Asymmetric Error Costs in Regression Models.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/MJannik/hu_wirtschaftsinformatik_2021/blob/main/Asymmetric%20Error%20Costs%20in%20Regression%20Models.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WpXYwaTzgVqm"
      },
      "source": [
        "# Asymmetric Error Costs in Regression Models\n",
        "\n",
        "## Seminar: Bachelor Seminar Wirtschaftsinformatik\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vm94H4oQgCcp"
      },
      "source": [
        "This Cell imports important libraries like \"pandas\" or \"numphy\". \n",
        "\n",
        "It also asks for permission to connect to your GDrive. After running the cell, you have to click on the link and insert the code."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gZil6i4J3EN9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "69463f62-21c5-4cfb-f253-a11d38073d7e"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import statsmodels.api as sm\n",
        "import statsmodels.stats.api as sms\n",
        "from sklearn.preprocessing import OrdinalEncoder\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGqs1ZUdfQTF"
      },
      "source": [
        "The next cell imports the car data into this notebook. \n",
        "\n",
        "**IMPORTANT:** Before running the next cell, go to the \"Bachelorseminar Wirtschaftsinformatik\" folder in GDrive and click \"Add shortcut to Drive\". This has to be done because Google Collab can only acces folders on YOUR Drive and not on a shared Drive."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cjeSCVEN3EOI"
      },
      "source": [
        "data = pd.read_csv(\"/content/drive/MyDrive/Bachelorseminar Wirtschaftsinformatik/semWI_usedCar.csv\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uhqwbATeiI4J"
      },
      "source": [
        "# Data Cleansing\n",
        "- Missing values\n",
        "- Handle Outliers\n",
        "- Necessary Transform"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TzTRvGWQpbxG"
      },
      "source": [
        "# remove engine sizes 0\n",
        "df = data\n",
        "df = df[df['engineSize'] != 0 ]\n",
        "\n",
        "# remove observation with year 2060\n",
        "df = df[df['year'] != 2060 ]\n",
        "df['carAge'] = 2020 - df['year']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4RdjedPZwZRD"
      },
      "source": [
        "Apply Box-Cox transformation on the variable price."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1e8Pz71o9DkP"
      },
      "source": [
        "from sklearn.preprocessing import PowerTransformer\n",
        "\n",
        "price_list = df[['price']]\n",
        "\n",
        "pt = PowerTransformer(method='box-cox')\n",
        "pt.fit(price_list)\n",
        "price_list_boxcox = pt.transform(price_list)\n",
        "\n",
        "df['price'] = price_list_boxcox\n",
        "\n",
        "lambda_ = pt.lambdas_[0] "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jkGmWsAywiqK"
      },
      "source": [
        "Apply dummy transformation on the variables brand"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ojmx8vRqSMoU"
      },
      "source": [
        "df_dummies = pd.get_dummies(df, columns=['brand', 'transmission', 'fuelType'])\n",
        "df_dummies = df_dummies.drop(['id', 'model', 'year'], axis=1)\n",
        "\n",
        "df_dummies = df_dummies.drop(['brand_merc', 'fuelType_Electric','fuelType_Other', 'transmission_Other'], axis=1)\n",
        "df = df_dummies"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "15LZU0QbgbbE"
      },
      "source": [
        "## Data Preperation\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uTNnfGGKg6XF"
      },
      "source": [
        "This cell splits the data into training, validation and test set. For this, it uses the numphy function split."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PgC85dUi3EOJ"
      },
      "source": [
        "train, validate, test = \\\n",
        "              np.split(df.sample(frac=1, random_state=42), \n",
        "                       [int(.6*len(df)), int(.8*len(df))])\n",
        "              \n",
        "X_train = train.drop(['price'], axis=1)\n",
        "y_train = train[['price']]\n",
        "\n",
        "X_validate = validate.drop(['price'], axis=1)\n",
        "y_validate = validate[['price']]\n",
        "\n",
        "X_test = test.drop(['price'], axis=1)\n",
        "y_test = test[['price']]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V8oX7UVJhjIo"
      },
      "source": [
        "## Estimate Model\n",
        "This cell uses the statsmodels library to run an OLS regression on the training dataset. Below you can see the results of the regression."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 812
        },
        "id": "eQbVR2Xh3EON",
        "outputId": "aed16dd5-c25d-4625-e14b-8b5ae19d4da7"
      },
      "source": [
        "model = sm.OLS(y_train, X_train).fit()\n",
        "predictions = model.predict(X_train) # make the predictions by the model\n",
        "\n",
        "# Print out the statistics\n",
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared (uncentered):</th>      <td>   0.886</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.886</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>2.428e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Mon, 30 Aug 2021</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>18:47:52</td>     <th>  Log-Likelihood:    </th>          <td> -19835.</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td> 59347</td>      <th>  AIC:               </th>          <td>3.971e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td> 59328</td>      <th>  BIC:               </th>          <td>3.988e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>    19</td>      <th>                     </th>              <td> </td>    \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "             <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>mileage</th>                <td>-9.073e-06</td> <td> 1.03e-07</td> <td>  -87.690</td> <td> 0.000</td> <td>-9.28e-06</td> <td>-8.87e-06</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>tax</th>                    <td>    0.0002</td> <td> 2.69e-05</td> <td>    8.405</td> <td> 0.000</td> <td>    0.000</td> <td>    0.000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>mpg</th>                    <td>   -0.0084</td> <td>    0.000</td> <td>  -55.595</td> <td> 0.000</td> <td>   -0.009</td> <td>   -0.008</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>engineSize</th>             <td>    0.6713</td> <td>    0.004</td> <td>  161.933</td> <td> 0.000</td> <td>    0.663</td> <td>    0.679</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>carAge</th>                 <td>   -0.2142</td> <td>    0.001</td> <td> -211.930</td> <td> 0.000</td> <td>   -0.216</td> <td>   -0.212</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_audi</th>             <td>    0.0503</td> <td>    0.006</td> <td>    8.561</td> <td> 0.000</td> <td>    0.039</td> <td>    0.062</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_bmw</th>              <td>   -0.1533</td> <td>    0.006</td> <td>  -26.592</td> <td> 0.000</td> <td>   -0.165</td> <td>   -0.142</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_ford</th>             <td>   -0.4191</td> <td>    0.006</td> <td>  -71.305</td> <td> 0.000</td> <td>   -0.431</td> <td>   -0.408</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_hyundi</th>           <td>   -0.6633</td> <td>    0.008</td> <td>  -83.699</td> <td> 0.000</td> <td>   -0.679</td> <td>   -0.648</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_skoda</th>            <td>   -0.4786</td> <td>    0.007</td> <td>  -67.095</td> <td> 0.000</td> <td>   -0.493</td> <td>   -0.465</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_toyota</th>           <td>   -0.7243</td> <td>    0.008</td> <td>  -93.990</td> <td> 0.000</td> <td>   -0.739</td> <td>   -0.709</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_vauxhall</th>         <td>   -0.8054</td> <td>    0.006</td> <td> -128.188</td> <td> 0.000</td> <td>   -0.818</td> <td>   -0.793</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>brand_vw</th>               <td>   -0.2570</td> <td>    0.006</td> <td>  -45.332</td> <td> 0.000</td> <td>   -0.268</td> <td>   -0.246</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>transmission_Automatic</th> <td>    1.0376</td> <td>    0.033</td> <td>   31.320</td> <td> 0.000</td> <td>    0.973</td> <td>    1.103</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>transmission_Manual</th>    <td>    0.8096</td> <td>    0.034</td> <td>   24.093</td> <td> 0.000</td> <td>    0.744</td> <td>    0.875</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>transmission_Semi-Auto</th> <td>    1.0597</td> <td>    0.033</td> <td>   31.752</td> <td> 0.000</td> <td>    0.994</td> <td>    1.125</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>fuelType_Diesel</th>        <td>   -0.3637</td> <td>    0.028</td> <td>  -12.827</td> <td> 0.000</td> <td>   -0.419</td> <td>   -0.308</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>fuelType_Hybrid</th>        <td>    0.2589</td> <td>    0.029</td> <td>    8.922</td> <td> 0.000</td> <td>    0.202</td> <td>    0.316</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>fuelType_Petrol</th>        <td>   -0.4946</td> <td>    0.029</td> <td>  -17.321</td> <td> 0.000</td> <td>   -0.551</td> <td>   -0.439</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>5785.338</td> <th>  Durbin-Watson:     </th> <td>   2.002</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>39922.216</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>           <td> 0.193</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>       <td> 6.999</td>  <th>  Cond. No.          </th> <td>1.65e+06</td> \n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.65e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                                 OLS Regression Results                                \n",
              "=======================================================================================\n",
              "Dep. Variable:                  price   R-squared (uncentered):                   0.886\n",
              "Model:                            OLS   Adj. R-squared (uncentered):              0.886\n",
              "Method:                 Least Squares   F-statistic:                          2.428e+04\n",
              "Date:                Mon, 30 Aug 2021   Prob (F-statistic):                        0.00\n",
              "Time:                        18:47:52   Log-Likelihood:                         -19835.\n",
              "No. Observations:               59347   AIC:                                  3.971e+04\n",
              "Df Residuals:                   59328   BIC:                                  3.988e+04\n",
              "Df Model:                          19                                                  \n",
              "Covariance Type:            nonrobust                                                  \n",
              "==========================================================================================\n",
              "                             coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------------------\n",
              "mileage                -9.073e-06   1.03e-07    -87.690      0.000   -9.28e-06   -8.87e-06\n",
              "tax                        0.0002   2.69e-05      8.405      0.000       0.000       0.000\n",
              "mpg                       -0.0084      0.000    -55.595      0.000      -0.009      -0.008\n",
              "engineSize                 0.6713      0.004    161.933      0.000       0.663       0.679\n",
              "carAge                    -0.2142      0.001   -211.930      0.000      -0.216      -0.212\n",
              "brand_audi                 0.0503      0.006      8.561      0.000       0.039       0.062\n",
              "brand_bmw                 -0.1533      0.006    -26.592      0.000      -0.165      -0.142\n",
              "brand_ford                -0.4191      0.006    -71.305      0.000      -0.431      -0.408\n",
              "brand_hyundi              -0.6633      0.008    -83.699      0.000      -0.679      -0.648\n",
              "brand_skoda               -0.4786      0.007    -67.095      0.000      -0.493      -0.465\n",
              "brand_toyota              -0.7243      0.008    -93.990      0.000      -0.739      -0.709\n",
              "brand_vauxhall            -0.8054      0.006   -128.188      0.000      -0.818      -0.793\n",
              "brand_vw                  -0.2570      0.006    -45.332      0.000      -0.268      -0.246\n",
              "transmission_Automatic     1.0376      0.033     31.320      0.000       0.973       1.103\n",
              "transmission_Manual        0.8096      0.034     24.093      0.000       0.744       0.875\n",
              "transmission_Semi-Auto     1.0597      0.033     31.752      0.000       0.994       1.125\n",
              "fuelType_Diesel           -0.3637      0.028    -12.827      0.000      -0.419      -0.308\n",
              "fuelType_Hybrid            0.2589      0.029      8.922      0.000       0.202       0.316\n",
              "fuelType_Petrol           -0.4946      0.029    -17.321      0.000      -0.551      -0.439\n",
              "==============================================================================\n",
              "Omnibus:                     5785.338   Durbin-Watson:                   2.002\n",
              "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            39922.216\n",
              "Skew:                           0.193   Prob(JB):                         0.00\n",
              "Kurtosis:                       6.999   Cond. No.                     1.65e+06\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.65e+06. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hoLCpOHqsmhZ"
      },
      "source": [
        "## Verifying the 5 key assumptions\n",
        "\n",
        "Those five test verify the 5 key assumptions of our regression model\n",
        "\n",
        "Source: https://towardsdatascience.com/perform-regression-diagnostics-and-tackle-uncertainties-of-linear-models-1372a03b1f56 "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ClzouNBtMYM"
      },
      "source": [
        "### 1. Linearity\n",
        "\n",
        "To confirm linearity we can use: i) Harvey-Collier multiplier test ii) Comparison of the Observed vs. Predicted values iii) Studentized residuals vs Fitted values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "id": "h3T-dM_HvsnQ",
        "outputId": "64d442e7-c72f-48bc-d92b-36b678370b32"
      },
      "source": [
        "## observed vs predicted values\n",
        "\n",
        "# Plot predicted values vs. Real values\n",
        "observed_vs_predicted = pd.DataFrame(columns = ['predicted_price', 'price'])\n",
        "observed_vs_predicted[\"predicted_price\"] = model.predict(X_train)\n",
        "observed_vs_predicted[\"price\"] = y_train\n",
        "\n",
        "X_plot = [observed_vs_predicted['price'].min(), observed_vs_predicted['price'].max()]\n",
        "\n",
        "ax = sns.scatterplot(x=\"price\", y=\"predicted_price\", data=observed_vs_predicted)\n",
        "ax.set(xlabel='observed_price', ylabel='predicted_sales')\n",
        "plt.plot(X_plot, X_plot, color='r')\n",
        "plt.show()\n",
        "\n",
        "## We should see that the data is symmetrically distributed along the red diagonal with a roughly constant variance. \n",
        "## For us this is not the case..."
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "R6nv5ObhzxhA",
        "outputId": "69535b0b-d3eb-4379-f04f-311e73dc5763"
      },
      "source": [
        "## studentized residuals vs fitted values\n",
        "\n",
        "# Get the studentized residual\n",
        "student_residuals = pd.Series(np.abs(model.get_influence().resid_studentized_internal))\n",
        "\n",
        "# Plot the studentized residual\n",
        "fig, ax = plt.subplots()\n",
        "ax.scatter(predictions, student_residuals, edgecolors = 'k')\n",
        "ax.set_ylabel('Studentized Residuals')\n",
        "ax.set_xlabel('Fitted Values')\n",
        "ax.set_title('Scale-Location')\n",
        "\n",
        "plt.show()\n",
        "\n",
        "## All residuals should be small and not form any clusters"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eGjs-KTG1qYZ"
      },
      "source": [
        "### 2. Normality\n",
        "\n",
        "Non-normality of the residuals is an indication of an inadequate model\n",
        "(i.e. the errors are not random)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 212
        },
        "id": "C24rNP1E2CtT",
        "outputId": "b918b160-3c27-4e63-8d74-c5ad314e68c3"
      },
      "source": [
        "## Plot residual Q-Q plot\n",
        "\n",
        "import scipy as sp\n",
        "fig, ax = plt.subplots(figsize=(6,2.5))\n",
        "\n",
        "residuals = model.resid\n",
        "_, (__, ___, r) = sp.stats.probplot(residuals, plot=ax, fit=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x180 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "j5eQxtKQ4wuW",
        "outputId": "d37df78a-2121-4e57-da3c-9aca846cfefe"
      },
      "source": [
        "## Histogram of residuals distribution\n",
        "\n",
        "# Get Residuals\n",
        "residuals = model.resid\n",
        "\n",
        "# Plot Histogram of the residuals\n",
        "plt.hist(residuals, )\n",
        "plt.xlabel('Residuals')\n",
        "plt.title('Residuals Histogram')\n",
        "plt.show()\n",
        "\n",
        "##  If the residuals are normally distributed, \n",
        "## we should see a bell-shaped histogram centred on 0 and with a variance of 1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1XKSdsUE7mBN"
      },
      "source": [
        "### 3. Homoscedasticity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "vvfzSj6D9AsL",
        "outputId": "255f3640-a3cc-4839-d196-83bdeacffa66"
      },
      "source": [
        "## studentized residuals vs fitted values\n",
        "\n",
        "# Get the studentized residual\n",
        "student_residuals = pd.Series(np.abs(model.get_influence().resid_studentized_internal))\n",
        "\n",
        "# Plot the studentized residual\n",
        "fig, ax = plt.subplots()\n",
        "ax.scatter(predictions, student_residuals, edgecolors = 'k')\n",
        "ax.set_ylabel('Studentized Residuals')\n",
        "ax.set_xlabel('Fitted Values')\n",
        "ax.set_title('Scale-Location')\n",
        "\n",
        "plt.show()\n",
        "\n",
        "## Residuals should be distributed equally far apart on a horizontal line"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YyztsxKNkEZO",
        "outputId": "8534c52a-9120-4bd3-c4be-73819914b39c"
      },
      "source": [
        "## Breush-Pagan test\n",
        "# measures how errors increase across the explanatory variable\n",
        "\n",
        "from statsmodels.compat import lzip\n",
        "\n",
        "name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']\n",
        "        \n",
        "test = sms.het_breuschpagan(model.resid, model.model.exog)\n",
        "lzip(name, test)\n",
        "\n",
        "# If the p-value is under alpha (eg. 0.05) => assume heteroskedasticity"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('Lagrange multiplier statistic', 14271.96595305622),\n",
              " ('p-value', 0.0),\n",
              " ('f-value', 988.6756651155777),\n",
              " ('f p-value', 0.0)]"
            ]
          },
          "metadata": {},
          "execution_count": 535
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BDDwtz5y-d1W"
      },
      "source": [
        "### 4. Independence\n",
        "\n",
        "Independence of residual is commonly referred to as the total absence of autocorrelation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "id": "wyLNlLlL-nLP",
        "outputId": "b4a26fe7-d563-4f70-b1c6-4fec0fc69a40"
      },
      "source": [
        "## ACF plot\n",
        "\n",
        "import statsmodels.tsa.api as smt\n",
        "acf = smt.graphics.plot_acf(model.resid, alpha=0.05)\n",
        "\n",
        "# if all values are in the confidence intervals, we don't have statistically significant autocorrelation"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RavS5cB5_IiH",
        "outputId": "82612f76-f182-493d-f712-ae51e76c3e38"
      },
      "source": [
        "## Durbin-Watson\n",
        "\n",
        "# The test will output values between 0 and 4. Here are how to interpret the results of the test:\n",
        "# — value = 2 means that there is no autocorrelation in the sample,\n",
        "# — values < 2 indicate positive autocorrelation,\n",
        "# — values > 2 negative autocorrelation.\n",
        "\n",
        "import statsmodels.stats.stattools as st\n",
        "\n",
        "st.durbin_watson(residuals, axis=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.001959431428672"
            ]
          },
          "metadata": {},
          "execution_count": 537
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "brGGQhjF_j8B"
      },
      "source": [
        "### 5. Multicollinearity\n",
        "\n",
        "occurs when your model includes multiple factors that are correlated not just to your response variable, but also to each other"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 657
        },
        "id": "Zs9RA6yH_sN8",
        "outputId": "698d0d44-ba5e-4a41-d411-3b96798e6725"
      },
      "source": [
        "## Variance Inflation Factor (VIF)\n",
        "\n",
        "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
        "from statsmodels.tools.tools import add_constant\n",
        "\n",
        "# For each X, calculate VIF and save in dataframe\n",
        "X = add_constant(X_train)\n",
        "\n",
        "vif = pd.DataFrame()\n",
        "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
        "vif[\"features\"] = X.columns\n",
        "\n",
        "# inspect results\n",
        "vif.round(1) \n",
        "\n",
        "## We generally consider that a VIF of 5 or 10 and above \n",
        "## (depends on the business problem) indicates a multicollinearity problem"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>VIF Factor</th>\n",
              "      <th>features</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>12467.9</td>\n",
              "      <td>const</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.5</td>\n",
              "      <td>mileage</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.5</td>\n",
              "      <td>tax</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2.3</td>\n",
              "      <td>mpg</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2.7</td>\n",
              "      <td>engineSize</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>2.4</td>\n",
              "      <td>carAge</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1.7</td>\n",
              "      <td>brand_audi</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1.6</td>\n",
              "      <td>brand_bmw</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>2.7</td>\n",
              "      <td>brand_ford</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1.5</td>\n",
              "      <td>brand_hyundi</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1.6</td>\n",
              "      <td>brand_skoda</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>2.0</td>\n",
              "      <td>brand_toyota</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>2.4</td>\n",
              "      <td>brand_vauxhall</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>2.2</td>\n",
              "      <td>brand_vw</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1910.8</td>\n",
              "      <td>transmission_Automatic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>2909.4</td>\n",
              "      <td>transmission_Manual</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>2090.2</td>\n",
              "      <td>transmission_Semi-Auto</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>105.0</td>\n",
              "      <td>fuelType_Diesel</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>13.5</td>\n",
              "      <td>fuelType_Hybrid</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>108.9</td>\n",
              "      <td>fuelType_Petrol</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    VIF Factor                features\n",
              "0      12467.9                   const\n",
              "1          2.5                 mileage\n",
              "2          1.5                     tax\n",
              "3          2.3                     mpg\n",
              "4          2.7              engineSize\n",
              "5          2.4                  carAge\n",
              "6          1.7              brand_audi\n",
              "7          1.6               brand_bmw\n",
              "8          2.7              brand_ford\n",
              "9          1.5            brand_hyundi\n",
              "10         1.6             brand_skoda\n",
              "11         2.0            brand_toyota\n",
              "12         2.4          brand_vauxhall\n",
              "13         2.2                brand_vw\n",
              "14      1910.8  transmission_Automatic\n",
              "15      2909.4     transmission_Manual\n",
              "16      2090.2  transmission_Semi-Auto\n",
              "17       105.0         fuelType_Diesel\n",
              "18        13.5         fuelType_Hybrid\n",
              "19       108.9         fuelType_Petrol"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 508
        },
        "id": "WimF4KKdA0ds",
        "outputId": "8b6c7e77-6826-49ab-c46f-6cc5bd991c35"
      },
      "source": [
        "plt.subplots(figsize=(15,7))\n",
        "sns.heatmap(df.corr(), annot = True, cmap='coolwarm')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f5eb70822d0>"
            ]
          },
          "metadata": {},
          "execution_count": 352
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c9VkcxHkhwM5"
      },
      "source": [
        "# Apply Model\n",
        "This cell applies the model on the validation dataset. (It predicts the price for every car in the validation set)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OYrgwO1k3EOO"
      },
      "source": [
        "validate_apply = pd.DataFrame(columns = ['predicted_price', 'actual_price'])\n",
        "validate_apply[\"predicted_price\"] = model.predict(X_validate)\n",
        "validate_apply[\"actual_price\"] = y_validate"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gs38TljTKFx3"
      },
      "source": [
        "# Rverse Box-Cox Transformation\n",
        "validate_apply[\"predicted_price\"] = pt.inverse_transform(validate_apply[[\"predicted_price\"]])\n",
        "validate_apply[\"actual_price\"] = pt.inverse_transform(validate_apply[[\"actual_price\"]])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AJmYj-Ged7dT"
      },
      "source": [
        "##LinLin Function\n",
        "This cell defines the LinearLinear cost function. It checks if the residual is greater than 0. If yes, it multiplies the ratio of asymetry which represents the asymetric costs. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DrnnXVi33EOU"
      },
      "source": [
        "def linlin(ratio, md, actual, prediction): \n",
        "    residual = (md + (prediction - actual))\n",
        "    \n",
        "    if residual < 0:            # Overprediction\n",
        "        actualCosts = abs(residual) * ratio\n",
        "    else:       # Underprediction\n",
        "        actualCosts = abs(residual)    \n",
        "    return actualCosts"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1pZhYLKpw1L8"
      },
      "source": [
        "## Quadratic Quadratic\n",
        "\n",
        "This cell defines the QuadraticQuadratic cost function. It checks if the residual is greater than 0. If yes, it multiplies the ratio of asymetry which represents the asymetric costs. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6byWKqxiw0gF"
      },
      "source": [
        "def qq(ratio, md, actual, prediction): \n",
        "    residual = (md + (prediction - actual))\n",
        "    \n",
        "    if residual < 0:            # Overprediction\n",
        "        actualCosts = ratio * (residual**2)   \n",
        "    else:                       # Underprediction\n",
        "        actualCosts = (residual)**2    \n",
        "    return actualCosts"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4k_CdhSW-S2E"
      },
      "source": [
        "## Linex\n",
        "\n",
        "This cell defines the Linear Exponential cost function. However we did not use it since our residuals are too big and would provoke an overflow error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3aHv4MYA-U7n"
      },
      "source": [
        "def linex(ratio, md, actual, prediction): \n",
        "    residual = (md + (prediction - actual))\n",
        "\n",
        "    actualCosts = np.exp(residual*ratio)-(residual*ratio)-1\n",
        "\n",
        "    return actualCosts"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ys60SJnAeWDi"
      },
      "source": [
        "## Actual Costs Function\n",
        "This cell defines the function that calculates the actual costs. It uses the linlin / qq / linex function from the previous cell and applies it on our dataset with the actual and predicted price. Finally it uses mean() to calculate the average misprediction over all residuals."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ud8auPOWisdU"
      },
      "source": [
        "def AMCosts(ratio, md, whichCostFunction):\n",
        "\n",
        "    if whichCostFunction ==\"linlin\":\n",
        "      validate_apply[\"MispredictionCosts\"] = validate_apply.apply(lambda x: linlin(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "      AverageMispredictionCosts = validate_apply[\"MispredictionCosts\"].mean()\n",
        "    \n",
        "    elif whichCostFunction ==\"qq\":\n",
        "      validate_apply[\"MispredictionCosts\"] = validate_apply.apply(lambda x: qq(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "      AverageMispredictionCosts = validate_apply[\"MispredictionCosts\"].mean()\n",
        "\n",
        "    elif whichCostFunction ==\"linex\":\n",
        "      validate_apply[\"MispredictionCosts\"] = validate_apply.apply(lambda x: linex(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "      AverageMispredictionCosts = validate_apply[\"MispredictionCosts\"].mean()\n",
        "\n",
        "    else:\n",
        "      print(\"set a value for the variable whichCostFunction to chose the cost function\")\n",
        "    \n",
        "    return AverageMispredictionCosts"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xKFxzrDaevWA"
      },
      "source": [
        "## Markdown Algorithm\n",
        "This cell is the implementation of the markdownalgorithm suggested by Gaurav Bansal.\n",
        "\n",
        "Source: Bansal, G, Sinha, A P, and Zhao, H 2008 Tuning Data Mining Methods for Cost-Sensitive Regression: A Study in Loan Charge-Off Forecasting. Journal of Management Information Systems, 25(3): 315–336. DOI: https://doi.org/10.2753/MIS0742-1222250309\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7S_KSAtwis2i"
      },
      "source": [
        "def find_md(ratio, whichCostFunction):\n",
        "  md = 0\n",
        "  p = 1\n",
        "  s = 1\n",
        "\n",
        "  # This part determines d which defines the \"direction\" of our markdown\n",
        "  if AMCosts(ratio, p, whichCostFunction) < AMCosts(ratio, 0, whichCostFunction):\n",
        "    d = 1\n",
        "  else:\n",
        "    d = -1\n",
        "\n",
        "  md_prev = 0\n",
        "  md_next = md + s * d * p\n",
        "\n",
        "  while True:\n",
        "   s = 1\n",
        "   md = md_prev\n",
        "\n",
        "   while True:  \n",
        "      #print(\"markdown is: \" + str(md))\n",
        "      md_prev = md\n",
        "      md = md + s * d * p\n",
        "      s = s * 2\n",
        "      md_next = md + s * d * p\n",
        "      if AMCosts(ratio, md_next, whichCostFunction) > AMCosts(ratio, md, whichCostFunction):\n",
        "        break\n",
        "        \n",
        "        #print(\"costs are: \" + str(AMCosts(ratio, md)))\n",
        "   if s <= 2:\n",
        "     break\n",
        "  optimal_md = md\n",
        "  #print(\"The optimal markdown value is: \" + str(md))\n",
        "  return optimal_md"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UCTHkn7hnCGR"
      },
      "source": [
        "This cell applies the linlin and qq costs function on the dataset with different ratios of cost asymetry (ratio: 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0) "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t7CXNgT-fZRU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "efcd16be-a49e-4b12-8d85-26f130214f57"
      },
      "source": [
        "ratio_list = [1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0]\n",
        "CostFunctions = [\"linlin\",\"qq\"]\n",
        "results = pd.DataFrame(columns=['CostFunction','Ratio','Markdown', 'Average Misprediction Costs', 'Average Misprediction Costs with md = 0'])\n",
        "\n",
        "for function in CostFunctions:\n",
        "  for ratio in ratio_list:\n",
        "    md = find_md(ratio, function)\n",
        "    AMC = AMCosts(ratio, md, function)\n",
        "    AMC_md0 = AMCosts(ratio, 0, function)\n",
        "    results = results.append({'CostFunction': function, 'Ratio': ratio, 'Markdown': md, 'Average Misprediction Costs':AMC, 'Average Misprediction Costs with md = 0':AMC_md0 }, ignore_index=True)\n",
        "    print(\"ratio: \" + str(ratio) + \" markdown: \" + str(md) + \" the average misprediction costs are: \" + str(AMC) + \" The AMC for md = 0 are: \" + str(AMC_md0))\n",
        "\n",
        "results"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ratio: 1.0 markdown: 67 the average misprediction costs are: 2357.1942797127886 The AMC for md = 0 are: 2357.9932175444337\n",
            "ratio: 1.1 markdown: 194 the average misprediction costs are: 2483.0222914433352 The AMC for md = 0 are: 2490.494741076381\n",
            "ratio: 1.2 markdown: 309 the average misprediction costs are: 2603.089925133421 The AMC for md = 0 are: 2622.99626460834\n",
            "ratio: 1.3 markdown: 418 the average misprediction costs are: 2718.1611117687125 The AMC for md = 0 are: 2755.497788140313\n",
            "ratio: 1.4 markdown: 518 the average misprediction costs are: 2828.7402710486167 The AMC for md = 0 are: 2887.999311672263\n",
            "ratio: 1.5 markdown: 620 the average misprediction costs are: 2934.985547197761 The AMC for md = 0 are: 3020.5008352042396\n",
            "ratio: 1.6 markdown: 711 the average misprediction costs are: 3037.495421255567 The AMC for md = 0 are: 3153.002358736187\n",
            "ratio: 1.7 markdown: 794 the average misprediction costs are: 3136.5733940706546 The AMC for md = 0 are: 3285.503882268137\n",
            "ratio: 1.8 markdown: 872 the average misprediction costs are: 3232.6697923543843 The AMC for md = 0 are: 3418.0054058001\n",
            "ratio: 1.9 markdown: 944 the average misprediction costs are: 3326.114043497743 The AMC for md = 0 are: 3550.5069293320785\n",
            "ratio: 2.0 markdown: 1022 the average misprediction costs are: 3416.9917535649006 The AMC for md = 0 are: 3683.008452864033\n",
            "ratio: 1.0 markdown: 292 the average misprediction costs are: 15266673.864917396 The AMC for md = 0 are: 15351959.620724663\n",
            "ratio: 1.1 markdown: 405 the average misprediction costs are: 16246061.722928766 The AMC for md = 0 are: 16417918.573126595\n",
            "ratio: 1.2 markdown: 509 the average misprediction costs are: 17200812.017495193 The AMC for md = 0 are: 17483877.52552852\n",
            "ratio: 1.3 markdown: 606 the average misprediction costs are: 18133674.427821938 The AMC for md = 0 are: 18549836.477930218\n",
            "ratio: 1.4 markdown: 697 the average misprediction costs are: 19046896.056682546 The AMC for md = 0 are: 19615795.430332124\n",
            "ratio: 1.5 markdown: 782 the average misprediction costs are: 19942337.38401549 The AMC for md = 0 are: 20681754.382734157\n",
            "ratio: 1.6 markdown: 862 the average misprediction costs are: 20821562.001622327 The AMC for md = 0 are: 21747713.335136093\n",
            "ratio: 1.7 markdown: 938 the average misprediction costs are: 21685893.902887933 The AMC for md = 0 are: 22813672.287537932\n",
            "ratio: 1.8 markdown: 1011 the average misprediction costs are: 22536467.69720417 The AMC for md = 0 are: 23879631.23993976\n",
            "ratio: 1.9 markdown: 1080 the average misprediction costs are: 23374277.0622263 The AMC for md = 0 are: 24945590.192341648\n",
            "ratio: 2.0 markdown: 1147 the average misprediction costs are: 24200187.252888333 The AMC for md = 0 are: 26011549.144743595\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CostFunction</th>\n",
              "      <th>Ratio</th>\n",
              "      <th>Markdown</th>\n",
              "      <th>Average Misprediction Costs</th>\n",
              "      <th>Average Misprediction Costs with md = 0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.0</td>\n",
              "      <td>67</td>\n",
              "      <td>2.357194e+03</td>\n",
              "      <td>2.357993e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.1</td>\n",
              "      <td>194</td>\n",
              "      <td>2.483022e+03</td>\n",
              "      <td>2.490495e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.2</td>\n",
              "      <td>309</td>\n",
              "      <td>2.603090e+03</td>\n",
              "      <td>2.622996e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.3</td>\n",
              "      <td>418</td>\n",
              "      <td>2.718161e+03</td>\n",
              "      <td>2.755498e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.4</td>\n",
              "      <td>518</td>\n",
              "      <td>2.828740e+03</td>\n",
              "      <td>2.887999e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.5</td>\n",
              "      <td>620</td>\n",
              "      <td>2.934986e+03</td>\n",
              "      <td>3.020501e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.6</td>\n",
              "      <td>711</td>\n",
              "      <td>3.037495e+03</td>\n",
              "      <td>3.153002e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.7</td>\n",
              "      <td>794</td>\n",
              "      <td>3.136573e+03</td>\n",
              "      <td>3.285504e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.8</td>\n",
              "      <td>872</td>\n",
              "      <td>3.232670e+03</td>\n",
              "      <td>3.418005e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.9</td>\n",
              "      <td>944</td>\n",
              "      <td>3.326114e+03</td>\n",
              "      <td>3.550507e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>linlin</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1022</td>\n",
              "      <td>3.416992e+03</td>\n",
              "      <td>3.683008e+03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.0</td>\n",
              "      <td>292</td>\n",
              "      <td>1.526667e+07</td>\n",
              "      <td>1.535196e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.1</td>\n",
              "      <td>405</td>\n",
              "      <td>1.624606e+07</td>\n",
              "      <td>1.641792e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.2</td>\n",
              "      <td>509</td>\n",
              "      <td>1.720081e+07</td>\n",
              "      <td>1.748388e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.3</td>\n",
              "      <td>606</td>\n",
              "      <td>1.813367e+07</td>\n",
              "      <td>1.854984e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.4</td>\n",
              "      <td>697</td>\n",
              "      <td>1.904690e+07</td>\n",
              "      <td>1.961580e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.5</td>\n",
              "      <td>782</td>\n",
              "      <td>1.994234e+07</td>\n",
              "      <td>2.068175e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.6</td>\n",
              "      <td>862</td>\n",
              "      <td>2.082156e+07</td>\n",
              "      <td>2.174771e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.7</td>\n",
              "      <td>938</td>\n",
              "      <td>2.168589e+07</td>\n",
              "      <td>2.281367e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.8</td>\n",
              "      <td>1011</td>\n",
              "      <td>2.253647e+07</td>\n",
              "      <td>2.387963e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1080</td>\n",
              "      <td>2.337428e+07</td>\n",
              "      <td>2.494559e+07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>qq</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1147</td>\n",
              "      <td>2.420019e+07</td>\n",
              "      <td>2.601155e+07</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   CostFunction  ...  Average Misprediction Costs with md = 0\n",
              "0        linlin  ...                             2.357993e+03\n",
              "1        linlin  ...                             2.490495e+03\n",
              "2        linlin  ...                             2.622996e+03\n",
              "3        linlin  ...                             2.755498e+03\n",
              "4        linlin  ...                             2.887999e+03\n",
              "5        linlin  ...                             3.020501e+03\n",
              "6        linlin  ...                             3.153002e+03\n",
              "7        linlin  ...                             3.285504e+03\n",
              "8        linlin  ...                             3.418005e+03\n",
              "9        linlin  ...                             3.550507e+03\n",
              "10       linlin  ...                             3.683008e+03\n",
              "11           qq  ...                             1.535196e+07\n",
              "12           qq  ...                             1.641792e+07\n",
              "13           qq  ...                             1.748388e+07\n",
              "14           qq  ...                             1.854984e+07\n",
              "15           qq  ...                             1.961580e+07\n",
              "16           qq  ...                             2.068175e+07\n",
              "17           qq  ...                             2.174771e+07\n",
              "18           qq  ...                             2.281367e+07\n",
              "19           qq  ...                             2.387963e+07\n",
              "20           qq  ...                             2.494559e+07\n",
              "21           qq  ...                             2.601155e+07\n",
              "\n",
              "[22 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "Ettv1-xU6ncc",
        "outputId": "cbda05cf-6f60-4e7e-81da-b1a4ca2b1907"
      },
      "source": [
        "  results.round(1)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CostFunction</th>\n",
              "      <th>Ratio</th>\n",
              "      <th>Markdown</th>\n",
              "      <th>Average Misprediction Costs</th>\n",
              "      <th>Average Misprediction Costs with md = 0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.0</td>\n",
              "      <td>67</td>\n",
              "      <td>2357.2</td>\n",
              "      <td>2358.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.1</td>\n",
              "      <td>194</td>\n",
              "      <td>2483.0</td>\n",
              "      <td>2490.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.2</td>\n",
              "      <td>309</td>\n",
              "      <td>2603.1</td>\n",
              "      <td>2623.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.3</td>\n",
              "      <td>418</td>\n",
              "      <td>2718.2</td>\n",
              "      <td>2755.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.4</td>\n",
              "      <td>518</td>\n",
              "      <td>2828.7</td>\n",
              "      <td>2888.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.5</td>\n",
              "      <td>620</td>\n",
              "      <td>2935.0</td>\n",
              "      <td>3020.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.6</td>\n",
              "      <td>711</td>\n",
              "      <td>3037.5</td>\n",
              "      <td>3153.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.7</td>\n",
              "      <td>794</td>\n",
              "      <td>3136.6</td>\n",
              "      <td>3285.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.8</td>\n",
              "      <td>872</td>\n",
              "      <td>3232.7</td>\n",
              "      <td>3418.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.9</td>\n",
              "      <td>944</td>\n",
              "      <td>3326.1</td>\n",
              "      <td>3550.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>linlin</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1022</td>\n",
              "      <td>3417.0</td>\n",
              "      <td>3683.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.0</td>\n",
              "      <td>292</td>\n",
              "      <td>15266673.9</td>\n",
              "      <td>15351959.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.1</td>\n",
              "      <td>405</td>\n",
              "      <td>16246061.7</td>\n",
              "      <td>16417918.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.2</td>\n",
              "      <td>509</td>\n",
              "      <td>17200812.0</td>\n",
              "      <td>17483877.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.3</td>\n",
              "      <td>606</td>\n",
              "      <td>18133674.4</td>\n",
              "      <td>18549836.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.4</td>\n",
              "      <td>697</td>\n",
              "      <td>19046896.1</td>\n",
              "      <td>19615795.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.5</td>\n",
              "      <td>782</td>\n",
              "      <td>19942337.4</td>\n",
              "      <td>20681754.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.6</td>\n",
              "      <td>862</td>\n",
              "      <td>20821562.0</td>\n",
              "      <td>21747713.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.7</td>\n",
              "      <td>938</td>\n",
              "      <td>21685893.9</td>\n",
              "      <td>22813672.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.8</td>\n",
              "      <td>1011</td>\n",
              "      <td>22536467.7</td>\n",
              "      <td>23879631.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1080</td>\n",
              "      <td>23374277.1</td>\n",
              "      <td>24945590.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>qq</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1147</td>\n",
              "      <td>24200187.3</td>\n",
              "      <td>26011549.1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   CostFunction  ...  Average Misprediction Costs with md = 0\n",
              "0        linlin  ...                                   2358.0\n",
              "1        linlin  ...                                   2490.5\n",
              "2        linlin  ...                                   2623.0\n",
              "3        linlin  ...                                   2755.5\n",
              "4        linlin  ...                                   2888.0\n",
              "5        linlin  ...                                   3020.5\n",
              "6        linlin  ...                                   3153.0\n",
              "7        linlin  ...                                   3285.5\n",
              "8        linlin  ...                                   3418.0\n",
              "9        linlin  ...                                   3550.5\n",
              "10       linlin  ...                                   3683.0\n",
              "11           qq  ...                               15351959.6\n",
              "12           qq  ...                               16417918.6\n",
              "13           qq  ...                               17483877.5\n",
              "14           qq  ...                               18549836.5\n",
              "15           qq  ...                               19615795.4\n",
              "16           qq  ...                               20681754.4\n",
              "17           qq  ...                               21747713.3\n",
              "18           qq  ...                               22813672.3\n",
              "19           qq  ...                               23879631.2\n",
              "20           qq  ...                               24945590.2\n",
              "21           qq  ...                               26011549.1\n",
              "\n",
              "[22 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gFuMNNhwmDDH"
      },
      "source": [
        "## Test Part\n",
        "Now we test if the markdown values calculated previously also decreases the AMC for the testset.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jy3amhlijD9V"
      },
      "source": [
        "test_apply = pd.DataFrame(columns = ['predicted_price', 'actual_price'])\n",
        "test_apply[\"predicted_price\"] = model.predict(X_test)\n",
        "test_apply[\"actual_price\"] = y_test\n",
        "\n",
        "# Rverse Box-Cox Transformation\n",
        "test_apply[\"predicted_price\"] = pt.inverse_transform(test_apply[[\"predicted_price\"]])\n",
        "test_apply[\"actual_price\"] = pt.inverse_transform(test_apply[[\"actual_price\"]])"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hiJPJvKEfUy_"
      },
      "source": [
        "def AMCosts_test(ratio, md, whichCostFunction):\n",
        "\n",
        "  if whichCostFunction ==\"linlin\":\n",
        "    test_apply[\"MispredictionCosts\"] = test_apply.apply(lambda x: linlin(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "    AverageMispredictionCosts = test_apply[\"MispredictionCosts\"].mean()\n",
        "    \n",
        "  elif whichCostFunction ==\"qq\":\n",
        "    test_apply[\"MispredictionCosts\"] = test_apply.apply(lambda x: qq(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "    AverageMispredictionCosts = test_apply[\"MispredictionCosts\"].mean()\n",
        "\n",
        "  elif whichCostFunction ==\"linex\":\n",
        "    test_apply[\"MispredictionCosts\"] = test_apply.apply(lambda x: linex(ratio, md, x[\"actual_price\"], x[\"predicted_price\"]),axis=1)\n",
        "    AverageMispredictionCosts = test_apply[\"MispredictionCosts\"].mean()\n",
        "\n",
        "  else:\n",
        "      print(\"set a value for the variable whichCostFunction to chose the cost function\")\n",
        "\n",
        "  return AverageMispredictionCosts"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z6CMfHbnjaKZ"
      },
      "source": [
        "results_testset = pd.DataFrame(columns=['CostFunction','Ratio','Markdown', 'Average Misprediction Costs', 'Average Misprediction Costs with md = 0'])\n",
        "\n",
        "for index, row in results.iterrows():\n",
        "  AMC_testset = AMCosts_test(row['Ratio'], row['Markdown'], row['CostFunction'])\n",
        "  results_testset = results_testset.append({'CostFunction': row['CostFunction'], 'Ratio': row['Ratio'], 'Markdown': row['Markdown'], 'Average Misprediction Costs':AMC_testset, 'Average Misprediction Costs with md = 0':AMCosts_test(row['Ratio'], 0, row['CostFunction']) }, ignore_index=True)\n",
        "  #print(\"ratio: \" + str(r) + \" markdown: \" + str(m) + \" the average misprediction costs is: \" + str(AMC_testset) + \" The AMC for md = 0 is: \" + str(AMCosts_test(r, 0)))"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "QYAAFR4zSsNM",
        "outputId": "b286b7e4-9640-4cf2-9f4f-dc35e6d078db"
      },
      "source": [
        "results_testset.round(1)\n"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CostFunction</th>\n",
              "      <th>Ratio</th>\n",
              "      <th>Markdown</th>\n",
              "      <th>Average Misprediction Costs</th>\n",
              "      <th>Average Misprediction Costs with md = 0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.0</td>\n",
              "      <td>67</td>\n",
              "      <td>2334.5</td>\n",
              "      <td>2335.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.1</td>\n",
              "      <td>194</td>\n",
              "      <td>2459.2</td>\n",
              "      <td>2467.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.2</td>\n",
              "      <td>309</td>\n",
              "      <td>2577.9</td>\n",
              "      <td>2599.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.3</td>\n",
              "      <td>418</td>\n",
              "      <td>2691.2</td>\n",
              "      <td>2730.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.4</td>\n",
              "      <td>518</td>\n",
              "      <td>2799.7</td>\n",
              "      <td>2862.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.5</td>\n",
              "      <td>620</td>\n",
              "      <td>2903.9</td>\n",
              "      <td>2994.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.6</td>\n",
              "      <td>711</td>\n",
              "      <td>3004.7</td>\n",
              "      <td>3126.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.7</td>\n",
              "      <td>794</td>\n",
              "      <td>3102.0</td>\n",
              "      <td>3258.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.8</td>\n",
              "      <td>872</td>\n",
              "      <td>3196.1</td>\n",
              "      <td>3389.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>linlin</td>\n",
              "      <td>1.9</td>\n",
              "      <td>944</td>\n",
              "      <td>3287.4</td>\n",
              "      <td>3521.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>linlin</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1022</td>\n",
              "      <td>3375.8</td>\n",
              "      <td>3653.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.0</td>\n",
              "      <td>292</td>\n",
              "      <td>15304414.5</td>\n",
              "      <td>15394501.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.1</td>\n",
              "      <td>405</td>\n",
              "      <td>16254461.0</td>\n",
              "      <td>16432368.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.2</td>\n",
              "      <td>509</td>\n",
              "      <td>17180365.0</td>\n",
              "      <td>17470235.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.3</td>\n",
              "      <td>606</td>\n",
              "      <td>18084838.2</td>\n",
              "      <td>18508103.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.4</td>\n",
              "      <td>697</td>\n",
              "      <td>18970099.6</td>\n",
              "      <td>19545970.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.5</td>\n",
              "      <td>782</td>\n",
              "      <td>19837985.7</td>\n",
              "      <td>20583837.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.6</td>\n",
              "      <td>862</td>\n",
              "      <td>20690035.7</td>\n",
              "      <td>21621704.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.7</td>\n",
              "      <td>938</td>\n",
              "      <td>21527560.5</td>\n",
              "      <td>22659572.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.8</td>\n",
              "      <td>1011</td>\n",
              "      <td>22351689.8</td>\n",
              "      <td>23697439.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>qq</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1080</td>\n",
              "      <td>23163408.4</td>\n",
              "      <td>24735306.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>qq</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1147</td>\n",
              "      <td>23963573.6</td>\n",
              "      <td>25773173.8</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   CostFunction  ...  Average Misprediction Costs with md = 0\n",
              "0        linlin  ...                                   2335.6\n",
              "1        linlin  ...                                   2467.4\n",
              "2        linlin  ...                                   2599.1\n",
              "3        linlin  ...                                   2730.9\n",
              "4        linlin  ...                                   2862.7\n",
              "5        linlin  ...                                   2994.5\n",
              "6        linlin  ...                                   3126.3\n",
              "7        linlin  ...                                   3258.1\n",
              "8        linlin  ...                                   3389.9\n",
              "9        linlin  ...                                   3521.7\n",
              "10       linlin  ...                                   3653.5\n",
              "11           qq  ...                               15394501.2\n",
              "12           qq  ...                               16432368.5\n",
              "13           qq  ...                               17470235.7\n",
              "14           qq  ...                               18508103.0\n",
              "15           qq  ...                               19545970.3\n",
              "16           qq  ...                               20583837.5\n",
              "17           qq  ...                               21621704.8\n",
              "18           qq  ...                               22659572.0\n",
              "19           qq  ...                               23697439.3\n",
              "20           qq  ...                               24735306.6\n",
              "21           qq  ...                               25773173.8\n",
              "\n",
              "[22 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aoXneryh1gI_"
      },
      "source": [
        "results_testset.to_excel(\"results.xlsx\")"
      ],
      "execution_count": 49,
      "outputs": []
    }
  ]
}