R_simpson_paradox.ipynb

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  "metadata": {
    "colab": {
      "name": "R_Simpson_Paradox.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    }
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  "cells": [
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      "cell_type": "markdown",
      "metadata": {
        "id": "W0lCCEGrytFd",
        "colab_type": "text"
      },
      "source": [
        "Colab Link: https://colab.research.google.com/drive/1jvXAqNAUx0vgOhMRTBLPJwJe26vsbRrQ\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TPLNmzb7qmVN",
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      "source": [
        "**Executive Summary**\n",
        "\n",
        "In this analysis we will be using the mtcars data available in the R data base to explore the relationship between transmission and miles per gallon. While we have shown that automatic cars in our date set tend to have lower miles per Gallons, we have also proven that transmission was not a significant element to define Miles per Gallon and that observed correlation was due to a Simpson paradox which is proven in this paper. We conclude the best elements to be used to predict Miles per Gallons are the weights if the cars and the horsepower. We succeeded to reach .9092 of correlation between the initial weights and the fitted results."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vpYnZoscyN6l",
        "colab_type": "text"
      },
      "source": [
        "**Set Environment**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rCEtur7fajGn",
        "colab_type": "code",
        "outputId": "0f086b1b-181e-43bf-93be-f05bfd3acd0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "#set R environment\n",
        "cat(system('python3 -c \"from google.colab import drive\\ndrive.mount()\"', intern=TRUE), sep='\\n', wait=TRUE)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning message in system(\"python3 -c \\\"from google.colab import drive\\ndrive.mount()\\\"\", :\n",
            "“running command 'python3 -c \"from google.colab import drive\n",
            "drive.mount()\"' had status 1”\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "TRUE\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3i0-FV1wrTWZ",
        "colab_type": "code",
        "outputId": "0d0e0d6a-3386-456a-ae9e-119dc4a32ed5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "source": [
        "\n",
        "install.packages(\"ggplot2\", repos='http://cran.us.r-project.org', quiet=TRUE)\n",
        "install.packages('dplyr')\n",
        "install.packages('PerformanceAnalytics')\n",
        "install.packages('car')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dQ5Kv5CXrbbO",
        "colab_type": "code",
        "outputId": "8f0cfc28-513e-44b9-ab5d-0a334c7bd646",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 969
        }
      },
      "source": [
        "library(ggplot2)\n",
        "library(dplyr)\n",
        "library(PerformanceAnalytics)\n",
        "library(car)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Attaching package: ‘dplyr’\n",
            "\n",
            "\n",
            "The following objects are masked from ‘package:stats’:\n",
            "\n",
            "    filter, lag\n",
            "\n",
            "\n",
            "The following objects are masked from ‘package:base’:\n",
            "\n",
            "    intersect, setdiff, setequal, union\n",
            "\n",
            "\n",
            "Loading required package: xts\n",
            "\n",
            "Loading required package: zoo\n",
            "\n",
            "\n",
            "Attaching package: ‘zoo’\n",
            "\n",
            "\n",
            "The following objects are masked from ‘package:base’:\n",
            "\n",
            "    as.Date, as.Date.numeric\n",
            "\n",
            "\n",
            "\n",
            "Attaching package: ‘xts’\n",
            "\n",
            "\n",
            "The following objects are masked from ‘package:dplyr’:\n",
            "\n",
            "    first, last\n",
            "\n",
            "\n",
            "\n",
            "Attaching package: ‘PerformanceAnalytics’\n",
            "\n",
            "\n",
            "The following object is masked from ‘package:graphics’:\n",
            "\n",
            "    legend\n",
            "\n",
            "\n",
            "Loading required package: carData\n",
            "\n",
            "\n",
            "Attaching package: ‘car’\n",
            "\n",
            "\n",
            "The following object is masked from ‘package:dplyr’:\n",
            "\n",
            "    recode\n",
            "\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_v_PBTjzs3K0",
        "colab_type": "text"
      },
      "source": [
        "**Exploratory Analysis**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gfYdBNPYswwu",
        "colab_type": "code",
        "outputId": "6a271708-7bdb-45fe-8129-55d645b4ed0f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "data(mtcars)\n",
        "head(mtcars)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "                  mpg  cyl disp hp  drat wt    qsec  vs am gear carb\n",
              "Mazda RX4         21.0 6   160  110 3.90 2.620 16.46 0  1  4    4   \n",
              "Mazda RX4 Wag     21.0 6   160  110 3.90 2.875 17.02 0  1  4    4   \n",
              "Datsun 710        22.8 4   108   93 3.85 2.320 18.61 1  1  4    1   \n",
              "Hornet 4 Drive    21.4 6   258  110 3.08 3.215 19.44 1  0  3    1   \n",
              "Hornet Sportabout 18.7 8   360  175 3.15 3.440 17.02 0  0  3    2   \n",
              "Valiant           18.1 6   225  105 2.76 3.460 20.22 1  0  3    1   "
            ],
            "text/latex": "A data.frame: 6 × 11\n\\begin{tabular}{r|lllllllllll}\n  & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\tMazda RX4 & 21.0 & 6 & 160 & 110 & 3.90 & 2.620 & 16.46 & 0 & 1 & 4 & 4\\\\\n\tMazda RX4 Wag & 21.0 & 6 & 160 & 110 & 3.90 & 2.875 & 17.02 & 0 & 1 & 4 & 4\\\\\n\tDatsun 710 & 22.8 & 4 & 108 &  93 & 3.85 & 2.320 & 18.61 & 1 & 1 & 4 & 1\\\\\n\tHornet 4 Drive & 21.4 & 6 & 258 & 110 & 3.08 & 3.215 & 19.44 & 1 & 0 & 3 & 1\\\\\n\tHornet Sportabout & 18.7 & 8 & 360 & 175 & 3.15 & 3.440 & 17.02 & 0 & 0 & 3 & 2\\\\\n\tValiant & 18.1 & 6 & 225 & 105 & 2.76 & 3.460 & 20.22 & 1 & 0 & 3 & 1\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA data.frame: 6 × 11\n\n| <!--/--> | mpg &lt;dbl&gt; | cyl &lt;dbl&gt; | disp &lt;dbl&gt; | hp &lt;dbl&gt; | drat &lt;dbl&gt; | wt &lt;dbl&gt; | qsec &lt;dbl&gt; | vs &lt;dbl&gt; | am &lt;dbl&gt; | gear &lt;dbl&gt; | carb &lt;dbl&gt; |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| Mazda RX4 | 21.0 | 6 | 160 | 110 | 3.90 | 2.620 | 16.46 | 0 | 1 | 4 | 4 |\n| Mazda RX4 Wag | 21.0 | 6 | 160 | 110 | 3.90 | 2.875 | 17.02 | 0 | 1 | 4 | 4 |\n| Datsun 710 | 22.8 | 4 | 108 |  93 | 3.85 | 2.320 | 18.61 | 1 | 1 | 4 | 1 |\n| Hornet 4 Drive | 21.4 | 6 | 258 | 110 | 3.08 | 3.215 | 19.44 | 1 | 0 | 3 | 1 |\n| Hornet Sportabout | 18.7 | 8 | 360 | 175 | 3.15 | 3.440 | 17.02 | 0 | 0 | 3 | 2 |\n| Valiant | 18.1 | 6 | 225 | 105 | 2.76 | 3.460 | 20.22 | 1 | 0 | 3 | 1 |\n\n",
            "text/html": [
              "<table>\n",
              "<caption>A data.frame: 6 × 11</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>Mazda RX4</th><td>21.0</td><td>6</td><td>160</td><td>110</td><td>3.90</td><td>2.620</td><td>16.46</td><td>0</td><td>1</td><td>4</td><td>4</td></tr>\n",
              "\t<tr><th scope=row>Mazda RX4 Wag</th><td>21.0</td><td>6</td><td>160</td><td>110</td><td>3.90</td><td>2.875</td><td>17.02</td><td>0</td><td>1</td><td>4</td><td>4</td></tr>\n",
              "\t<tr><th scope=row>Datsun 710</th><td>22.8</td><td>4</td><td>108</td><td> 93</td><td>3.85</td><td>2.320</td><td>18.61</td><td>1</td><td>1</td><td>4</td><td>1</td></tr>\n",
              "\t<tr><th scope=row>Hornet 4 Drive</th><td>21.4</td><td>6</td><td>258</td><td>110</td><td>3.08</td><td>3.215</td><td>19.44</td><td>1</td><td>0</td><td>3</td><td>1</td></tr>\n",
              "\t<tr><th scope=row>Hornet Sportabout</th><td>18.7</td><td>8</td><td>360</td><td>175</td><td>3.15</td><td>3.440</td><td>17.02</td><td>0</td><td>0</td><td>3</td><td>2</td></tr>\n",
              "\t<tr><th scope=row>Valiant</th><td>18.1</td><td>6</td><td>225</td><td>105</td><td>2.76</td><td>3.460</td><td>20.22</td><td>1</td><td>0</td><td>3</td><td>1</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eTtISdSRs-pP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# encode all categorical variables as factor\n",
        "mtcars$am     <- as.factor(mtcars$am)\n",
        "mtcars$cyl    <- as.factor(mtcars$cyl)\n",
        "mtcars$vs     <- as.factor(mtcars$vs)\n",
        "mtcars$gear   <- as.factor(mtcars$gear)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oj28_zuHtFbM",
        "colab_type": "text"
      },
      "source": [
        "A data frame with 32 observations on 11 variables.\n",
        "\n",
        "* mpg = Miles/(US) gallon\n",
        "* cyl = Number of cylinders\n",
        "* disp = Displacement (cu.in.)\n",
        "* hp = Gross horsepower\n",
        "* drat = Rear axle ratio\n",
        "* wt = Weight (1000 lbs)\n",
        "* qsec = 1/4 mile time\n",
        "* vs = V engine or straight engine\n",
        "* am = Transmission (0 = automatic, 1 = manual)\n",
        "* gear = Number of forward gears\n",
        "* carb = Number of carburetors\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzO39INDuZk6",
        "colab_type": "text"
      },
      "source": [
        "The box plot and the table below show that manual engines tend to have higher Miles per Gallon. The average MPG for manual cars is 24.39 and 17.14 for automatic transmissions. However, we need to prove that transmission is a significant regressor to evaluate Miles per Gallon (Simpson’s paradox)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j5gFZU82tCDx",
        "colab_type": "code",
        "outputId": "92574af9-ff32-419d-8afa-7c15a530fdb2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "boxplot(mpg~am, data = mtcars,\n",
        "        col = c(\"green\", \"red\"),\n",
        "        xlab = \"Transmission\",\n",
        "        ylab = \"Miles per Gallon\",\n",
        "        main = \"MPG by Transmission Type\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CAmBDsAgJgQ7AAAYkKwAwCICcEOACAmBDsAgJgQ7AAAYkKwAwCICcEOACAmBDsA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\nqwAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “MPG by Transmission Type”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hqg2ASD3ueQS",
        "colab_type": "code",
        "outputId": "ffba3878-7ef3-4895-8efc-0690455b3e26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 137
        }
      },
      "source": [
        "aggregate(mpg~am, data = mtcars, mean)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  am mpg     \n",
              "1 0  17.14737\n",
              "2 1  24.39231"
            ],
            "text/latex": "A data.frame: 2 × 2\n\\begin{tabular}{ll}\n am & mpg\\\\\n <fct> & <dbl>\\\\\n\\hline\n\t 0 & 17.14737\\\\\n\t 1 & 24.39231\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA data.frame: 2 × 2\n\n| am &lt;fct&gt; | mpg &lt;dbl&gt; |\n|---|---|\n| 0 | 17.14737 |\n| 1 | 24.39231 |\n\n",
            "text/html": [
              "<table>\n",
              "<caption>A data.frame: 2 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>am</th><th scope=col>mpg</th></tr>\n",
              "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>0</td><td>17.14737</td></tr>\n",
              "\t<tr><td>1</td><td>24.39231</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pnmc5UGEujhB",
        "colab_type": "text"
      },
      "source": [
        "Imagine you find a correlation between chewing gum usage and cancer. However, you see that smokers tend to use more chewing gums to improve their breath. Would you tend conclude that cancer is due to chewing gum or smoking? This is a simple example Simpson paradox. Another well-known one is the UC Berkeley gender Bias I invite you to look at.\n",
        "\n",
        "The below plot shows a chart between weight and Miles per Gallon. As you can see, heavier are the cars the less Miles per gallons the cars do. The dark dots represent cars with automatic transmissions and light dots represent manual transmissions. The automatic cats of our datasets tend to be heavier than manual cars.\n",
        "\n",
        "Now, would you think that MPG is dictated by the transmission or the weight of the cars? This is a classic Simpson Paradox.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L6Yok6kDum78",
        "colab_type": "code",
        "outputId": "4f6dad89-fd82-43fb-826e-a87e537372bd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "ggplot(aes(x = mpg, y = wt), data = mtcars) + \n",
        "geom_point(alpha = 0.5, size = 5, position = 'jitter',aes(color=am))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QAAgCUIdgAAAJYg2AEAAFiCYAcAAGAJ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\nFUn34ieSuvdypRzwPCFEqi0Zj8cLtVoYhkIpEYuL0tzFe7t1U0E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0Y5mJtFMpiZlCtH1XuGf/RrmBKJUKt+/UnXnn1Anv8MvajwnfE9IR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",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QdH-QNBiyFWC",
        "colab_type": "text"
      },
      "source": [
        "And just for the fun we can do the same with the number of cylinders and the displacement. We have similar results, while we can see that 8 cylinders and higher displacement tend to have lower miles per gallons, we see in fact that heavier cars in our dataset tend to have higher displacement and higher number of cylinders."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fHG4zgGguxed",
        "colab_type": "code",
        "outputId": "ae4342a2-3c9c-444f-91a0-dc78a833f16a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "ggplot(aes(x = mpg, y = wt, col = cyl, size = disp), data = mtcars) + \n",
        "geom_point()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ttvP+usszZu3FhWVpaCimPAd36uWrPb9selhYekuoN5guqrX7j+vLzAE1S6a4Ms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",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "egzl9pfLyIFd",
        "colab_type": "text"
      },
      "source": [
        "On the charts below are the representations of transmission types (Manual = 1, Automatic = 0), numbers of cylinders and displacement (CU. in.) against the weight. As you can see the higher number of cylinders, automatic transmission and higher displacement tend to be heavier cars. As a result, the impact on MPG could only be the weight.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HpSR5T8gyJL0",
        "colab_type": "code",
        "outputId": "04c5e2af-9bfb-4c43-f017-7b76a5f46c73",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "\n",
        "par(mfrow=c(1,3))\n",
        "boxplot(wt~am, data = mtcars,\n",
        "        col = c(\"green\", \"red\"),\n",
        "        xlab = \"Transmission\",\n",
        "        ylab = \"Weigth\",\n",
        "        main = \"Weigth per Transmission\")\n",
        "boxplot(wt~disp, data = mtcars,\n",
        "        col = c(\"green\", \"red\"),\n",
        "        xlab = \"Displacement\",\n",
        "        ylab = \"Weigth\",\n",
        "        main = \"Weigth per Displacement\")\n",
        "boxplot(wt~cyl, data = mtcars,\n",
        "        col = c(\"green\", \"red\"),\n",
        "        xlab = \"Cylinders\",\n",
        "        ylab = \"Weigth\",\n",
        "        main = \"Weigth per Cylinders\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9aCBQuEEH5+fk899dQjjzxi+Npwu+bv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\nAQAAAHAECjsAAAAAjkBhBwAAAMAR/wcv8jZY6/z0KwAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “Weigth per Cylinders”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dc8cNGZ9zDht",
        "colab_type": "text"
      },
      "source": [
        "**Regression Analysis**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KgsTuqHgzHl-",
        "colab_type": "text"
      },
      "source": [
        "In the exploration of our data, we have seen that transmission type is correlated with Miles per Gallons results. However, we have also shown that the transmission might not be the factor impacting the Miles per Gallon but the weight of the cars. Do to do, we can fit a linear model and define which data provides the most significance.\n",
        "\n",
        "Only two of our data provides significance in defining the miles per gallon. They have the lowest P Value and are defined by a “.” on the right on the P value."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YYmkqOLmzF3Q",
        "colab_type": "code",
        "outputId": "d982de2a-31a8-4c0b-9c24-2faeb2628378",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 510
        }
      },
      "source": [
        "all <- lm(mpg ~ ., data = mtcars)\n",
        "summary(all)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "lm(formula = mpg ~ ., data = mtcars)\n",
              "\n",
              "Residuals:\n",
              "    Min      1Q  Median      3Q     Max \n",
              "-3.2015 -1.2319  0.1033  1.1953  4.3085 \n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)  \n",
              "(Intercept) 15.09262   17.13627   0.881   0.3895  \n",
              "cyl6        -1.19940    2.38736  -0.502   0.6212  \n",
              "cyl8         3.05492    4.82987   0.633   0.5346  \n",
              "disp         0.01257    0.01774   0.708   0.4873  \n",
              "hp          -0.05712    0.03175  -1.799   0.0879 .\n",
              "drat         0.73577    1.98461   0.371   0.7149  \n",
              "wt          -3.54512    1.90895  -1.857   0.0789 .\n",
              "qsec         0.76801    0.75222   1.021   0.3201  \n",
              "vs1          2.48849    2.54015   0.980   0.3396  \n",
              "am1          3.34736    2.28948   1.462   0.1601  \n",
              "gear4       -0.99922    2.94658  -0.339   0.7382  \n",
              "gear5        1.06455    3.02730   0.352   0.7290  \n",
              "carb         0.78703    1.03599   0.760   0.4568  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "Residual standard error: 2.616 on 19 degrees of freedom\n",
              "Multiple R-squared:  0.8845,\tAdjusted R-squared:  0.8116 \n",
              "F-statistic: 12.13 on 12 and 19 DF,  p-value: 1.764e-06\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FD43u6p5zNAd",
        "colab_type": "text"
      },
      "source": [
        "Now that we have defines our model1 with horsepower (hp) and weight (wt) we can compare it with Model2 which includes the Transmission.\n",
        "\n",
        "The summary of Model1 shows that an increase in MPG is defined by a decrease in horsepower (hp) and weight (wt) which proves the significance of those two elements to define the MPG. However, in model 2, we can see the estimate in positive while we have earlier proven that we had a correlation between the transmission and the MPG.\n",
        "\n",
        "The second important element is that the P value of the transmission is 0.14 and so is not significant of determining MPG.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HiRkygMhzN_M",
        "colab_type": "code",
        "outputId": "7489088d-c588-42c0-8951-5fd699fa58e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        }
      },
      "source": [
        "Model1 <- lm(mpg ~ hp + wt, data = mtcars)\n",
        "summary(Model1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "lm(formula = mpg ~ hp + wt, data = mtcars)\n",
              "\n",
              "Residuals:\n",
              "   Min     1Q Median     3Q    Max \n",
              "-3.941 -1.600 -0.182  1.050  5.854 \n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept) 37.22727    1.59879  23.285  < 2e-16 ***\n",
              "hp          -0.03177    0.00903  -3.519  0.00145 ** \n",
              "wt          -3.87783    0.63273  -6.129 1.12e-06 ***\n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "Residual standard error: 2.593 on 29 degrees of freedom\n",
              "Multiple R-squared:  0.8268,\tAdjusted R-squared:  0.8148 \n",
              "F-statistic: 69.21 on 2 and 29 DF,  p-value: 9.109e-12\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C_RJtOaVzSF8",
        "colab_type": "code",
        "outputId": "32c6f339-29f8-44af-fb61-bbf44090e0c4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "Model2 <- lm(mpg ~ hp + wt + am, data = mtcars)\n",
        "summary(Model2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "lm(formula = mpg ~ hp + wt + am, data = mtcars)\n",
              "\n",
              "Residuals:\n",
              "    Min      1Q  Median      3Q     Max \n",
              "-3.4221 -1.7924 -0.3788  1.2249  5.5317 \n",
              "\n",
              "Coefficients:\n",
              "             Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept) 34.002875   2.642659  12.867 2.82e-13 ***\n",
              "hp          -0.037479   0.009605  -3.902 0.000546 ***\n",
              "wt          -2.878575   0.904971  -3.181 0.003574 ** \n",
              "am1          2.083710   1.376420   1.514 0.141268    \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "Residual standard error: 2.538 on 28 degrees of freedom\n",
              "Multiple R-squared:  0.8399,\tAdjusted R-squared:  0.8227 \n",
              "F-statistic: 48.96 on 3 and 28 DF,  p-value: 2.908e-11\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pUumtnJbzUl0",
        "colab_type": "text"
      },
      "source": [
        "Another way to perform an analysis of variance with Anova on the two models to define is am has brought significance to the whole model. As we can see below the P value is 0.1413 and the conclusion is that transmission has not brought significance to the model.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jerwWmazzWA0",
        "colab_type": "code",
        "outputId": "3ec03c5e-3d96-4419-ea01-0c0458634e8e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 120
        }
      },
      "source": [
        "anova(Model1, Model2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  Res.Df RSS      Df Sum of Sq F        Pr(>F)   \n",
              "1 29     195.0478 NA       NA        NA        NA\n",
              "2 28     180.2911  1 14.75668  2.291778 0.1412682"
            ],
            "text/latex": "A anova: 2 × 6\n\\begin{tabular}{r|llllll}\n  & Res.Df & RSS & Df & Sum of Sq & F & Pr(>F)\\\\\n  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & 29 & 195.0478 & NA &       NA &       NA &        NA\\\\\n\t2 & 28 & 180.2911 &  1 & 14.75668 & 2.291778 & 0.1412682\\\\\n\\end{tabular}\n",
            "text/markdown": "\nA anova: 2 × 6\n\n| <!--/--> | Res.Df &lt;dbl&gt; | RSS &lt;dbl&gt; | Df &lt;dbl&gt; | Sum of Sq &lt;dbl&gt; | F &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n|---|---|---|---|---|---|---|\n| 1 | 29 | 195.0478 | NA |       NA |       NA |        NA |\n| 2 | 28 | 180.2911 |  1 | 14.75668 | 2.291778 | 0.1412682 |\n\n",
            "text/html": [
              "<table>\n",
              "<caption>A anova: 2 × 6</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>Res.Df</th><th scope=col>RSS</th><th scope=col>Df</th><th scope=col>Sum of Sq</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>1</th><td>29</td><td>195.0478</td><td>NA</td><td>      NA</td><td>      NA</td><td>       NA</td></tr>\n",
              "\t<tr><th scope=row>2</th><td>28</td><td>180.2911</td><td> 1</td><td>14.75668</td><td>2.291778</td><td>0.1412682</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s3DLurzZzgHF",
        "colab_type": "text"
      },
      "source": [
        "We can also analyse the compute the Variance inflation factor of the two models to see if the result per element is not inflated due to adding the am as a new regressor. the VIF quantifies the severity of multicollinearity in an ordinary least squares regression analysis. In other words. For example, if MPG is defined by weight and AM is also defined by weight, using the two elements to define MPG would added multicollinearity to your model.\n",
        "\n",
        "In below analysis, we can see that the multicollinearity increases for each element if we add the transmission.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nXLm-TIfzhoL",
        "colab_type": "code",
        "outputId": "8abbab4d-0f69-4e34-fea6-3e4eb99d4561",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "vif(Model1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      hp       wt \n",
              "1.766625 1.766625 "
            ],
            "text/latex": "\\begin{description*}\n\\item[hp] 1.76662457926828\n\\item[wt] 1.76662457926828\n\\end{description*}\n",
            "text/markdown": "hp\n:   1.76662457926828wt\n:   1.76662457926828\n\n",
            "text/html": [
              "<style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>hp</dt><dd>1.76662457926828</dd><dt>wt</dt><dd>1.76662457926828</dd></dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QSQjbGbnzk6t",
        "colab_type": "code",
        "outputId": "7e17ba9d-fbed-415d-9780-707976178a0a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "vif(Model2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      hp       wt       am \n",
              "2.088124 3.774838 2.271082 "
            ],
            "text/latex": "\\begin{description*}\n\\item[hp] 2.08812444062907\n\\item[wt] 3.77483756888811\n\\item[am] 2.27108208336145\n\\end{description*}\n",
            "text/markdown": "hp\n:   2.08812444062907wt\n:   3.77483756888811am\n:   2.27108208336145\n\n",
            "text/html": [
              "<style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>hp</dt><dd>2.08812444062907</dd><dt>wt</dt><dd>3.77483756888811</dd><dt>am</dt><dd>2.27108208336145</dd></dl>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N-xIm-L0zoZG",
        "colab_type": "text"
      },
      "source": [
        "**diagnostic of our Model 1**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kANPmqJXzsjW",
        "colab_type": "text"
      },
      "source": [
        "We should have a strong correlation between our fitted results and the initial results. Below shows a correlation of .9092."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jVLovNEazu-Y",
        "colab_type": "code",
        "outputId": "1b41facb-07d8-45e4-c388-58e668f240d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "cor(Model1$fitted, mtcars$mpg)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 0.9092774"
            ],
            "text/latex": "0.909277433945653",
            "text/markdown": "0.909277433945653",
            "text/html": [
              "0.909277433945653"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "teDUYWJPzx0Y",
        "colab_type": "code",
        "outputId": "3567fe1f-f810-489c-fdf1-6dbf8d049eba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "par(mfrow=c(1,1))\n",
        "plot(Model1$fitted, mtcars$mpg, ylab=\"Observed\", xlab=\"Fitted\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_KvO1IdAz0nk",
        "colab_type": "text"
      },
      "source": [
        "The residuals do not display any obvious heteroscedasticity. However, as we can see in the Residuals vs Fitted, we can observe a smile effect which is due to two cars the model as failed to predict as well as the others. we can also see on our normal QQ plot the same two cars are out of their standardised residuals. This might mean that we could improve our model by removing the two times of the list."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1vWO0OSAz1Qp",
        "colab_type": "code",
        "outputId": "cbaa03c1-fa04-48af-ea08-2b50b73c6f9e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "par(mfrow=c(2,2))\n",
        "plot(lm(mpg ~ hp + wt, data=mtcars))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JjRv3//1NTUXbt2/f33325ubpcuXTpx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\nQqZ86K9GQUGBjo6Oj48PU4kdXsW+x8SJE+Pi4jp27ChU/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ICCQGIHAAAAoCCQ2AEAAAAoCCR2AAAAAAoCiR0AAACAgkBiBwAAAKAgkNgB\nAAAAKAgkdgAAAAAKAokdAAAAgIJAYgcAAACgIJDYAQAAACgIJHYAAAAACuL/AT8Mp8vK5Gwn\nAAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            },
            "text/plain": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "thP3Sr3Uz4m0",
        "colab_type": "text"
      },
      "source": [
        "**Conclusion**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z7-VVaGuz7yO",
        "colab_type": "text"
      },
      "source": [
        "We succeeded to build a model that was strong enough to be able to predict the MPG given the weight and the horse power.\n",
        "\n",
        "Unfortunately, while we earlier saw a correlation between the transmission type and the Miles per Gallons, we have proved that we were facing a Simpson Paradox and that the transmission was not a factor strong enough to define the MPG. As a result, to the initial question \" Is manual transmission better and automatic regarding MPG\" the answer is no, we cannot prove that.\n",
        "\n",
        "We have also proven that two cars types are out of their standardised residuals which means that by removing those two items we could create a stronger model."
      ]
    }
  ]
}