Simple_Linear_Regression_by_Hand.ipynb

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  "metadata": {
    "colab": {
      "name": "Simple Linear Regression by Hand",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPB8tIzZecKW2voyQTvth9W",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/vishalrshukla/Learnings/blob/master/Simple_Linear_Regression_by_Hand.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x9ULva3nrDkL",
        "colab_type": "text"
      },
      "source": [
        "# This is to Show how to calculate Simple Linear Regression without using any Libaray"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BhFqsKYU6Q-n",
        "colab_type": "text"
      },
      "source": [
        "## *Linear Regerssion function*\n",
        "> # y = a + b*$x$\n",
        "---\n",
        "## *Slope(b) of Regerssion Line*\n",
        "> # b= $r(Sy/Sx$)\n",
        "---\n",
        "## Pearson Correlation Coefficient(r)\n",
        "> # r=$\\sum((x-\\bar{x})(y-\\bar{y}))/\\sqrt{\\sum(x-\\bar{x})^2\\sum(y-\\bar{y})^2}$\n",
        "---\n",
        "## Standad deviation of Y  $(Sy)$\n",
        "> # $Sy=  \\sqrt {\\sum(y-\\bar{y})^2}/(n-1)$ \n",
        "## Standad deviation of X  $(Sx)$\n",
        "> # $Sx=  \\sqrt {\\sum(x-\\bar{x})^2}/(n-1)$ \n",
        "---\n",
        "## *Y-Intercept(a) of Regeression Line*\n",
        "> # a = $\\bar{y}$ *- b* $\\bar{x}$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1_cx_IYnqZDA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import math as math"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VSwAchprr_43",
        "colab_type": "text"
      },
      "source": [
        "### Sample Data Frame of Correct Answears(X) Vs Attitude(Y) to pass exame"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "unkP-DgDsFVS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "8c4ea0dc-f8d6-4a43-cafb-f663d96e4312"
      },
      "source": [
        "SampleDF=pd.DataFrame({'Correct(X)':[17,13,12,15,16,14,16,16,18,19],\n",
        "                       'Attitude(Y)':[94,73,59,80,93,85,66,79,77,91]\n",
        "                       })\n",
        "SampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)\n",
              "0          17           94\n",
              "1          13           73\n",
              "2          12           59\n",
              "3          15           80\n",
              "4          16           93\n",
              "5          14           85\n",
              "6          16           66\n",
              "7          16           79\n",
              "8          18           77\n",
              "9          19           91"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SGud0ftLwVKU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "f1b1a7dc-33bf-4904-8a79-db0159dc4306"
      },
      "source": [
        "plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100,  data=SampleDF)\n",
        "plt.ylim(bottom=0)\n",
        "plt.xlim(left=0)\n",
        "plt.title(label=\"Correct(X) vs Attitude(Y)\",loc='center')\n",
        "plt.xlabel('Correct(X)')\n",
        "plt.ylabel('Attitude(Y)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "61N_pnxbLMEZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "575394a5-0772-40b9-f29e-02907a2ed717"
      },
      "source": [
        "## MeanX , MeanY & Count of Rows(N)\n",
        "n=SampleDF['Correct(X)'].count()\n",
        "MeanX=SampleDF['Correct(X)'].mean()\n",
        "MeanY=SampleDF['Attitude(Y)'].mean()\n",
        "print('No of Element :',n)\n",
        "print('Mean of X :', MeanX)\n",
        "print('Mean of Y : ',MeanY)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "No of Element : 10\n",
            "Mean of X : 15.6\n",
            "Mean of Y :  79.7\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ASBpZvznPuVD",
        "colab_type": "text"
      },
      "source": [
        "## Pearson Correlation Coefficient(r)\n",
        "> # r=$\\sum((x-\\bar{x})(y-\\bar{y}))/\\sqrt{\\sum(x-\\bar{x})^2\\sum(y-\\bar{y})^2}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eaX_C2W6Pvw8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "ddb2eeec-91a5-4b6b-b997-c783ae59ae09"
      },
      "source": [
        "SampleDF['X-MeanX']=SampleDF['Correct(X)'].map(lambda a: a-MeanX )\n",
        "SampleDF['Y-MeanY']=SampleDF['Attitude(Y)'].map(lambda a: a-MeanY )\n",
        "SampleDF['X-MeanX*Y-MeanY']=SampleDF['X-MeanX']*SampleDF['Y-MeanY']\n",
        "SampleDF['X-MeanX**2']=SampleDF['X-MeanX'].map(lambda a: a**2)\n",
        "SampleDF['Y-MeanY**2']=SampleDF['Y-MeanY'].map(lambda a: a**2)\n",
        "SampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  X-MeanX*Y-MeanY  X-MeanX**2  Y-MeanY**2\n",
              "0          17           94      1.4  ...            20.02        1.96      204.49\n",
              "1          13           73     -2.6  ...            17.42        6.76       44.89\n",
              "2          12           59     -3.6  ...            74.52       12.96      428.49\n",
              "3          15           80     -0.6  ...            -0.18        0.36        0.09\n",
              "4          16           93      0.4  ...             5.32        0.16      176.89\n",
              "5          14           85     -1.6  ...            -8.48        2.56       28.09\n",
              "6          16           66      0.4  ...            -5.48        0.16      187.69\n",
              "7          16           79      0.4  ...            -0.28        0.16        0.49\n",
              "8          18           77      2.4  ...            -6.48        5.76        7.29\n",
              "9          19           91      3.4  ...            38.42       11.56      127.69\n",
              "\n",
              "[10 rows x 7 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rFIY8IS3aubZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "a8ee5a03-5090-4584-d786-56ab97886a6f"
      },
      "source": [
        "Numrator=SampleDF['X-MeanX*Y-MeanY'].sum()\n",
        "Dinominator=math.sqrt(SampleDF['X-MeanX**2'].sum()*SampleDF['Y-MeanY**2'].sum())\n",
        "r=Numrator/Dinominator\n",
        "print('Pearson Correlation Coefficient(r) : ', r)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Persion Corelation Coeefficent(r) :  0.5960947613894624\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W47465dW93mB",
        "colab_type": "text"
      },
      "source": [
        "## Standad deviation of Y  $(Sy)$\n",
        "> # $Sy=  \\sqrt {\\sum(y-\\bar{y})^2}/n-1$ \n",
        "## Standad deviation of X  $(Sx)$\n",
        "> # $Sx=  \\sqrt {\\sum(x-\\bar{x})^2}/n-1$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PZXdPpTt95a7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Sy=math.sqrt(SampleDF['Y-MeanY**2'].sum()/(n-1))\n",
        "Sx=math.sqrt(SampleDF['X-MeanX**2'].sum()/(n-1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O1jWxNzi-9ni",
        "colab_type": "text"
      },
      "source": [
        "## *Slope(b) of Regerssion Line*\n",
        "> # b= $r(Sy/Sx$)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "voTDG4km--2g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "3ec1491b-a7aa-43e4-a803-7b25e9c940db"
      },
      "source": [
        "b=r*(Sy/Sx)\n",
        "print('Slope(b) of Regerssion Line',b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Slope(b) of Regerssion Line 3.179245283018868\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QbpAR3a1A954",
        "colab_type": "text"
      },
      "source": [
        "## *Y-Intercept(a) of Regeression Line*\n",
        "> # a = $\\bar{y}$ *- b* $\\bar{x}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "COF7DJdIA_jV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "917fc7a6-751d-4244-d1cb-f764976ece7a"
      },
      "source": [
        "a= MeanY-(b*MeanX)\n",
        "print('Y-Intercept(a) of Regeression Line : ', a)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Y-Intercept(a) of Regeression Line :  30.10377358490566\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dmnAzDGIB2kD",
        "colab_type": "text"
      },
      "source": [
        "## *Linear Regerssion function*\n",
        "> # y = a + b*$x$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3yY3OsXNCCqN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "0ad2153e-29b8-46d7-e33d-af9791d74cb6"
      },
      "source": [
        "#Suppose x=20\n",
        "y= a + (b*20)\n",
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "93.68867924528303"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p--ioqqNNTeq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "d6a86cd3-e349-4f4e-b182-3dabde5ed8ed"
      },
      "source": [
        "plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=SampleDF)\n",
        "plt.plot(pd.RangeIndex(0,20),a +(b*pd.RangeIndex(0,20) ))\n",
        "plt.ylim(bottom=0)\n",
        "plt.xlim(left=0)\n",
        "plt.title(label=\"Correct(X) vs Attitude(Y)\",loc='center')\n",
        "plt.xlabel('Correct(X)')\n",
        "plt.ylabel('Attitude(Y)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wRaFx-93svJR",
        "colab_type": "text"
      },
      "source": [
        "## Perdict Y for ith Value of X ($\\bar{y_i}$)\n",
        "> # $\\hat{y_i} = a + bx_i$ \n",
        "---\n",
        "## Mean Square Error\n",
        "> # MSE = $\\frac1{n}\\sum(y_i-\\hat{y_i})^2$\n",
        "---\n",
        "## Root Mean Square Error (Loss Function)\n",
        "> # RMSE = $\\sqrt{\\frac1{n}\\sum(y_i-\\hat{y_i})^2}$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TfcOuD2Xwwau",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "5a853d3c-cdd7-498c-e656-57bfc13b5935"
      },
      "source": [
        "SampleDF['Perdict_Y']=SampleDF['Correct(X)'].map(lambda row: a + b*row )\n",
        "SampleDF['Perdict_Y']=SampleDF['Perdict_Y'].round(2)\n",
        "SampleDF['Y-Perdict_Y']=SampleDF['Attitude(Y)']-SampleDF['Perdict_Y']\n",
        "SampleDF['Y-Perdict_Y**2']=np.round(SampleDF['Y-Perdict_Y'].map(lambda row: np.square(row)),2)\n",
        "SampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "      <th>Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y**2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "      <td>84.15</td>\n",
              "      <td>9.85</td>\n",
              "      <td>97.02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "      <td>71.43</td>\n",
              "      <td>1.57</td>\n",
              "      <td>2.46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "      <td>68.25</td>\n",
              "      <td>-9.25</td>\n",
              "      <td>85.56</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "      <td>77.79</td>\n",
              "      <td>2.21</td>\n",
              "      <td>4.88</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "      <td>80.97</td>\n",
              "      <td>12.03</td>\n",
              "      <td>144.72</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "      <td>74.61</td>\n",
              "      <td>10.39</td>\n",
              "      <td>107.95</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-14.97</td>\n",
              "      <td>224.10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-1.97</td>\n",
              "      <td>3.88</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "      <td>87.33</td>\n",
              "      <td>-10.33</td>\n",
              "      <td>106.71</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "      <td>90.51</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.24</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  Perdict_Y  Y-Perdict_Y  Y-Perdict_Y**2\n",
              "0          17           94      1.4  ...      84.15         9.85           97.02\n",
              "1          13           73     -2.6  ...      71.43         1.57            2.46\n",
              "2          12           59     -3.6  ...      68.25        -9.25           85.56\n",
              "3          15           80     -0.6  ...      77.79         2.21            4.88\n",
              "4          16           93      0.4  ...      80.97        12.03          144.72\n",
              "5          14           85     -1.6  ...      74.61        10.39          107.95\n",
              "6          16           66      0.4  ...      80.97       -14.97          224.10\n",
              "7          16           79      0.4  ...      80.97        -1.97            3.88\n",
              "8          18           77      2.4  ...      87.33       -10.33          106.71\n",
              "9          19           91      3.4  ...      90.51         0.49            0.24\n",
              "\n",
              "[10 rows x 10 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RCu_PJhb40K6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "f3c19dd7-4bb8-4b04-8b20-2fa085887765"
      },
      "source": [
        "MSE=SampleDF['Y-Perdict_Y**2'].sum()/n\n",
        "print('Mean Square Error : ',np.round(MSE,2))\n",
        "RMSE=math.sqrt(MSE)\n",
        "print('Root Mean Square Error (Loss function): ',np.round(RMSE,2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean Square Error :  77.75\n",
            "Root Mean Square Error (Loss function):  8.82\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QB9693ycWwoz",
        "colab_type": "text"
      },
      "source": [
        "---\n",
        "# Below is Linear Regression with Gradient Descent\n",
        "### Gradient descent is an iterative optimization algorithm to find the minimum of a function. Here that function is our Loss Function.\n",
        "---\n",
        "### For Gradient we will use same linear regression but changing variable name to avoid confusion so \n",
        "> # $Y = c + mX$\n",
        "## here *Slope of Regerssion Line is $m$ & Y-Intercept of Regeression Line is $c$*\n",
        "---\n",
        "\n",
        "###Initially let m = 0 and c = 0. Let L be our learning rate. This controls how much the value of m changes with each step. L could be a small value like 0.0001 for good accuracy.\n",
        "# $ m = 0 $\n",
        "# $ c = 0 $\n",
        "# $ L = 0.0001 $\n",
        "---\n",
        "### Calculate the Partial derivative of the loss function with respect to m, and plug in the current values of x, y, m and c in it to obtain the derivative value D. **$D_m, D_c$**\n",
        "\n",
        "> #$D_m=(-2)\\frac1{n}\\sum x_i(y_i-\\hat{y_i})$\n",
        "\n",
        "> #$D_c=(-2)\\frac1{n}\\sum(y_i-\\hat{y_i})$\n",
        "\n",
        "### Now we update the current value of m and c using the following equation:\n",
        "> # $m=m- L\\,D_m$\n",
        "\n",
        "> # $c=c- L\\,D_c$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V13mK6rnXMqF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "67e12f81-5ae7-4238-a39a-11268b46710e"
      },
      "source": [
        " GDSampleDF=SampleDF # We will use GDSampleDF for further Calculation\n",
        " GDSampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "      <th>Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y**2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "      <td>84.15</td>\n",
              "      <td>9.85</td>\n",
              "      <td>97.02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "      <td>71.43</td>\n",
              "      <td>1.57</td>\n",
              "      <td>2.46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "      <td>68.25</td>\n",
              "      <td>-9.25</td>\n",
              "      <td>85.56</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "      <td>77.79</td>\n",
              "      <td>2.21</td>\n",
              "      <td>4.88</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "      <td>80.97</td>\n",
              "      <td>12.03</td>\n",
              "      <td>144.72</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "      <td>74.61</td>\n",
              "      <td>10.39</td>\n",
              "      <td>107.95</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-14.97</td>\n",
              "      <td>224.10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-1.97</td>\n",
              "      <td>3.88</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "      <td>87.33</td>\n",
              "      <td>-10.33</td>\n",
              "      <td>106.71</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "      <td>90.51</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.24</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  Perdict_Y  Y-Perdict_Y  Y-Perdict_Y**2\n",
              "0          17           94      1.4  ...      84.15         9.85           97.02\n",
              "1          13           73     -2.6  ...      71.43         1.57            2.46\n",
              "2          12           59     -3.6  ...      68.25        -9.25           85.56\n",
              "3          15           80     -0.6  ...      77.79         2.21            4.88\n",
              "4          16           93      0.4  ...      80.97        12.03          144.72\n",
              "5          14           85     -1.6  ...      74.61        10.39          107.95\n",
              "6          16           66      0.4  ...      80.97       -14.97          224.10\n",
              "7          16           79      0.4  ...      80.97        -1.97            3.88\n",
              "8          18           77      2.4  ...      87.33       -10.33          106.71\n",
              "9          19           91      3.4  ...      90.51         0.49            0.24\n",
              "\n",
              "[10 rows x 10 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FENS4b-ntZML",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Initialize Variable \n",
        "m = 0\n",
        "c = 0\n",
        "L = 0.0001\n",
        "n = GDSampleDF['Correct(X)'].count()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jmm8xeXXFrQd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "3075b8f8-6f2e-4d8d-b440-61993b5f769b"
      },
      "source": [
        "plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=GDSampleDF)\n",
        "plt.ylim(bottom=0)\n",
        "plt.xlim(left=0)\n",
        "plt.plot(pd.RangeIndex(0,20),c +(m*pd.RangeIndex(0,20) ))\n",
        "plt.title(label=\"Correct(X) vs Attitude(Y)\",loc='center')\n",
        "plt.xlabel('Correct(X)')\n",
        "plt.ylabel('Attitude(Y)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EQDIMvVIFKGK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "epoch = 1000\n",
        "for i in range(epoch):\n",
        "  GDSampleDF['GD_Perdict_Y'] = GDSampleDF['Correct(X)'].map(lambda x: m*x+c )\n",
        "  GDSampleDF['Diff-in-Y'] = GDSampleDF['Attitude(Y)'] - GDSampleDF['GD_Perdict_Y']\n",
        "  GDSampleDF['Diff-y-Square'] = GDSampleDF['Diff-in-Y'].map(lambda y: y**2)\n",
        "  GDSampleDF['Diff-in-Y*x'] = GDSampleDF['Diff-in-Y'] * GDSampleDF['Correct(X)']\n",
        " \n",
        "  GDMSE = GDSampleDF['Diff-y-Square'].sum()/n\n",
        "  Dm = (-2/n) * GDSampleDF['Diff-in-Y*x'].sum()\n",
        "  Dc = (-2/n) * GDSampleDF['Diff-in-Y'].sum()\n",
        "  GDRMSE = math.sqrt(GDMSE)\n",
        "  \n",
        "  m = m - L * Dm\n",
        "  c = c - L * Dc\n",
        "  \"\"\"\n",
        "  plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=GDSampleDF)\n",
        "  plt.ylim(bottom=0)\n",
        "  plt.xlim(left=0)\n",
        "  plt.plot(pd.RangeIndex(0,20),c +(m*pd.RangeIndex(0,20) ))\n",
        "  plt.title(label=\"Correct(X) vs Attitude(Y)\"+str(i),loc='center')\n",
        "  plt.legend()\n",
        "  plt.show()\n",
        " \"\"\""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WXmoIlCpjfsm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 124
        },
        "outputId": "cf105f0e-3115-4e18-ce44-a375f8e3ea87"
      },
      "source": [
        "print(\"Slope(m) of Regerssion Line : \", m)\n",
        "print(\"Y-Intercept(c) of Regeression Line :\", c)\n",
        "print(\"Mean Square Error :\", GDMSE)\n",
        "print(\"Partial derivative of m(Dm) :\", Dm)\n",
        "print(\"Partial derivative of c(Dc) :\", Dc)\n",
        "print(\"Roont Mean Square Error :\", GDRMSE)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Slope(m) of Regerssion Line :  5.043225690296916\n",
            "Y-Intercept(c) of Regeression Line : 0.5210969488419269\n",
            "Mean Square Error : 92.74003245586387\n",
            "Partial derivative of m(Dm) : 0.06358685581692214\n",
            "Partial derivative of c(Dc) : -1.0091680076637601\n",
            "Roont Mean Square Error : 9.630162639117986\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sGTR7LZvP83C",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "827e7ad7-41b2-48ec-fff5-a068f58c6b72"
      },
      "source": [
        "  plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=GDSampleDF)\n",
        "  plt.ylim(bottom=0)\n",
        "  plt.xlim(left=0)\n",
        "  plt.plot(pd.RangeIndex(0,20),c +(m*pd.RangeIndex(0,20) ))\n",
        "  plt.plot(pd.RangeIndex(0,20),a +(b*pd.RangeIndex(0,20) ))\n",
        "  plt.title(label=\"Correct(X) vs Attitude(Y)\"+str(i),loc='center')\n",
        "  plt.xlabel('Correct(X)')\n",
        "  plt.ylabel('Attitude(Y)')\n",
        "  plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O7hWE_PClbsP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "46448d8f-4c4d-4c97-fd50-510bea441eaf"
      },
      "source": [
        "GDSampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "      <th>Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y**2</th>\n",
              "      <th>GD_Perdict_Y</th>\n",
              "      <th>Diff-in-Y</th>\n",
              "      <th>Diff-y-Square</th>\n",
              "      <th>Diff-in-Y*x</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "      <td>84.15</td>\n",
              "      <td>9.85</td>\n",
              "      <td>97.02</td>\n",
              "      <td>86.263134</td>\n",
              "      <td>7.736866</td>\n",
              "      <td>59.859096</td>\n",
              "      <td>131.526722</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "      <td>71.43</td>\n",
              "      <td>1.57</td>\n",
              "      <td>2.46</td>\n",
              "      <td>66.064728</td>\n",
              "      <td>6.935272</td>\n",
              "      <td>48.098004</td>\n",
              "      <td>90.158541</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "      <td>68.25</td>\n",
              "      <td>-9.25</td>\n",
              "      <td>85.56</td>\n",
              "      <td>61.015126</td>\n",
              "      <td>-2.015126</td>\n",
              "      <td>4.060733</td>\n",
              "      <td>-24.181512</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "      <td>77.79</td>\n",
              "      <td>2.21</td>\n",
              "      <td>4.88</td>\n",
              "      <td>76.163931</td>\n",
              "      <td>3.836069</td>\n",
              "      <td>14.715427</td>\n",
              "      <td>57.541038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "      <td>80.97</td>\n",
              "      <td>12.03</td>\n",
              "      <td>144.72</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>11.786468</td>\n",
              "      <td>138.920819</td>\n",
              "      <td>188.583482</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "      <td>74.61</td>\n",
              "      <td>10.39</td>\n",
              "      <td>107.95</td>\n",
              "      <td>71.114329</td>\n",
              "      <td>13.885671</td>\n",
              "      <td>192.811854</td>\n",
              "      <td>194.399391</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-14.97</td>\n",
              "      <td>224.10</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-15.213532</td>\n",
              "      <td>231.451568</td>\n",
              "      <td>-243.416518</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-1.97</td>\n",
              "      <td>3.88</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-2.213532</td>\n",
              "      <td>4.899726</td>\n",
              "      <td>-35.416518</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "      <td>87.33</td>\n",
              "      <td>-10.33</td>\n",
              "      <td>106.71</td>\n",
              "      <td>91.312736</td>\n",
              "      <td>-14.312736</td>\n",
              "      <td>204.854400</td>\n",
              "      <td>-257.629241</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "      <td>90.51</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.24</td>\n",
              "      <td>96.362337</td>\n",
              "      <td>-5.362337</td>\n",
              "      <td>28.754660</td>\n",
              "      <td>-101.884407</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  Diff-in-Y  Diff-y-Square  Diff-in-Y*x\n",
              "0          17           94      1.4  ...   7.736866      59.859096   131.526722\n",
              "1          13           73     -2.6  ...   6.935272      48.098004    90.158541\n",
              "2          12           59     -3.6  ...  -2.015126       4.060733   -24.181512\n",
              "3          15           80     -0.6  ...   3.836069      14.715427    57.541038\n",
              "4          16           93      0.4  ...  11.786468     138.920819   188.583482\n",
              "5          14           85     -1.6  ...  13.885671     192.811854   194.399391\n",
              "6          16           66      0.4  ... -15.213532     231.451568  -243.416518\n",
              "7          16           79      0.4  ...  -2.213532       4.899726   -35.416518\n",
              "8          18           77      2.4  ... -14.312736     204.854400  -257.629241\n",
              "9          19           91      3.4  ...  -5.362337      28.754660  -101.884407\n",
              "\n",
              "[10 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o6b8RJkmeRWi",
        "colab_type": "text"
      },
      "source": [
        "---\n",
        "# Below is using SKlearn\n",
        "### This is to understand how internally the *LinearRegression* from *sklearn* library works"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p7VYSdKVe-zh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# import library\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error, explained_variance_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QxNcYcG1ej9r",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "1e5ff842-9f16-4b41-fc26-6b2aca5a67b8"
      },
      "source": [
        "skSampleDF=GDSampleDF#SampleDF[['Correct(X)','Attitude(Y)']]\n",
        "skSampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "      <th>Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y**2</th>\n",
              "      <th>GD_Perdict_Y</th>\n",
              "      <th>Diff-in-Y</th>\n",
              "      <th>Diff-y-Square</th>\n",
              "      <th>Diff-in-Y*x</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "      <td>84.15</td>\n",
              "      <td>9.85</td>\n",
              "      <td>97.02</td>\n",
              "      <td>86.263134</td>\n",
              "      <td>7.736866</td>\n",
              "      <td>59.859096</td>\n",
              "      <td>131.526722</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "      <td>71.43</td>\n",
              "      <td>1.57</td>\n",
              "      <td>2.46</td>\n",
              "      <td>66.064728</td>\n",
              "      <td>6.935272</td>\n",
              "      <td>48.098004</td>\n",
              "      <td>90.158541</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "      <td>68.25</td>\n",
              "      <td>-9.25</td>\n",
              "      <td>85.56</td>\n",
              "      <td>61.015126</td>\n",
              "      <td>-2.015126</td>\n",
              "      <td>4.060733</td>\n",
              "      <td>-24.181512</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "      <td>77.79</td>\n",
              "      <td>2.21</td>\n",
              "      <td>4.88</td>\n",
              "      <td>76.163931</td>\n",
              "      <td>3.836069</td>\n",
              "      <td>14.715427</td>\n",
              "      <td>57.541038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "      <td>80.97</td>\n",
              "      <td>12.03</td>\n",
              "      <td>144.72</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>11.786468</td>\n",
              "      <td>138.920819</td>\n",
              "      <td>188.583482</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "      <td>74.61</td>\n",
              "      <td>10.39</td>\n",
              "      <td>107.95</td>\n",
              "      <td>71.114329</td>\n",
              "      <td>13.885671</td>\n",
              "      <td>192.811854</td>\n",
              "      <td>194.399391</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-14.97</td>\n",
              "      <td>224.10</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-15.213532</td>\n",
              "      <td>231.451568</td>\n",
              "      <td>-243.416518</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-1.97</td>\n",
              "      <td>3.88</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-2.213532</td>\n",
              "      <td>4.899726</td>\n",
              "      <td>-35.416518</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "      <td>87.33</td>\n",
              "      <td>-10.33</td>\n",
              "      <td>106.71</td>\n",
              "      <td>91.312736</td>\n",
              "      <td>-14.312736</td>\n",
              "      <td>204.854400</td>\n",
              "      <td>-257.629241</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "      <td>90.51</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.24</td>\n",
              "      <td>96.362337</td>\n",
              "      <td>-5.362337</td>\n",
              "      <td>28.754660</td>\n",
              "      <td>-101.884407</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  Diff-in-Y  Diff-y-Square  Diff-in-Y*x\n",
              "0          17           94      1.4  ...   7.736866      59.859096   131.526722\n",
              "1          13           73     -2.6  ...   6.935272      48.098004    90.158541\n",
              "2          12           59     -3.6  ...  -2.015126       4.060733   -24.181512\n",
              "3          15           80     -0.6  ...   3.836069      14.715427    57.541038\n",
              "4          16           93      0.4  ...  11.786468     138.920819   188.583482\n",
              "5          14           85     -1.6  ...  13.885671     192.811854   194.399391\n",
              "6          16           66      0.4  ... -15.213532     231.451568  -243.416518\n",
              "7          16           79      0.4  ...  -2.213532       4.899726   -35.416518\n",
              "8          18           77      2.4  ... -14.312736     204.854400  -257.629241\n",
              "9          19           91      3.4  ...  -5.362337      28.754660  -101.884407\n",
              "\n",
              "[10 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ixOajEwSgwy6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "02bf4dac-6446-46d0-df25-0a4fe0557e90"
      },
      "source": [
        "plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=skSampleDF)\n",
        "plt.ylim(bottom=0)\n",
        "plt.xlim(left=0)\n",
        "plt.title(label=\"Correct(X) vs Attitude(Y)\",loc='center')\n",
        "plt.xlabel('Correct(X)')\n",
        "plt.ylabel('Attitude(Y)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bU_e2USqhahe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "29b205fe-ba53-42c2-d9d9-3e085601875e"
      },
      "source": [
        "LR = LinearRegression(normalize=True)\n",
        "LR.fit(skSampleDF[['Correct(X)']], skSampleDF[['Attitude(Y)']])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JEmYNCgikvBZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "0bfbf87c-89a8-40a5-da66-14c1a7a08408"
      },
      "source": [
        "#perdict Y using linear Model developed(LR)\n",
        "skSampleDF['SK_Perdict_Y']=pd.DataFrame (LR.predict(skSampleDF[['Correct(X)']]))\n",
        "skSampleDF"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Correct(X)</th>\n",
              "      <th>Attitude(Y)</th>\n",
              "      <th>X-MeanX</th>\n",
              "      <th>Y-MeanY</th>\n",
              "      <th>X-MeanX*Y-MeanY</th>\n",
              "      <th>X-MeanX**2</th>\n",
              "      <th>Y-MeanY**2</th>\n",
              "      <th>Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y</th>\n",
              "      <th>Y-Perdict_Y**2</th>\n",
              "      <th>GD_Perdict_Y</th>\n",
              "      <th>Diff-in-Y</th>\n",
              "      <th>Diff-y-Square</th>\n",
              "      <th>Diff-in-Y*x</th>\n",
              "      <th>SK_Perdict_Y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17</td>\n",
              "      <td>94</td>\n",
              "      <td>1.4</td>\n",
              "      <td>14.3</td>\n",
              "      <td>20.02</td>\n",
              "      <td>1.96</td>\n",
              "      <td>204.49</td>\n",
              "      <td>84.15</td>\n",
              "      <td>9.85</td>\n",
              "      <td>97.02</td>\n",
              "      <td>86.263134</td>\n",
              "      <td>7.736866</td>\n",
              "      <td>59.859096</td>\n",
              "      <td>131.526722</td>\n",
              "      <td>84.150943</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>13</td>\n",
              "      <td>73</td>\n",
              "      <td>-2.6</td>\n",
              "      <td>-6.7</td>\n",
              "      <td>17.42</td>\n",
              "      <td>6.76</td>\n",
              "      <td>44.89</td>\n",
              "      <td>71.43</td>\n",
              "      <td>1.57</td>\n",
              "      <td>2.46</td>\n",
              "      <td>66.064728</td>\n",
              "      <td>6.935272</td>\n",
              "      <td>48.098004</td>\n",
              "      <td>90.158541</td>\n",
              "      <td>71.433962</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>12</td>\n",
              "      <td>59</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-20.7</td>\n",
              "      <td>74.52</td>\n",
              "      <td>12.96</td>\n",
              "      <td>428.49</td>\n",
              "      <td>68.25</td>\n",
              "      <td>-9.25</td>\n",
              "      <td>85.56</td>\n",
              "      <td>61.015126</td>\n",
              "      <td>-2.015126</td>\n",
              "      <td>4.060733</td>\n",
              "      <td>-24.181512</td>\n",
              "      <td>68.254717</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>80</td>\n",
              "      <td>-0.6</td>\n",
              "      <td>0.3</td>\n",
              "      <td>-0.18</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.09</td>\n",
              "      <td>77.79</td>\n",
              "      <td>2.21</td>\n",
              "      <td>4.88</td>\n",
              "      <td>76.163931</td>\n",
              "      <td>3.836069</td>\n",
              "      <td>14.715427</td>\n",
              "      <td>57.541038</td>\n",
              "      <td>77.792453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>16</td>\n",
              "      <td>93</td>\n",
              "      <td>0.4</td>\n",
              "      <td>13.3</td>\n",
              "      <td>5.32</td>\n",
              "      <td>0.16</td>\n",
              "      <td>176.89</td>\n",
              "      <td>80.97</td>\n",
              "      <td>12.03</td>\n",
              "      <td>144.72</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>11.786468</td>\n",
              "      <td>138.920819</td>\n",
              "      <td>188.583482</td>\n",
              "      <td>80.971698</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14</td>\n",
              "      <td>85</td>\n",
              "      <td>-1.6</td>\n",
              "      <td>5.3</td>\n",
              "      <td>-8.48</td>\n",
              "      <td>2.56</td>\n",
              "      <td>28.09</td>\n",
              "      <td>74.61</td>\n",
              "      <td>10.39</td>\n",
              "      <td>107.95</td>\n",
              "      <td>71.114329</td>\n",
              "      <td>13.885671</td>\n",
              "      <td>192.811854</td>\n",
              "      <td>194.399391</td>\n",
              "      <td>74.613208</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>16</td>\n",
              "      <td>66</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-13.7</td>\n",
              "      <td>-5.48</td>\n",
              "      <td>0.16</td>\n",
              "      <td>187.69</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-14.97</td>\n",
              "      <td>224.10</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-15.213532</td>\n",
              "      <td>231.451568</td>\n",
              "      <td>-243.416518</td>\n",
              "      <td>80.971698</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>16</td>\n",
              "      <td>79</td>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.7</td>\n",
              "      <td>-0.28</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.49</td>\n",
              "      <td>80.97</td>\n",
              "      <td>-1.97</td>\n",
              "      <td>3.88</td>\n",
              "      <td>81.213532</td>\n",
              "      <td>-2.213532</td>\n",
              "      <td>4.899726</td>\n",
              "      <td>-35.416518</td>\n",
              "      <td>80.971698</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>18</td>\n",
              "      <td>77</td>\n",
              "      <td>2.4</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>-6.48</td>\n",
              "      <td>5.76</td>\n",
              "      <td>7.29</td>\n",
              "      <td>87.33</td>\n",
              "      <td>-10.33</td>\n",
              "      <td>106.71</td>\n",
              "      <td>91.312736</td>\n",
              "      <td>-14.312736</td>\n",
              "      <td>204.854400</td>\n",
              "      <td>-257.629241</td>\n",
              "      <td>87.330189</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>19</td>\n",
              "      <td>91</td>\n",
              "      <td>3.4</td>\n",
              "      <td>11.3</td>\n",
              "      <td>38.42</td>\n",
              "      <td>11.56</td>\n",
              "      <td>127.69</td>\n",
              "      <td>90.51</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.24</td>\n",
              "      <td>96.362337</td>\n",
              "      <td>-5.362337</td>\n",
              "      <td>28.754660</td>\n",
              "      <td>-101.884407</td>\n",
              "      <td>90.509434</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Correct(X)  Attitude(Y)  X-MeanX  ...  Diff-y-Square  Diff-in-Y*x  SK_Perdict_Y\n",
              "0          17           94      1.4  ...      59.859096   131.526722     84.150943\n",
              "1          13           73     -2.6  ...      48.098004    90.158541     71.433962\n",
              "2          12           59     -3.6  ...       4.060733   -24.181512     68.254717\n",
              "3          15           80     -0.6  ...      14.715427    57.541038     77.792453\n",
              "4          16           93      0.4  ...     138.920819   188.583482     80.971698\n",
              "5          14           85     -1.6  ...     192.811854   194.399391     74.613208\n",
              "6          16           66      0.4  ...     231.451568  -243.416518     80.971698\n",
              "7          16           79      0.4  ...       4.899726   -35.416518     80.971698\n",
              "8          18           77      2.4  ...     204.854400  -257.629241     87.330189\n",
              "9          19           91      3.4  ...      28.754660  -101.884407     90.509434\n",
              "\n",
              "[10 rows x 15 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MMpXkHys1eiK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "skLearm=LR.coef_\n",
        "skLearnc=LR.intercept_\n",
        "skLearMSE=mean_squared_error(skSampleDF['Attitude(Y)'],skSampleDF['SK_Perdict_Y'])\n",
        "skLearRMSE=math.sqrt(skLearMSE)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "01YyuiJ1XH5M",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "outputId": "996ad6a4-9b5c-4b71-e1d1-b5946f5d880b"
      },
      "source": [
        "print(\"Slope(m) of Regerssion Line  using skLearn: \", skLearm.item())\n",
        "print(\"Y-Intercept(c) of Regeression Line skLearn:\", skLearnc.item())\n",
        "print(\"Mean Square Error skLearn:\", skLearMSE)\n",
        "print(\"Roont Mean Square Error skLearn:\", skLearRMSE)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Slope(m) of Regerssion Line  using skLearn:  3.179245283018869\n",
            "Y-Intercept(c) of Regeression Line skLearn: 30.103773584905646\n",
            "Mean Square Error skLearn: 77.75377358490563\n",
            "Roont Mean Square Error skLearn: 8.81781002204661\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qMWXHzRe4lpg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "12f91e8f-1149-4a76-e165-08e483c90c2e"
      },
      "source": [
        "  plt.scatter('Correct(X)','Attitude(Y)',c='green', s=100, data=GDSampleDF)\n",
        "  plt.ylim(bottom=0)\n",
        "  plt.xlim(left=0)\n",
        "  plt.plot(pd.RangeIndex(0,20),c +(m*pd.RangeIndex(0,20) ))\n",
        "  plt.plot(pd.RangeIndex(0,20),a +(b*pd.RangeIndex(0,20) ))\n",
        "  plt.plot(pd.RangeIndex(0,20),skLearnc.item() +(skLearm.item()*pd.RangeIndex(0,20) ))\n",
        "  plt.title(label=\"Correct(X) vs Attitude(Y)\"+str(i),loc='center')\n",
        "  plt.xlabel('Correct(X)')\n",
        "  plt.ylabel('Attitude(Y)')\n",
        "  plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mc-dXLmDjGvA",
        "colab_type": "text"
      },
      "source": [
        "## Coefficient of determination of the prediction ($R^2$).\n",
        "> # $R^2=1-(\\frac{u}{v})$\n",
        "## where $u$ is the residual sum of squares\n",
        "> # $u=\\sum(y_i-\\hat{y_i})^2$\n",
        "##  and $v$ is the total sum of squares \n",
        "> # $v=\\sum(y_i-\\bar{y_i})^2$\n",
        "---\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8vKoBGFLs2uN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "220dba15-70dc-4142-9b88-421f26033ef5"
      },
      "source": [
        "# Get Score\n",
        "sklearnScore=LR.score(skSampleDF[['Correct(X)']],skSampleDF[['Attitude(Y)']])\n",
        "print('Score for sklearn linear regerssion Model :',sklearnScore)\n",
        "# gdScore\n",
        "gdu=skSampleDF['Diff-in-Y'].sum()**2\n",
        "v=skSampleDF['Y-MeanY**2'].sum()**2\n",
        "gdScore=1-(gdu/v)\n",
        "print('Score for linear resgression with gradient descent :',gdScore)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Score for sklearn linear regerssion Model : 0.3553289645559603\n",
            "Score for linear resgression with gradient descent : 0.9999824974904967\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}