Simple_Linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNCWlrJzWMPNA8WctHlyHr0",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sfansaria/Machine-Learning/blob/main/Simple_Linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "rIU0NAPPzyjT",
        "outputId": "a86af8cc-b6bf-480e-f8b9-06f596569761"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimate co-efficients:\n",
            "b_0=1.2363636363636363 \\nb_1=1.1696969696969697\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#import libraries\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def estimate_coef(x, y):\n",
        "  # number of observation or data points\n",
        "  n = np.size(x)\n",
        "\n",
        "  mean_x = np.mean(x)\n",
        "  mean_y = np.mean(y)\n",
        "\n",
        "  #Calculating cross-deviation and deviation about x\n",
        "  SS_xy = np.sum(y*x) - n*mean_y*mean_x\n",
        "  SS_xx = np.sum(x*x) - n*mean_x*mean_x\n",
        "\n",
        "  #Calculate the regression coefficients\n",
        "  b_1 = SS_xy / SS_xx\n",
        "  b_0 = mean_y - b_1*mean_x\n",
        "\n",
        "  return (b_0, b_1)\n",
        "\n",
        "def plot_regression_line(x, y, b):\n",
        "    #plotting the actual points as scatter plot\n",
        "    plt.scatter(x, y, color=\"b\",marker=\"o\",s=30)\n",
        "\n",
        "    #predicted response vector\n",
        "    y_pred = b[0]+b[1]*x\n",
        "\n",
        "    #plotting the regression line\n",
        "    plt.plot(x,y_pred, color=\"c\")\n",
        "    #labelling\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('y')\n",
        "\n",
        "\n",
        "    #function to show plot\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    #observations/data\n",
        "\n",
        "    x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
        "    y = np.array([1, 3, 2, 5, 7, 8, 8, 9, 10, 12])\n",
        "\n",
        "    #estimating coefficients\n",
        "    b = estimate_coef(x,y)\n",
        "    print(\"Estimate co-efficients:\\nb_0={} \\\\nb_1={}\".format(b[0],b[1]))\n",
        "    plot_regression_line(x, y, b)\n",
        "\n",
        "if __name__==\"__main__\":\n",
        "    main()\n"
      ]
    }
  ]
}