linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "linear_regression.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNaZdToYxAxpJ5ZzH6yGJvE",
      "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/AjayKadoula/Mtech_Lab_1/blob/main/linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ghpIse_IiaiU"
      },
      "source": [
        "# **Linear Regression**\r\n",
        "Linear regression is perhaps one of the most well known and well understood algorithms in statistics and machine learning. It is a statistical approach for modelling relationship between a dependent variable with a given set of independent variables.\r\n",
        "\r\n",
        "**Simple Linear Regression :** Simple linear regression is an approach for predicting a response using a single feature.\r\n",
        "\r\n",
        "**Multiple linear regression :** Multiple linear regression attempts to model the relationship between two or more features and a response by fitting a linear equation to observed data.\r\n",
        "\r\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 330
        },
        "id": "5F7oEdB0jlMq",
        "outputId": "b3d8e2d2-3fcd-4974-bf88-e0bf4f6d3859"
      },
      "source": [
        "import numpy as np \r\n",
        "import matplotlib.pyplot as plt \r\n",
        "\r\n",
        "def estimate_coef(x, y): \r\n",
        "\t\r\n",
        "\tn = np.size(x) \r\n",
        "\r\n",
        "\r\n",
        "\tm_x, m_y = np.mean(x), np.mean(y) \r\n",
        "\r\n",
        "\t\r\n",
        "\tSS_xy = np.sum(y*x) - n*m_y*m_x \r\n",
        "\tSS_xx = np.sum(x*x) - n*m_x*m_x \r\n",
        "\r\n",
        "\t\r\n",
        "\tb_1 = SS_xy / SS_xx \r\n",
        "\tb_0 = m_y - b_1*m_x \r\n",
        "\r\n",
        "\treturn(b_0, b_1) \r\n",
        "\r\n",
        "def plot_regression_line(x, y, b): \r\n",
        "\t \r\n",
        "\tplt.scatter(x, y, color = \"m\", \r\n",
        "\t\t\tmarker = \"o\", s = 30) \r\n",
        "\r\n",
        "\t\r\n",
        "\ty_pred = b[0] + b[1]*x \r\n",
        "\r\n",
        "\r\n",
        "\tplt.plot(x, y_pred, color = \"g\") \r\n",
        "\r\n",
        " \r\n",
        "\tplt.xlabel('x') \r\n",
        "\tplt.ylabel('y') \r\n",
        "\r\n",
        " \r\n",
        "\tplt.show() \r\n",
        "\r\n",
        "def main(): \r\n",
        "\r\n",
        "\tx = np.array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) \r\n",
        "\ty = np.array([22, 24, 26, 28, 20, 28, 28, 34, 30,32]) \r\n",
        "\r\n",
        "\r\n",
        "\tb = estimate_coef(x, y) \r\n",
        "\tprint(\"Estimated coefficients:\\n b_0 = {} \\\r\n",
        "  \\n b_1 = {}\".format(b[0], b[1])) \r\n",
        "  \r\n",
        "\r\n",
        "\tplot_regression_line(x, y, b) \r\n",
        "\r\n",
        "if __name__ == \"__main__\": \r\n",
        "\tmain() \r\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Estimated coefficients:\n",
            " b_0 = 11.381818181818183   \n",
            " b_1 = 1.0909090909090908\n"
          ],
          "name": "stdout"
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}