Assignment2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Assignment_2 (2).ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.5"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NO1ga5T_aIx-"
      },
      "source": [
        "# Linear Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 330
        },
        "id": "FiJ5-avGN-Ox",
        "outputId": "90b41e4d-4fbd-43a0-c9f6-fec896e76b41"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "x = np.array([20,25,30,35,40,45,50,55,60,65])\n",
        "y = np.array([0.5,1.8,5,6,6.2,6.5,7.8,9.4,9.8,10.9])\n",
        "def LR(x,y):\n",
        "    n = np.size(x)\n",
        "\n",
        "    mean_x = np.mean(x)\n",
        "    mean_y = np.mean(y)\n",
        "\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",
        "    b = SS_xy / SS_xx\n",
        "    a = mean_y - b*mean_x\n",
        "\n",
        "    plt.scatter(x, y)\n",
        "\n",
        "    y_pred = a + b*x\n",
        "\n",
        "    print(\"Estimated coefficients: \\n a:\",a,\"\\n b: \",b)\n",
        "\n",
        "    plt.plot(x, y_pred, color = \"g\")\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('y')\n",
        "    plt.show()\n",
        "\n",
        "LR(x,y)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Estimated coefficients: \n",
            " a: -2.743636363636363 \n",
            " b:  0.2149090909090909\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"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "blObEgPkboji"
      },
      "source": [
        "# Multilinear Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iL0kgv8DWbCK"
      },
      "source": [
        "def MultiLR(x,y):\n",
        "  x_tran = x.T\n",
        "  first = np.matmul(x_tran,x)\n",
        "  first_inv = np.linalg.inv(first)\n",
        "  second = np.matmul(x_tran,y)\n",
        "  W = np.matmul(first_inv,second)\n",
        "  return W"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7e0nljGLbojk"
      },
      "source": [
        "## 2nd Degree MLR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z-dWd9TKbojk"
      },
      "source": [
        "X = np.array([x,x**2,np.ones(len(x))]).T\n",
        "w = MultiLR(X,y)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "08eTQa4VMLJV"
      },
      "source": [
        "generated = np.linspace(20,65,num=100)\n",
        "X_gen = np.array([generated,generated**2,np.ones(len(generated))]).T\n",
        "Y_Prediction = np.matmul(X_gen,w.T)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "V8MaUu1NM_y0",
        "outputId": "26c45759-588f-4eb7-9c54-d49d949ca0ab"
      },
      "source": [
        "plt.plot(generated,Y_Prediction)\n",
        "plt.scatter(X[:,0],y);"
      ],
      "execution_count": 5,
      "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": "LatNql1WQqUK"
      },
      "source": [
        "## 3rd Degree MLR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PtEC3kombojn"
      },
      "source": [
        "X = np.array([x,x**2,x**3,np.ones(len(x))]).T\n",
        "w = MultiLR(X,y)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LD98BfDebojn"
      },
      "source": [
        "generated = np.linspace(20,65,num=100)\n",
        "X_gen = np.array([generated,generated**2,generated**3,np.ones(len(generated))]).T\n",
        "Y_Prediction = np.matmul(X_gen,w.T)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "Wq8yfjPubojo",
        "outputId": "4d265cda-cb5c-47d7-a266-53276bb47c52"
      },
      "source": [
        "plt.plot(generated,Y_Prediction)\n",
        "plt.scatter(X[:,0],y);"
      ],
      "execution_count": 8,
      "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": "cV7DWVorbojo"
      },
      "source": [
        "## 5th Degree MLR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jsg5dcxbbojp"
      },
      "source": [
        "X = np.array([x,x**2,x**3,x**4,x**5,np.ones(len(x))]).T\n",
        "w = MultiLR(X,y)"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lNYfsqhAbojp"
      },
      "source": [
        "generated = np.linspace(20,65,num=100)\n",
        "X_gen = np.array([generated,generated**2,generated**3,\n",
        "                  generated**4,generated**5,np.ones(len(generated))]).T\n",
        "Y_Prediction = np.matmul(X_gen,w.T)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "rnEB9Lohbojp",
        "outputId": "950031ea-114f-4132-b7ba-607498bc1a55"
      },
      "source": [
        "plt.plot(generated,Y_Prediction)\n",
        "plt.scatter(X[:,0],y);"
      ],
      "execution_count": 11,
      "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": "xSPvuKZZbojq"
      },
      "source": [
        "## 8th Degree MLR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hXw7BxaUbojq"
      },
      "source": [
        "X = np.array([x,x**2,x**3,x**4,x**5,x**6,x**7,x**8,np.ones(len(x))]).T\n",
        "w = MultiLR(X,y)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cgHjhgifbojq"
      },
      "source": [
        "generated = np.linspace(20,65,num=100)\n",
        "X_gen = np.array([generated,generated**2,generated**3,generated**4,generated**5,\n",
        "                 generated**6,generated**7,generated**8,np.ones(len(generated))]).T\n",
        "Y_Prediction = np.matmul(X_gen,w.T)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "FgLd1nOKbojr",
        "outputId": "7d022297-ffd1-452c-9454-746ca6fb3812"
      },
      "source": [
        "plt.plot(generated,Y_Prediction)\n",
        "plt.scatter(X[:,0],y);"
      ],
      "execution_count": 14,
      "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"
          }
        }
      ]
    }
  ]
}