regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled11.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNbXfT9NvXYInYZ3J2bY4fW",
      "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/shaneahmed/StatswithPython/blob/main/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": "VRIbruKhGuTE"
      },
      "source": [
        "# CS909 Regression Exercise\n",
        "(Fayyaz Minhas)\n",
        "\n",
        "---\n",
        "\n",
        "Your Name: (Your name goes here)\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "The objective of this exercise is to enable you to do regression with sklearn models. Please use the accompanying lecture slides for conceptural information. \n",
        "\n",
        "## Ordinary Least Squares Regression (OLS)\n",
        "\n",
        "Please try to understand the simple code for OLS given below and relate it to the concepts covere din the class.\n",
        "\n",
        "This is a simple implementation of OLS as covered in the class. Please try to understand what individual lines in the code are doing."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cx2ZDXmv_QzO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 591
        },
        "outputId": "ff9d8b1d-f2f2-441d-861e-3703b607e8e0"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "X0 = np.array([[1],[2]]) #independent variable values\n",
        "y =np.array([3.5,4.75]) # dependent variable (target) values\n",
        "X = np.hstack((X0,np.ones((X0.shape[0],1)))) #append 1 to each example\n",
        "w = np.linalg.pinv(X)@y #finding weights or parameters of the line\n",
        "f = X@w #computing predictions f = w^Tx\n",
        "e = f-y #computing error\n",
        "L = e@e #computing squared error and summing the squared error for all examples\n",
        "plt.figure();plt.plot(X0,f,'ro');plt.plot(X0,y,'bx');plt.grid();plt.xlabel('x');plt.ylabel('output');plt.legend(['Prediction','True']);plt.title('Data Plot')\n",
        "plt.figure();plt.plot(y,f,'o');plt.grid();plt.xlabel('True value');plt.ylabel('Predicted value');plt.title('Regression Scatter Plot')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Regression Scatter Plot')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njjQKsyQU7n0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEWCAYAAABi5jCmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6lTrdCHV0QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ZTVm3kKKkDO"
      },
      "source": [
        "Please answer the following questions: (optional)\n",
        "0. Can you see a linear relationship between the input and output variables for the given data?\n",
        "1. What is the pseudo inverse? What is the pseudo inverse of the given Matrix?\n",
        "2. What does the model predict for an example with a feature value of 1.4?\n",
        "3. How do the model's predictions change when you add another example (say, 1.6) with a feature value (say, 4.6)?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Sko572nLG6i"
      },
      "source": [
        "### OLS using sklearn\n",
        "\n",
        "The code below uses sk-learn for OLS over the same data as above. Please try to understand the role of fit_intercept in the code below and answer the following questions:\n",
        "\n",
        "1. Are your weights from sklearn OLS the same as you got above?\n",
        "2. What is the role of fit_intercept? \n",
        "3. Generate a prediction for a new example using the trained model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7TICxq1kLCnr"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glYFwJf1KSXL"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "imIKESWe_esr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 625
        },
        "outputId": "dd466ad8-bd6c-45e1-c277-ad8b9005f6e3"
      },
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "regr = LinearRegression(fit_intercept = False).fit(X, y)\n",
        "f = regr.predict(X)\n",
        "print('Weights:',regr.coef_)\n",
        "\n",
        "plt.figure();plt.plot(y,f,'o');plt.grid();plt.xlabel('True value');plt.ylabel('Predicted value');plt.title('Regression Scatter Plot')\n",
        "\n",
        "# No need to append 1 to feature vector using below\n",
        "from sklearn.linear_model import LinearRegression\n",
        "regr = LinearRegression(fit_intercept = True).fit(X0, y)\n",
        "f = regr.predict(X0)\n",
        "print('Weights:',regr.coef_)\n",
        "plt.figure();plt.plot(y,f,'o');plt.grid();plt.xlabel('True value');plt.ylabel('Predicted value');plt.title('Regression Scatter Plot')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.25 2.25]\n",
            "[1.25]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Regression Scatter Plot')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEWCAYAAABi5jCmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6lTrdCHV0QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEWCAYAAABi5jCmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0\ndHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAeZElEQVR4nO3de5QcZZ3/8feHEElkgKCBWSFAlGAE\nUcGJChs9ZiAsCDHi+hPwdzhHdlnihbOi4WZ2kQVWlwV0RVfwhq4gsiPyA34hCvHCxF1UZBPDRYJ4\ngSAkIhcJMBC5fvePeka62p7umplUV/fk8zqnTury1FPfpydd367bU4oIzMzMhm1RdQBmZtZZnBjM\nzCzHicHMzHKcGMzMLMeJwczMcpwYzMwsx4nBNkuS/kHSRVXH0U0khaRZVcdh5XNisDGRtFbSRklD\nku6X9DVJPVXHVVRE/EtE/N2mrlfSiyR9StJ96bNZK+n8TVDvWknza6Znph31luOtu0GdQzWxf3QM\n9Rwj6YZNFZe1nxODjcfbI6IH2AfYF1hSxkYkTSqj3pIsAeYAbwS2AeYBP6syoEZaJJRp6e/6HuB0\nSYe0KSzrEE4MNm4RcT+wnCxBACBpK0mflPRbSb+X9AVJU2uWnyLpd5LWS/q72tMU6ejj85K+I+kJ\noL9ZfZKmS1omaYOkP0j6b0lbpGWnSlon6XFJd0o6MM0/Q9KlNfEslHR7qmOFpD1rlq2VdJKkWyU9\nKumbkqaM8HG8AbgqItZHZm1EXFJT1y6SrpT0oKSHJX0uzd9d0vVp3kOSviFpWlr2dWBX4Jr0S/4U\n4L9SlRvSvP1T2b+VdIekRyQtl7RbzbZD0vGSfgX8qsDf9SfA7cDe9cskbSfpktSOeySdJmmL9Ll9\nAdg/xbWh1XasA0WEBw+jHoC1wPw0PgO4DfhMzfJPA0uBl5D9cr4GODstOwS4H3g18GLgUiCAWWn5\n14BHgblkP16mtKjvbLKd0eQ0vAUQMBu4F9gplZsJ7J7GzwAuTeOvBJ4ADkrrnwL8GnhRTVtvAnZK\n278DeP8In8tpwG+BDwKvAVSzbBJwS2rL1qldb07LZqXtbwXsQLbjP7/R513TlgC2rJn3jhT3nsCW\nKZYf1ywP4HupDVMbxP6nOtPnNxd4EjiwZv3hv9ElwP9Pf4uZwC+BY9OyY4Abqv4/6mEc3++qA/DQ\nnUPaUQ0Bj6cdxg/ITkGQdipPDO+E07z9gbvT+FeHd+ppehZ/nhguqVneqr6z0k5qVl2Ms4AHgPnA\n5LpltYnhY8DlNcu2ANYB82raenTN8nOBL4zwuUwCjgd+BDwFrAfeWxPzg7U78yaf7+HA6rrPu1Vi\nuHZ451zTjieB3dJ0AAc02eZwnRuAR8gS4Idqlkf6TCcBTwN71Sx7H7AijTsxdPngU0k2HodHxPB5\n9FcB09P8HciOBFalUzMbgOvSfMh+ed9bU0/teKN5reo7j+yX8ncl3TV8wTQifg18mCwJPCBpQNJO\nDba1E3DP8EREPJ+2v3NNmftrxp8EGl5oj4jnIuKCiJgLTAM+AXw1nWLZBbgnIp6tX09Sb4pvnaTH\nyI6ipteXa2E34DM1n9EfyJJqbTsafdb1pkfE9hGxZ0R8ttFysiOre2rm3VO3HetiTgw2bhHxQ7Jf\n+Z9Msx4CNgKvjohpadgusguaAL8jO/00bJdG1daMN60vIh6PiBMj4hXAQmDx8LWEiLgsIt5MttMM\n4JwG21qflgMgSSmmdcU/hQYNiNgYEReQ/frei2ynvOsIF37/JcX3mojYFjiabKf+p+rqq29Qx73A\n+2o+o2kRMTUiftxivdF6CHiGms+M7BrI8OflLpu7nBODbSrnAwdJel36xf1l4NOSdgSQtLOkg1PZ\ny4G/kbSnpBeTncoZUav6JC2QNCvt0B8FngOelzRb0gGStgL+SJZcnm+wicuBwyQdKGkycCLZaaAf\nNyjblKQPS5onaaqkLSW9l+w8/Gqy6xS/A/5V0taSpkiam1bdhuzU3KOSdgZOrqv698AraqYfTG2p\nnfcFYImkV6dYtpP07tG2oZWIeI7sM/uEpG3SBe7FZEc5w7HOkPSiTb1taw8nBtskIuJBsguSp6dZ\np5Kd3rkxnRr5PtnFYCLiWuCzwOBwmbTOU002MWJ9wB5pegj4CXBhRAySXcj9V7JfuPcDO9LgltqI\nuJPsF/q/p7JvJ7sV9+lRfQiZJ4FPpe09RHa94V0RcVfaob6d7Dz9b4H7gCPTemcCrydLbN8Grqyr\n92zgtHSa6KSIeJLsNNWP0rz9IuIqsiOigfQZ/Rx42xjaUMTfk133uQu4AbiM7NoRwPVkdzPdL+mh\nkrZvJVKEj/qsWun8+8+BrRqdfzez9vIRg1VC0jvTswnbk/3KvcZJwawzODFYVd5Hdivpb8iuCXyg\n2nDMbJhPJZmZWU7pRwySJklaLWlZg2W7ShpMy2+VdGjZ8ZiZWXObrGfGJk4ge4Jy2wbLTiN74vTz\nkvYCvkP29OWIpk+fHjNnNi1SqSeeeIKtt9666jDGrNvjB7ehE3R7/DDx2rBq1aqHImKHFqsAJScG\nSTOAw8huq1vcoEjwQsLYjuxBo6ZmzpzJypUrN1mMm9qKFSuYN29e1WGMWbfHD25DJ+j2+GHitUHS\nPc1Lv6DUawySriC7/3ob4KSIWFC3/GXAd4HtyToVmx8RqxrUswhYBNDb29s3MDBQWszjNTQ0RE9P\n17yW4M90e/zgNnSCbo8fJl4b+vv7V0XEnEIrltUJE7CA7EEjyPrSWdagzGLgxDS+P7AG2KJZvX19\nfdHJBgcHqw5hXLo9/gi3oRN0e/wRE68NwMrogE705gILJa0FBoADavu/T44le7SeyPp+n8LoOw4z\nM7NNqLTEEBFLImJGRMwEjgKuj4ij64r9Fhh+ccqeZInhwbJiMjOz1tr+gJuksyQtTJMnAsdJugX4\nT+CYdMhjZmYVacftqkTECmBFGj+9Zv4aslNOZmY2gqtXr+O85XeyfsNGdpo2lZMPns3h+5b3+ou2\nJAYzMxubq1evY8mVt7HxmecAWLdhI0uuvA2gtOTgvpLMzDrYecvv/FNSGLbxmec4b/mdpW3TicHM\nrIOt37BxVPM3BScGM7MOttO0qaOavyk4MZiZdbCTD57N1MmTcvOmTp7EyQfPHmGN8fPFZzOzDjZ8\ngdl3JZmZ2Z8cvu/OpSaCej6VZGZmOU4MZmaW48RgZmY5TgxmZpbjxGBmZjlODGZmluPEYGZmOU4M\nZmaW48RgZmY5TgxmZpbjxGBmZjlODGZmluPEYGZmOU4MZmaW48RgZmY5TgxmZpZTemKQNEnSaknL\nRlh+hKQ1km6XdFnZ8ZiZWXPteIPbCcAdwLb1CyTtASwB5kbEI5J2bEM8ZmbWRKlHDJJmAIcBF41Q\n5Djggoh4BCAiHigzHjMza00RUV7l0hXA2cA2wEkRsaBu+dXAL4G5wCTgjIi4rkE9i4BFAL29vX0D\nAwOlxTxeQ0ND9PT0VB3GmHV7/OA2dIJujx8mXhv6+/tXRcScQitGRCkDsAC4MI3PA5Y1KLMMuAqY\nDLwcuBeY1qzevr6+6GSDg4NVhzAu3R5/hNvQCbo9/oiJ1wZgZRTcf5d5KmkusFDSWmAAOEDSpXVl\n7gOWRsQzEXE32dHDHiXGZGZmLZSWGCJiSUTMiIiZwFHA9RFxdF2xq8mOJpA0HXglcFdZMZmZWWtt\nf45B0lmSFqbJ5cDDktYAg8DJEfFwu2MyM7MXtON2VSJiBbAijZ9eMz+AxWkwM7MO4Cefzcwsx4nB\nzMxynBjMzCzHicHMzHKcGMzMLMeJwczMcpwYzMwsx4nBzMxynBjMzCzHicHMzHKcGMzMLMeJwczM\ncpwYzMwsx4nBzMxynBjMzCzHicHMzHKcGMzMLMeJwczMcpwYzMwsx4nBzMxynBjMzCzHicHMzHJK\nTwySJklaLWlZkzLvkhSS5pQdj5mZNdeOI4YTgDtGWihpm1Tmp22IxczMWig1MUiaARwGXNSk2D8D\n5wB/LDMWMzMrpuwjhvOBU4DnGy2U9Hpgl4j4dslxmJlZQYqIciqWFgCHRsQHJc0DToqIBTXLtwCu\nB46JiLWSVqQyKxvUtQhYBNDb29s3MDBQSsybwtDQED09PVWHMWbdHj+4DZ2g2+OHideG/v7+VRFR\n7DpuRJQyAGcD9wFrgfuBJ4FLa5ZvBzyUlq8lO5W0HpjTrN6+vr7oZIODg1WHMC7dHn+E29AJuj3+\niInXBmBlFNx/l3YqKSKWRMSMiJgJHAVcHxFH1yx/NCKmR8TMVOZGYGE0OGIwM7P2aftzDJLOkrSw\n3ds1M7NitmzHRiJiBbAijZ8+Qpl57YjFzMya85PPZmaWUygxSNpN0vw0PjU9lGZmZhNQy8Qg6Tjg\nCuCLadYM4OoygzIzs+oUOWI4HpgLPAYQEb8CdiwzKDMzq06RxPBURDw9PCFpS6Ccp+LMzKxyRRLD\nDyX9AzBV0kHAt4Bryg3LzMyqUiQxfBR4ELgNeB/wHeC0MoMyM7PqtHyOISKeB76cBjMzm+BaJgZJ\nd9PgmkJEvKKUiMzMrFJFnnyu7Y1vCvBu4CXlhGNmZlVreY0hIh6uGdZFxPlkL98xM7MJqMippNfX\nTG5BdgTRlj6WzMys/Yrs4D9VM/4s2bsTjiglGjMzq1yRu5L62xGImZl1hhETg6TFzVaMiH/b9OGY\nmVnVmh0xuAdVM7PN0IiJISLObGcgZmbWGYrclTQFOBZ4NdlzDABExN+WGJeZmVWkSF9JXwf+AjgY\n+CHZ+xgeLzMoMzOrTpHEMCsiPgY8EREXkz3c9qZywzIzs6oUSQzPpH83SNob2A6/qMfMbMIq8oDb\nlyRtD3wMWAr0pHEzM5uAiiSG/4iI58iuL7hHVTOzCa7IqaS7JX1J0oGSNNoNSJokabWkZQ2WLZa0\nRtKtkn4gabfR1m9mZptWkcTwKuD7wPHAWkmfk/TmUWzjBOCOEZatBuZExGuBK4BzR1GvmZmVoEi3\n209GxOUR8dfAPsC2ZKeVWpI0g+wupotGqHswIp5MkzeS3QprZmYVUsSfvZztzwtJbwWOBA4BVgLf\njIj/V2C9K4CzybrXOCkiFjQp+zng/oj4eINli4BFAL29vX0DAwMtY67K0NAQPT09VYcxZt0eP7gN\nnaDb44eJ14b+/v5VETGnxSqZiGg6kHWzfRXwHmDrVuVr1lsAXJjG5wHLmpQ9muyIYatW9fb19UUn\nGxwcrDqEcen2+CPchk7Q7fFHTLw2ACuj4P67yF1Jr42IxwqnqBfMBRZKOpSsK41tJV0aEUfXFpI0\nH/hH4K0R8dQYtmNmZptQkWsMY0kKRMSSiJgRETOBo4DrGySFfYEvAgsj4oGxbMfMzDatInclbVKS\nzpK0ME2eR/bA3Lck3SxpabvjMTOzvLa8uzkiVgAr0vjpNfPnt2P7ZmZWnN/gZmZmOUXe4DYbeANZ\nP0kAbwduKjMoMzOrTss3uEn6L+D1EfF4mj4D+HZbojMzs7YrcvG5F3i6ZvrpNM/MzCagIhefLwFu\nknRVmj4cuLi8kMzMrEotE0NEfELStcBb0qy/iYjV5YZlZmZVKfocw4uBxyLiM8B9kl5eYkxmZlah\nlolB0j8BpwJL0qzJwKVlBmVmZtUpcsTwTmAh8ARARKznhVtZzcxsgimSGJ5OPfMFgKStyw3JzMyq\nVCQxXC7pi8A0SceRvc2t4Yt3zMys+xW5K+mTkg4CHiN7Cvr0iPhe6ZGZmVklWiYGSedExKnA9xrM\nMzOzCabIqaSDGsx726YOxMzMOkOz3lU/AHwQ2F3SrTWLtgF+XHZgZmZWjWanki4DrgXOBj5aM//x\niPhDqVGZmVllRjyVFBGPRsRa4DPAHyLinoi4B3hW0pvaFaCZmbVXkWsMnweGaqaH0jwzM5uAiiQG\npQfcAIiI52nTK0HNzKz9iiSGuyR9SNLkNJwA3FV2YGZmVo0iieH9wF8C64D7gDcBi8oMyszMqlPk\nyecHgKPaEIuZmXWAZs8xnBIR50r6d1IHerUi4kOlRmZmZpVodsRwR/p35Xg2IGlSqmNdRCyoW7YV\n2atD+4CHgSPTLbJmZlaRERNDRFyT/h3v+51PIEsy2zZYdizwSETMknQUcA5w5Di3Z2Zm49DsVNI1\nNDiFNCwiFraqXNIM4DDgE8DiBkXeAZyRxq8APicpd3usmZm1l0baB0t6axr9a+AveOF1nu8Bfh8R\nH2lZuXQFWZca2wAnNTiV9HPgkIi4L03/BnhTRDxUV24R6U6o3t7evoGBgWKtq8DQ0BA9PT1VhzFm\n3R4/uA2doNvjh4nXhv7+/lURMafQihHRdABWFpnXoMwC4MI0Pg9Y1qDMz4EZNdO/AaY3q7evry86\n2eDgYNUhjEu3xx/hNnSCbo8/YuK1och+e3go8hzD1pJeMTwh6eVAkdd7zgUWSloLDAAHSLq0rsw6\nYJdU75bAdmQXoc3MrCJFEsNHgBWSVkj6ITAIfLjVShGxJCJmRMRMsucgro+Io+uKLQXem8b/Tyrj\n6wtmZhUq8oDbdZL2AF6VZv0iIp4a6wYlnUV2SLMU+ArwdUm/Bv6AH6QzM6tckVd7vpjsjqLdIuI4\nSXtImh0Ry4puJCJWACvS+Ok18/8IvHu0QZuZWXmKnEr6D+BpYP80vQ74eGkRmZlZpYokht0j4lzg\nGYCIeBJQqVGZmVlliiSGpyVNJT3sJml3YMzXGMzMrLMVeeHOPwHXAbtI+gbZbajHlBmUmZlVp2li\nkCTgF2RPP+9HdgrphKh7MtnMzCaOpokhIkLSdyLiNcC32xSTmZlVqMg1hp9JekPpkZiZWUcoco3h\nTcDRqWuLJ8hOJ0VEvLbMwMzMrBpFEsPBpUdhZmYdo9n7GKYA7wdmAbcBX4mIZ9sVmJmZVaPZNYaL\ngTlkSeFtwKfaEpGZmVWq2amkvdLdSEj6CnBTe0IyM7MqNTtieGZ4xKeQzMw2H82OGF4n6bE0LmBq\nmh6+K2nb0qMzM7O2GzExRMSkdgZiZmadocgDbmZmthlxYjAzsxwnBjMzy3FiMDOzHCcGMzPLcWIw\nM7McJwYzM8spLTFImiLpJkm3SLpd0pkNyuwqaVDSakm3Sjq0rHjMzKyYMo8YngIOiIjXAfsAh0ja\nr67MacDlEbEvcBRwYYnxmJlZAUXexzAmERHAUJqcnIaoLwYMd62xHbC+rHjMzKwYZfvvkiqXJgGr\nyN7pcEFEnFq3/GXAd4Htga2B+RGxqkE9i4BFAL29vX0DAwOlxTxeQ0ND9PT0VB3GmHV7/OA2dIJu\njx8mXhv6+/tXRcScQitGROkDMA0YBPaum78YODGN7w+sAbZoVldfX190ssHBwapDGJdujz/CbegE\n3R5/xMRrA7AyCu6z23JXUkRsSInhkLpFxwKXpzI/AaYA09sRk5mZNVbmXUk7SJqWxqcCBwG/qCv2\nW+DAVGZPssTwYFkxmZlZa6VdfAZeBlycrjNsQXb30TJJZ5Ed0iwFTgS+LOkjZBeij0mHPGZmVpEy\n70q6Fdi3wfzTa8bXAHPLisHMzEbPTz6bmVmOE4OZmeU4MZiZWY4Tg5mZ5TgxmJlZjhODmZnlODGY\nmVmOE4OZmeU4MZiZWY4Tg5mZ5TgxmJlZjhODmZnlODGYmVmOE4OZmeU4MZiZWY4Tg5mZ5TgxmJlZ\njhODmZnlODGYmVmOE4OZmeU4MZiZWY4Tg5mZ5TgxmJlZTmmJQdIUSTdJukXS7ZLOHKHcEZLWpDKX\nlRWPmZkVs2WJdT8FHBARQ5ImAzdIujYibhwuIGkPYAkwNyIekbRjifGYmVkBpSWGiAhgKE1OTkPU\nFTsOuCAiHknrPFBWPGZmVoyy/XdJlUuTgFXALLIEcGrd8quBXwJzgUnAGRFxXYN6FgGLAHp7e/sG\nBgZKi3m8hoaG6OnpqTqMMev2+MFt6ATdHj9MvDb09/eviog5hVaMiNIHYBowCOxdN38ZcBXZ0cTL\ngXuBac3q6uvri042ODhYdQjj0u3xR7gNnaDb44+YeG0AVkbBfXZb7kqKiA0pMRxSt+g+YGlEPBMR\nd5MdPezRjpjMzKyxMu9K2kHStDQ+FTgI+EVdsauBeanMdOCVwF1lxWRmZq2VeVfSy4CL03WGLYDL\nI2KZpLPIDmmWAsuBv5K0BngOODkiHi4xJjMza6HMu5JuBfZtMP/0mvEAFqfBzMw6gJ98NjOzHCcG\nMzPLcWIwM7McJwYzM8txYjAzsxwnBjMzy3FiMDOznDIfcOsYV69ex3nL72T9ho3sNG0qJx88m8P3\n3bnqsMzMOtKETwxXr17HkitvY+MzzwGwbsNGllx5G4CTg5lZAxP+VNJ5y+/8U1IYtvGZ5zhv+Z0V\nRWRm1tkmfGJYv2HjqOabmW3uJnxi2Gna1FHNNzPb3E34xHDywbOZOnlSbt7UyZM4+eDZFUVkZtbZ\nJvzF5+ELzL4rycysmAmfGCBLDk4EZmbFTPhTSWZmNjpODGZmluPEYGZmOU4MZmaW48RgZmY5ioiq\nYxgVSQ8C91QdRxPTgYeqDmIcuj1+cBs6QbfHDxOvDbtFxA5FVuq6xNDpJK2MiDlVxzFW3R4/uA2d\noNvjh827DT6VZGZmOU4MZmaW48Sw6X2p6gDGqdvjB7ehE3R7/LAZt8HXGMzMLMdHDGZmluPEYGZm\nOU4MoyRpiqSbJN0i6XZJZ45Q7ghJa1KZy9odZzNF2iBpV0mDklZLulXSoVXE2oqkSSnGZQ2WbSXp\nm5J+Lemnkma2P8LmWsS/OP0fulXSDyTtVkWMrTRrQ02Zd0kKSR15+2erNnTy9xla/j8a9Xd5s+h2\nexN7CjggIoYkTQZukHRtRNw4XEDSHsASYG5EPCJpx6qCHUHLNgCnAZdHxOcl7QV8B5hZQaytnADc\nAWzbYNmxwCMRMUvSUcA5wJHtDK6AZvGvBuZExJOSPgCcS+fFD83bgKRtUpmftjOoURqxDV3wfYbm\nf4NRf5d9xDBKkRlKk5PTUH8F/zjggoh4JK3zQBtDbKlgG4IX/pNtB6xvU3iFSZoBHAZcNEKRdwAX\np/ErgAMlqR2xFdEq/ogYjIgn0+SNwIx2xVZUgb8BwD+TJeU/tiWoUSrQho7+PheIf9TfZSeGMUiH\nbTcDDwDfi4j6X0KvBF4p6UeSbpR0SPujbK5AG84AjpZ0H9kvjL9vc4hFnA+cAjw/wvKdgXsBIuJZ\n4FHgpe0JrZBW8dc6Fri23HDGpGkbJL0e2CUivt3WqEan1d+h07/PreI/g1F+l50YxiAinouIfch+\nwb1R0t51RbYE9gDmAe8BvixpWnujbK5AG94DfC0iZgCHAl+X1DH/XyQtAB6IiFVVxzIWo4lf0tHA\nHOC80gMbhVZtSP9f/g04sa2BjULBv0PHfp8Lxj/q73LHfNG7UURsAAaB+l8Q9wFLI+KZiLgb+CXZ\nf6yO06QNxwKXpzI/AaaQdcjVKeYCCyWtBQaAAyRdWldmHbALgKQtyQ6jH25nkE0UiR9J84F/BBZG\nxFPtDbGlVm3YBtgbWJHK7Acs7bAL0EX+Dp38fS4S/+i/yxHhYRQDsAMwLY1PBf4bWFBX5hDg4jQ+\nnex0xkurjn2UbbgWOCaN70l2XlJVxz5Ce+YByxrMPx74Qho/iuwCXOXxjiL+fYHfAHtUHeNY21BX\nZgXZxfTK4x3l36Gjv88F4h/1d9lHDKP3MmBQ0q3A/5Cdn18m6SxJC1OZ5cDDktaQ/Ro/OSI65Zcq\nFGvDicBxkm4B/pPsP1bHPyZf14avAC+V9GtgMfDR6iIrpi7+84Ae4FuSbpa0tMLQCqtrQ1fqsu/z\nnxnvd9ldYpiZWY6PGMzMLMeJwczMcpwYzMwsx4nBzMxynBjMzCzHicEmPEkvTbd73izpfknraqZf\nVGFc8yVdXdX2zUbi3lVtwkv3nO8DIOkMYCgiPllbJnWup4go0m+R2YTmIwbbbEmalfrY/wZwO7CL\npA01y4+SdFEa75V0paSVyt5lsV+D+lZKml0zfYOkfSTtJ+knqT/8H6VunOvX/bikD9dM/yL1momk\n96Zt3izpwk7qs8omJv8Hs83dq4BPR8ReZH0rjeSzwLkRMQc4gsZdHH8zLRvuCvklEXEzWT/5b4mI\nfcm6oP540eBS54bvBP4ysk4PtyTr3sOsND6VZJu730TEygLl5gOza17nsL2kqRGxsabM5cA1ZDv/\nI4FvpfnTgEsk7T6G+OYDbwBWpm1PJXUlblYWJwbb3D1RM/48UPsinyk14wLeGBFPj1RRRNwjaSi9\nJetI4Ji06BPA8oi4UNIs4LoGqz9L/gh+eNsCvhoRHyvSGLNNwaeSzJJ04fkRSXuk8/jvrFn8fbLe\nWgGQtM8I1XyT7DWQW0XEmjRvO144TXXMCOutBfpS3W8kdReetnuEpOlp2Usl7TqKZpmNmhODWd6p\nZL1p/pisH/5hxwNzlb1MfQ3Z6x4b+Rbwf0n93yfnAOdJ+hn5I5L69Xol/RxYBNwFEBG3AWcC30+9\n4X4X6B1Lw8yKcu+qZmaW4yMGMzPLcWIwM7McJwYzM8txYjAzsxwnBjMzy3FiMDOzHCcGMzPL+V/l\n6lTrdCHV0QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sGjlCeQmVomD"
      },
      "source": [
        "# Regression Exercise: \r\n",
        "\r\n",
        "1. You are given the height and weight data for a set of individuals below. Use OLS to find the linear function that allows you to predict weight of a person given their height. [40]\r\n",
        "2. Plot the scatter plot of the true vs. predicted dependent variable. [20]\r\n",
        "3. Calculate the pearson correlation between the true and predicted variables. [20]\r\n",
        "4. Write, in your own words, the limitations of OLS. [20]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cE-bXiBZVcHt"
      },
      "source": [
        "import numpy as np\r\n",
        "weights = np.array([73,95,72,69,76,82,95,89,89,83,94,89,103]) #in kg\r\n",
        "heights = np.array([56,73,60,54,56,62,77,73,72,69,74,67,84,]) #in inches\r\n",
        "\r\n",
        "# your code goes here."
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}