n",
    "$$\n",
    "\n",
    "assuming m < n which is required for the matrix to be invertible; then since {\\displaystyle \\mathbf {X} } \\mathbf {X}  is a Vandermonde matrix, the invertibility condition is guaranteed to hold if all the {\\displaystyle x_{i}} x_{i} values are distinct. This is the unique least-squares solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>xx</th>\n",
       "      <th>xxx</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.646079</td>\n",
       "      <td>7.001732</td>\n",
       "      <td>18.527131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.600236</td>\n",
       "      <td>0.360283</td>\n",
       "      <td>0.216255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.468107</td>\n",
       "      <td>2.155338</td>\n",
       "      <td>3.164267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.361340</td>\n",
       "      <td>11.298605</td>\n",
       "      <td>37.978451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.801337</td>\n",
       "      <td>7.847489</td>\n",
       "      <td>21.983461</td>\n",
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      "text/plain": [
       "          x         xx        xxx\n",
       "0  2.646079   7.001732  18.527131\n",
       "1  0.600236   0.360283   0.216255\n",
       "2  1.468107   2.155338   3.164267\n",
       "3  3.361340  11.298605  37.978451\n",
       "4  2.801337   7.847489  21.983461"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_data = raw_data.iloc[:750,:]\n",
    "train_data_x = raw_data.iloc[:750,0]\n",
    "train_data_y = raw_data.iloc[:750,1]\n",
    "\n",
    "test_data  = raw_data.iloc[750:,:]\n",
    "test_data_x = raw_data.iloc[750:,0]\n",
    "test_data_y =raw_data.iloc[750:,1]\n",
    "test_data_y = np.array(test_data_y).reshape(len(test_data_y) , 1)\n",
    "\n",
    "\n",
    "train_data_x = poly_Feature(3,pd.DataFrame(train_data_x))\n",
    "train_data_x.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now, we apply Linear regression on this data. and try to minimize the least square as a cost function. We expand the same feature by 3 degree. Now we have 3 different features and we have to calculate 3 coefficents and 1 intercept\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "initial cost 1433.8480034579559 final cost 1433.846542211598\n",
      "initial cost 1433.846542211598 final cost 1433.8450986018038\n",
      "initial cost 1433.8450986018038 final cost 1433.843672415615\n",
      "initial cost 1433.843672415615 final cost 1433.8422634426474\n",
      "initial cost 1433.8422634426474 final cost 1433.8408714750585\n",
      "initial cost 1433.8408714750585 final cost 1433.8394963075161\n",
      "initial cost 1433.8394963075161 final cost 1433.8381377371697\n",
      "initial cost 1433.8381377371697 final cost 1433.8367955636188\n",
      "initial cost 1433.8367955636188 final cost 1433.835469588884\n",
      "initial cost 1433.835469588884 final cost 1433.8341596173777\n",
      "initial cost 1433.8341596173777 final cost 1433.8328654558757\n",
      "initial cost 1433.8328654558757 final cost 1433.8315869134872\n",
      "initial cost 1433.8315869134872 final cost 1433.8303238016279\n",
      "initial cost 1433.8303238016279 final cost 1433.8290759339923\n",
      "initial cost 1433.8290759339923 final cost 1433.8278431265244\n",
      "initial cost 1433.8278431265244 final cost 1433.8266251973928\n",
      "initial cost 1433.8266251973928 final cost 1433.8254219669616\n",
      "initial cost 1433.8254219669616 final cost 1433.8242332577656\n",
      "initial cost 1433.8242332577656 final cost 1433.8230588944837\n",
      "initial cost 1433.8230588944837 final cost 1433.8218987039118\n",
      "initial cost 1433.8218987039118 final cost 1433.8207525149385\n",
      "initial cost 1433.8207525149385 final cost 1433.8196201585192\n",
      "initial cost 1433.8196201585192 final cost 1433.818501467652\n",
      "initial cost 1433.818501467652 final cost 1433.8173962773512\n",
      "initial cost 1433.8173962773512 final cost 1433.816304424625\n",
      "initial cost 1433.816304424625 final cost 1433.8152257484498\n",
      "initial cost 1433.8152257484498 final cost 1433.8141600897475\n",
      "initial cost 1433.8141600897475 final cost 1433.8131072913607\n",
      "initial cost 1433.8131072913607 final cost 1433.8120671980314\n",
      "initial cost 1433.8120671980314 final cost 1433.8110396563764\n",
      "initial cost 1433.8110396563764 final cost 1433.810024514865\n",
      "initial cost 1433.810024514865 final cost 1433.809021623797\n"
     ]
    }
   ],
   "source": [
    "it = []\n",
    "ft = []\n",
    "def y_cap(theta0 , theta , data):\n",
    "        return theta0 + np.dot(np.array(data),theta)\n",
    "    \n",
    "def gradient_decent():\n",
    "    global train_data_y , it , ft\n",
    "    initial_theta0 = np.random.rand(1,1)\n",
    "    initial_theta = np.random.rand(train_data_x.shape[1],1)\n",
    "    alpha = 0.01\n",
    "    epsilon = 0.001\n",
    "\n",
    "    train_data_y = np.array(train_data_y).reshape(len(train_data_y),1)\n",
    "\n",
    "    def y_cap(theta0 , theta , data):\n",
    "        return theta0 + np.dot(np.array(data),theta)\n",
    "    it = []\n",
    "    ft = []\n",
    "    i = 0\n",
    "    while(True):\n",
    "        del_theta0 = (1/train_data_x.shape[0]) *  np.sum(y_cap(initial_theta0 ,initial_theta , train_data_x) - train_data_y)\n",
    "        del_theta = (1/train_data_x.shape[0]) * np.dot((train_data_x).T , (y_cap(initial_theta0 ,initial_theta, train_data_x) \n",
    "                                                                       - (train_data_y)))\n",
    "\n",
    "        final_theta0 = initial_theta0 - alpha * del_theta0\n",
    "        final_theta  = initial_theta  - alpha * del_theta\n",
    "\n",
    "        initial_cost =  (1/2) * np.sum((y_cap(initial_theta0 , initial_theta , train_data_x) - (train_data_y)) **2 )\n",
    "        final_cost  =  (1/2) * np.sum((y_cap(final_theta0 , final_theta, train_data_x) - (train_data_y)) **2 )\n",
    "\n",
    "        if(abs(initial_cost - final_cost)) < epsilon:\n",
    "            break\n",
    "        \n",
    "        print(\"initial cost {} final cost {}\".format(initial_cost , final_cost))\n",
    "        it.append(i)\n",
    "        ft.append(final_cost)\n",
    "        i+=1\n",
    "        initial_theta0 = final_theta0\n",
    "        initial_theta = final_theta\n",
    "        \n",
    "    return final_theta0 , final_theta\n",
    "final_theta0 , final_theta = gradient_decent()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x25a12cb36d8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(it , ft) # cost function plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25a13d7d588>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y = y_cap(final_theta0 , final_theta , train_data_x)\n",
    "plt.scatter(train_data['x'] , train_data['y'])\n",
    "plt.plot(train_data['x'] ,predict_y , c='r')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This graph is good but the values we are plotting is not shorted. So we need to sort the values of  'y_predict'  with 'x'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25a13def4e0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y = y_cap(final_theta0 , final_theta , train_data_x)\n",
    "\n",
    "s = sorted(zip(train_data['x'] , predict_y) )\n",
    "new_x , new_y = zip(*s)\n",
    "\n",
    "# this sort the values according to 'x'\n",
    "plt.scatter(train_data['x'] , train_data['y'] , s=10)\n",
    "plt.plot(new_x ,new_y , c='r')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rs_quare(true_data , predict_data):\n",
    "    #deno = np.sum(( train_data_y - np.mean(train_data_y) )** 2)\n",
    "    #num = np.sum(( y_cap(final_theta0 ,final_theta, train_data_x) - np.mean(train_data_y)) ** 2)\n",
    "    #r2 = num / deno\n",
    "    rss = np.sum(( true_data  - predict_data )** 2)\n",
    "    tss = np.sum(( true_data - np.mean(true_data) )** 2)\n",
    "    r2 = ( (tss - rss) / tss)\n",
    "    return r2\n",
    "\n",
    "def rs_error(true_data , predict_data):\n",
    "    rss = np.sqrt(np.sum(( true_data  - predict_data )** 2) / (true_data.shape[0] - 2) )\n",
    "    return rss\n",
    "\n",
    "def mse(true_data , predict_data):\n",
    "    return  np.sum(( true_data  - predict_data )** 2) / true_data.shape[0]\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we test with Testing Data.  We are getting our coefficents from trained data now we calculate y_cap i.e equation of line of 3 degree polynomial  by passing the testing data with coeffients which we get from trained data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25a13e66e10>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_d =  poly_Feature( 3 , pd.DataFrame(test_data['x']))\n",
    "\n",
    "predicted_y = y_cap(final_theta0 , final_theta , t_d)  \n",
    "\n",
    "s = sorted(zip(test_data['x'] , predicted_y))\n",
    "new_x , new_y = zip(*s)\n",
    "\n",
    "plt.scatter(test_data['x'] , test_data['y'] , s=10)\n",
    "plt.plot(new_x ,new_y , c='r')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing R2 Score :  0.9305919476782984\n",
      "Testing Residual Standard Error :  1.8840256837507436\n",
      "Testing Mean square error : 3.5211563548161973\n",
      "\n",
      "Training R2 Score :  0.9088197746991521\n",
      "Training Residual Standard Error :  1.9579865455088803\n",
      "Training Mean square error : 3.8234880822274153\n"
     ]
    }
   ],
   "source": [
    "print(\"Testing R2 Score : \",rs_quare(test_data_y , predicted_y))\n",
    "print('Testing Residual Standard Error : ',rs_error(test_data_y , predicted_y))\n",
    "print(\"Testing Mean square error :\", mse(test_data_y , predicted_y))\n",
    "\n",
    "print(\"\\nTraining R2 Score : \",rs_quare(train_data_y , predict_y))\n",
    "print('Training Residual Standard Error : ',rs_error(train_data_y , predict_y))\n",
    "print(\"Training Mean square error :\", mse(train_data_y , predict_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now we check our answers with sklearn library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R2 Score :  0.9088249344033336\n",
      "Training Mean Squared Error :  3.823271718784786\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# it takes only 10 lines by using library\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import sklearn.metrics as m\n",
    "\n",
    "poly = PolynomialFeatures( degree = 3 )\n",
    "new_training_data = poly.fit_transform(np.array(train_data['x']).reshape(750,1))\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(new_training_data , train_data['y'])\n",
    "y_poly_pred = model.predict(new_training_data)\n",
    "\n",
    "ss = sorted(zip(train_data['x'] , y_poly_pred))\n",
    "new_x , new_y = zip(*ss)\n",
    "plt.scatter(train_data['x'] , train_data['y'])\n",
    "plt.plot(new_x,new_y , c = 'r')\n",
    "\n",
    "print(\"Training R2 Score : \" , m.r2_score(train_data['y'] , y_poly_pred))\n",
    "print(\"Training Mean Squared Error : \" , m.mean_squared_error(train_data['y'] , y_poly_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}