linearRegressionSingleFeature_prob2.ipynb

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      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "FNVKUjDbz8wX",
        "outputId": "199c7e74-534b-4694-dc25-39e66cb54b13"
      },
      "source": [
        "# Assignment 3, Problem 1\n",
        "# Purpose:  Build a linear regression model that predicts output\n",
        "#           based on a single input feature.\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn import metrics\n",
        "\n",
        "\n",
        "#\n",
        "# Function:   estimate_coeffs\n",
        "# Purpose:    To calculate the intercept and slope of the \n",
        "#             regression line based on the training data\n",
        "# Input:      \n",
        "#     x:      input training data\n",
        "#     y:      training output\n",
        "# Output:\n",
        "#     ( w0, w1): intercept and slope of the linear regression model\n",
        "#\n",
        "def estimate_coeffs(x, y):\n",
        "\n",
        "    # reshape data as .fit() wants 2D arrays, and currently x and y are only 1D arrays\n",
        "    x = x.reshape(-1,1)\n",
        "    y = y.reshape(-1,1)\n",
        "\n",
        "    x_mean = np.mean(x)\n",
        "    y_mean = np.mean(y)\n",
        "    numerator = 0\n",
        "    denominator = 0\n",
        "\n",
        "    for i in range(len(x)):\n",
        "        numerator += (x[i] - x_mean)*(y[i] - y_mean)\n",
        "        denominator += (x[i] - x_mean)*(x[i] - x_mean) \n",
        "    \n",
        "    slope = numerator / denominator\n",
        "    intercept = y_mean - slope*x_mean\n",
        "\n",
        "\n",
        "    return ( intercept, slope )\n",
        "    \n",
        "\n",
        "#\n",
        "# Function:   plot_regression_line\n",
        "# Purpose:    To plot the x and y data along with the \n",
        "#             trained linear model.\n",
        "# Input:      \n",
        "#     x:      input training data\n",
        "#     y:      training output\n",
        "#     w:      [0] intercept and [1] slope of trained model\n",
        "\n",
        "#    NOTE: Actually plotting testing data not training data\n",
        "#\n",
        "def plot_regression_line(x, y, w):\n",
        "    # plot data points\n",
        "    plt.scatter(x, y, color = \"gray\", alpha=0.5, marker = \"o\", s = 30)\n",
        "    \n",
        "    # calculate prediction vector\n",
        "    y_pred = w[0] + w[1]*x\n",
        "\n",
        "    # plot the regression line\n",
        "    plt.plot(x, y_pred, color = \"g\", linewidth = 3 )\n",
        "    \n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('y')\n",
        "    \n",
        "    plt.show()\n",
        "    \n",
        "\n",
        "def main():\n",
        "    # Import data.\n",
        "    npData = np.array(data)\n",
        "    y = npData[:,0]\n",
        "    x = npData[:,1]\n",
        "\n",
        "    \n",
        "    ################################################\n",
        "    x_train, x_test, y_train, y_test = train_test_split(x,y, test_size=0.2)\n",
        "    ################################################\n",
        "\n",
        "    \n",
        "    ################################################\n",
        "    # To Do: Call the estimate_coeffs function to calculate\n",
        "    # the weights for the 'best fit' line.\n",
        "    w = estimate_coeffs(x_train, y_train)\n",
        "    ################################################\n",
        "\n",
        "\n",
        "    print ( \"Estimated Coefficients:\" )\n",
        "    print ( \"  w0: \" + np.str(w[0]) + \"   w1: \" + np.str(w[1]) )\n",
        "    \n",
        "    # Plot the regression line with data\n",
        "    plot_regression_line ( x_test, y_test, w )\n",
        "    \n",
        "    \n",
        "if __name__ == \"__main__\": \n",
        "    main() "
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated Coefficients:\n  w0: [6.97650091]   w1: [-1.00144416]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Scatter Plot')"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "npData = np.array(data)\n",
        "plt.scatter(npData[:,1], npData[:,0], color = \"gray\", alpha=0.5, marker = \"o\", s = 30)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Scatter Plot')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The R^2 of this model is: \n0.9608\n"
          ]
        }
      ],
      "source": [
        "npData = np.array(data)\n",
        "y = npData[:,0]\n",
        "x = npData[:,1]\n",
        "x = x.reshape(-1,1)\n",
        "y = y.reshape(-1,1)\n",
        "reg = LinearRegression()\n",
        "reg.fit(x, y)\n",
        "print(\"The R^2 of this model is: \") \n",
        "print(str((reg.score(x, y)).round(4)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ]
}