linear_regression.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOjBhK9cb6nfR7NHMFmPc9R",
      "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/mobley-trent/ml-from-scratch/blob/mobley-trent-patch-1/linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear Regression is a widely used statistical approach to model the relationship between a dependent variable and one or more independent variables. In the context of machine learning, it is used as a predictive modelling tool for predicting a continuous outcome variable Y from one or more predictor variables X.\n",
        "\n",
        "The basic idea of linear regression is to find the equation of a straight line that best fits the data points in a scatter plot. The equation of the line is represented as `y = mx + b`, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.\n",
        "\n",
        "The goal of linear regression is to find the values of m and b that minimize the sum of the squared differences between the actual and predicted values of y. This is called the least squares method.\n",
        "\n",
        "Once the line of best fit is determined, it can be used to predict the values of y for new values of x. This is useful for making predictions and understanding the relationship between the dependent and independent variables.\n",
        "\n",
        "There are two main types of linear regression: simple linear regression and multiple linear regression. Simple linear regression involves only one independent variable, while multiple linear regression involves two or more independent variables.\n",
        "\n",
        "Linear regression has a wide range of applications, including finance, marketing, economics, and science. It is commonly used in areas such as predicting stock prices, analyzing marketing campaigns, and studying the relationship between environmental factors and health outcomes."
      ],
      "metadata": {
        "id": "PM82XgObq1bd"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b-CFIPjzhKPa"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "class LinearRegression:\n",
        "\n",
        "    def __init__(self, lr=0.01, n_iter=1000):\n",
        "        self.lr = lr\n",
        "        self.n_iter = n_iter\n",
        "        self.weights = None\n",
        "        self.bias = None\n",
        "\n",
        "    def fit(self, X, y):\n",
        "        n_samples, n_features = X.shape\n",
        "\n",
        "        # Initialize weights and bias to zero\n",
        "        self.weights = np.zeros(n_features)\n",
        "        self.bias = 0\n",
        "\n",
        "        # Gradient descent\n",
        "        for i in range(self.n_iter):\n",
        "            y_pred = np.dot(X, self.weights) + self.bias\n",
        "\n",
        "            dw = (1/n_samples) * np.dot(X.T, (y_pred - y))\n",
        "            db = (1/n_samples) * np.sum(y_pred - y)\n",
        "\n",
        "            self.weights -= self.lr * dw\n",
        "            self.bias -= self.lr * db\n",
        "\n",
        "    def predict(self, X):\n",
        "        y_pred = np.dot(X, self.weights) + self.bias\n",
        "        return y_pred\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this implementation, the `fit` method takes a 2D array `X` of shape `(n_samples, n_features)` and a 1D array `y` of shape `(n_samples,)` as input, where `n_samples` is the number of training samples and `n_features` is the number of features. The algorithm initializes the weights and bias to zero, and then performs gradient descent for `n_iter` iterations to minimize the mean squared error between the predicted and actual values.\n",
        "\n",
        "The predict method takes a 2D array `X` of shape `(n_samples, n_features)` as input and returns the predicted values of `y` for each sample."
      ],
      "metadata": {
        "id": "PNrFpF22sAFg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# TRAINING AND VALIDATION\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn import datasets\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "X, y = datasets.make_regression(n_samples=100, n_features=1, noise=20, random_state=4)\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1234)\n",
        "\n",
        "fig = plt.figure(figsize=(8,6))\n",
        "plt.scatter(X[:, 0], y, color = \"b\", marker = \"o\", s = 30)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "id": "_90vXoQ3rVGw",
        "outputId": "aa345c55-2576-429b-fbc9-c18c287c7b20"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "reg = LinearRegression()\n",
        "reg.fit(X_train,y_train)\n",
        "predictions = reg.predict(X_test)"
      ],
      "metadata": {
        "id": "JT4JK8V8ri7H"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def mse(y_test, predictions):\n",
        "    return np.mean((y_test-predictions)**2)\n",
        "\n",
        "mse = mse(y_test, predictions)\n",
        "print(mse)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mmikHn0SrtLT",
        "outputId": "cb36dfc3-59cb-4c3c-c210-5b6d55b3baba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "305.7719958301902\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred_line = reg.predict(X)\n",
        "cmap = plt.get_cmap('viridis')\n",
        "fig = plt.figure(figsize=(8,6))\n",
        "m1 = plt.scatter(X_train, y_train, color=cmap(0.9), s=10)\n",
        "m2 = plt.scatter(X_test, y_test, color=cmap(0.5), s=10)\n",
        "plt.plot(X, y_pred_line, color='black', linewidth=2, label='Prediction')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "id": "1jmFCdzqrzkQ",
        "outputId": "a7fc519b-ca80-4459-dc8f-790e3c1d9959"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}