Housing_price_prediction.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/KushalPatil/Blockchain-authentitcation-simulation/blob/master/Housing_price_prediction.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "metadata": {
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": "OK"
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "d8vHywlsVM9F",
        "outputId": "63f41d4e-8d6b-40f2-f920-740c92264ff5"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "\n",
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              "        style=\"border:none\" />\n",
              "     <output id=\"result-58ef2834-00a8-44c7-84af-a9c903827e4b\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "e6a8376b4f432d323d023d8a938ed56fecf352f2",
        "id": "0WWJOj757ZCh"
      },
      "source": [
        "# Predicting Housing Prices in Ames, Iowa"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "22080ccd36043ff0dd260cfcde044a7ee474aadb",
        "id": "He_OLS6T7ZCi"
      },
      "source": [
        "The goal of this exercise to build a housing price predictor for the Ames, Iowa dataset. The Ames Housing dataset was compiled by Dean De Cock for use in data science education. It's a wonderful alternative for data scientists looking for a modernized and expanded version of the often cited Boston Housing dataset."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "48ac98ee10626fcfc4f1edc83c627a3e370c981d",
        "id": "3OwxNhQs7ZCj"
      },
      "source": [
        "## Part 1: Preliminary checks on file and loading the data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "4622d34d5253f625721574d3856446b9610fd2a5",
        "id": "BxBDDbqm7ZCl"
      },
      "source": [
        "It's always good to do a few preliminary checks such as file size, line numbers, and printing the first few lines to not load corrupt data or exceed one's memory constraints."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "_cell_guid": "a5e604e7-3c20-409b-ad29-5c2a4fe40738",
        "_uuid": "44b399828f0b07fe63abbdcdf74bbf3b22bb8067",
        "id": "Uj61g1no7ZCl"
      },
      "outputs": [],
      "source": [
        "from os import path\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "iowa_file = '/content/train.csv'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "_uuid": "f50092271c3111ba40a041c3805fe2df37f9e7ee",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "szP_GEPI7ZCm",
        "outputId": "237dede2-0197-4692-b075-0bfc2d6def0f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "File size in MB:\n",
            "0.4393348693847656\n"
          ]
        }
      ],
      "source": [
        "print('File size in MB:')\n",
        "print(path.getsize(iowa_file) / (1<<20))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "_uuid": "b5c1319fc0083b44297b293ca59bad418d694324",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-1lYScgn7ZCn",
        "outputId": "17ee1094-7cce-47ef-e7ea-01e0bac49e15"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of rows in file:\n",
            "1461\n"
          ]
        }
      ],
      "source": [
        "print('Number of rows in file:')\n",
        "with open(iowa_file) as file:\n",
        "    print(sum(1 for line in file))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "33b2c9c6398c50b82a2ba88e16cc7fe542e9abdb",
        "id": "jffZC2zo7ZCn"
      },
      "source": [
        "First few rows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "_uuid": "44c4c5b29051ba666f2abf38451deba29475dc01",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wzg_fl4u7ZCo",
        "outputId": "e35e1637-b4f8-482a-99c2-5ad66148c743"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Id,MSSubClass,MSZoning,LotFrontage,LotArea,Street,Alley,LotShape,LandContour,Utilities,LotConfig,LandSlope,Neighborhood,Condition1,Condition2,BldgType,HouseStyle,OverallQual,OverallCond,YearBuilt,YearRemodAdd,RoofStyle,RoofMatl,Exterior1st,Exterior2nd,MasVnrType,MasVnrArea,ExterQual,ExterCond,Foundation,BsmtQual,BsmtCond,BsmtExposure,BsmtFinType1,BsmtFinSF1,BsmtFinType2,BsmtFinSF2,BsmtUnfSF,TotalBsmtSF,Heating,HeatingQC,CentralAir,Electrical,1stFlrSF,2ndFlrSF,LowQualFinSF,GrLivArea,BsmtFullBath,BsmtHalfBath,FullBath,HalfBath,BedroomAbvGr,KitchenAbvGr,KitchenQual,TotRmsAbvGrd,Functional,Fireplaces,FireplaceQu,GarageType,GarageYrBlt,GarageFinish,GarageCars,GarageArea,GarageQual,GarageCond,PavedDrive,WoodDeckSF,OpenPorchSF,EnclosedPorch,3SsnPorch,ScreenPorch,PoolArea,PoolQC,Fence,MiscFeature,MiscVal,MoSold,YrSold,SaleType,SaleCondition,SalePrice\n",
            "\n",
            "1,60,RL,65,8450,Pave,NA,Reg,Lvl,AllPub,Inside,Gtl,CollgCr,Norm,Norm,1Fam,2Story,7,5,2003,2003,Gable,CompShg,VinylSd,VinylSd,BrkFace,196,Gd,TA,PConc,Gd,TA,No,GLQ,706,Unf,0,150,856,GasA,Ex,Y,SBrkr,856,854,0,1710,1,0,2,1,3,1,Gd,8,Typ,0,NA,Attchd,2003,RFn,2,548,TA,TA,Y,0,61,0,0,0,0,NA,NA,NA,0,2,2008,WD,Normal,208500\n",
            "\n",
            "2,20,RL,80,9600,Pave,NA,Reg,Lvl,AllPub,FR2,Gtl,Veenker,Feedr,Norm,1Fam,1Story,6,8,1976,1976,Gable,CompShg,MetalSd,MetalSd,None,0,TA,TA,CBlock,Gd,TA,Gd,ALQ,978,Unf,0,284,1262,GasA,Ex,Y,SBrkr,1262,0,0,1262,0,1,2,0,3,1,TA,6,Typ,1,TA,Attchd,1976,RFn,2,460,TA,TA,Y,298,0,0,0,0,0,NA,NA,NA,0,5,2007,WD,Normal,181500\n",
            "\n"
          ]
        }
      ],
      "source": [
        "with open(iowa_file) as file:\n",
        "    for lnum, line in enumerate(file):\n",
        "        print(line)\n",
        "        if lnum > 1:\n",
        "            break"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "9e56f1936cd6fcd5146acd6546bbcd03aeb96b0d",
        "id": "1b5eOyZ77ZCp"
      },
      "source": [
        "Looks good! Note that the data comes split into a train and a test portion. In practice, you'd need to run these tests on each portion but since this is a demonstration we proceed immediately with loading both files into memory."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "_uuid": "a91bb59aab4b7e6ffd531499194775388a92c881",
        "id": "dk4QG5gP7ZCq"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "\n",
        "iowa_train_data = pd.read_csv('/content/train.csv')\n",
        "iowa_test_data = pd.read_csv('/content/train.csv')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "_uuid": "7621475c4bed1de283a7128857531a251f632b6b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WzJV1QFW7ZCq",
        "outputId": "15cde803-25ee-465e-d392-606e6383ae89"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Length of train data portion: 1460\n",
            "Length of test data portion: 1460\n"
          ]
        }
      ],
      "source": [
        "print('Length of train data portion: {}\\nLength of test data portion: {}'.format(len(iowa_train_data),\n",
        "len(iowa_test_data)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "_uuid": "c5431f53c62fc94a323cd451f8bb907100462774",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "P6K7UmaH7ZCr",
        "outputId": "23faeb97-8e85-4957-c3cc-4908f1e93a85"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-b8a7534c-c342-4815-bf22-f2ddca1a5a1f\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Id</th>\n",
              "      <th>MSSubClass</th>\n",
              "      <th>MSZoning</th>\n",
              "      <th>LotFrontage</th>\n",
              "      <th>LotArea</th>\n",
              "      <th>Street</th>\n",
              "      <th>Alley</th>\n",
              "      <th>LotShape</th>\n",
              "      <th>LandContour</th>\n",
              "      <th>Utilities</th>\n",
              "      <th>LotConfig</th>\n",
              "      <th>LandSlope</th>\n",
              "      <th>Neighborhood</th>\n",
              "      <th>Condition1</th>\n",
              "      <th>Condition2</th>\n",
              "      <th>BldgType</th>\n",
              "      <th>HouseStyle</th>\n",
              "      <th>OverallQual</th>\n",
              "      <th>OverallCond</th>\n",
              "      <th>YearBuilt</th>\n",
              "      <th>YearRemodAdd</th>\n",
              "      <th>RoofStyle</th>\n",
              "      <th>RoofMatl</th>\n",
              "      <th>Exterior1st</th>\n",
              "      <th>Exterior2nd</th>\n",
              "      <th>MasVnrType</th>\n",
              "      <th>MasVnrArea</th>\n",
              "      <th>ExterQual</th>\n",
              "      <th>ExterCond</th>\n",
              "      <th>Foundation</th>\n",
              "      <th>BsmtQual</th>\n",
              "      <th>BsmtCond</th>\n",
              "      <th>BsmtExposure</th>\n",
              "      <th>BsmtFinType1</th>\n",
              "      <th>BsmtFinSF1</th>\n",
              "      <th>BsmtFinType2</th>\n",
              "      <th>BsmtFinSF2</th>\n",
              "      <th>BsmtUnfSF</th>\n",
              "      <th>TotalBsmtSF</th>\n",
              "      <th>Heating</th>\n",
              "      <th>...</th>\n",
              "      <th>CentralAir</th>\n",
              "      <th>Electrical</th>\n",
              "      <th>1stFlrSF</th>\n",
              "      <th>2ndFlrSF</th>\n",
              "      <th>LowQualFinSF</th>\n",
              "      <th>GrLivArea</th>\n",
              "      <th>BsmtFullBath</th>\n",
              "      <th>BsmtHalfBath</th>\n",
              "      <th>FullBath</th>\n",
              "      <th>HalfBath</th>\n",
              "      <th>BedroomAbvGr</th>\n",
              "      <th>KitchenAbvGr</th>\n",
              "      <th>KitchenQual</th>\n",
              "      <th>TotRmsAbvGrd</th>\n",
              "      <th>Functional</th>\n",
              "      <th>Fireplaces</th>\n",
              "      <th>FireplaceQu</th>\n",
              "      <th>GarageType</th>\n",
              "      <th>GarageYrBlt</th>\n",
              "      <th>GarageFinish</th>\n",
              "      <th>GarageCars</th>\n",
              "      <th>GarageArea</th>\n",
              "      <th>GarageQual</th>\n",
              "      <th>GarageCond</th>\n",
              "      <th>PavedDrive</th>\n",
              "      <th>WoodDeckSF</th>\n",
              "      <th>OpenPorchSF</th>\n",
              "      <th>EnclosedPorch</th>\n",
              "      <th>3SsnPorch</th>\n",
              "      <th>ScreenPorch</th>\n",
              "      <th>PoolArea</th>\n",
              "      <th>PoolQC</th>\n",
              "      <th>Fence</th>\n",
              "      <th>MiscFeature</th>\n",
              "      <th>MiscVal</th>\n",
              "      <th>MoSold</th>\n",
              "      <th>YrSold</th>\n",
              "      <th>SaleType</th>\n",
              "      <th>SaleCondition</th>\n",
              "      <th>SalePrice</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>60</td>\n",
              "      <td>RL</td>\n",
              "      <td>65.0</td>\n",
              "      <td>8450</td>\n",
              "      <td>Pave</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Reg</td>\n",
              "      <td>Lvl</td>\n",
              "      <td>AllPub</td>\n",
              "      <td>Inside</td>\n",
              "      <td>Gtl</td>\n",
              "      <td>CollgCr</td>\n",
              "      <td>Norm</td>\n",
              "      <td>Norm</td>\n",
              "      <td>1Fam</td>\n",
              "      <td>2Story</td>\n",
              "      <td>7</td>\n",
              "      <td>5</td>\n",
              "      <td>2003</td>\n",
              "      <td>2003</td>\n",
              "      <td>Gable</td>\n",
              "      <td>CompShg</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>BrkFace</td>\n",
              "      <td>196.0</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>PConc</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>No</td>\n",
              "      <td>GLQ</td>\n",
              "      <td>706</td>\n",
              "      <td>Unf</td>\n",
              "      <td>0</td>\n",
              "      <td>150</td>\n",
              "      <td>856</td>\n",
              "      <td>GasA</td>\n",
              "      <td>...</td>\n",
              "      <td>Y</td>\n",
              "      <td>SBrkr</td>\n",
              "      <td>856</td>\n",
              "      <td>854</td>\n",
              "      <td>0</td>\n",
              "      <td>1710</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>Gd</td>\n",
              "      <td>8</td>\n",
              "      <td>Typ</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Attchd</td>\n",
              "      <td>2003.0</td>\n",
              "      <td>RFn</td>\n",
              "      <td>2</td>\n",
              "      <td>548</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>Y</td>\n",
              "      <td>0</td>\n",
              "      <td>61</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2008</td>\n",
              "      <td>WD</td>\n",
              "      <td>Normal</td>\n",
              "      <td>208500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>20</td>\n",
              "      <td>RL</td>\n",
              "      <td>80.0</td>\n",
              "      <td>9600</td>\n",
              "      <td>Pave</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Reg</td>\n",
              "      <td>Lvl</td>\n",
              "      <td>AllPub</td>\n",
              "      <td>FR2</td>\n",
              "      <td>Gtl</td>\n",
              "      <td>Veenker</td>\n",
              "      <td>Feedr</td>\n",
              "      <td>Norm</td>\n",
              "      <td>1Fam</td>\n",
              "      <td>1Story</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "      <td>1976</td>\n",
              "      <td>1976</td>\n",
              "      <td>Gable</td>\n",
              "      <td>CompShg</td>\n",
              "      <td>MetalSd</td>\n",
              "      <td>MetalSd</td>\n",
              "      <td>None</td>\n",
              "      <td>0.0</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>CBlock</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>Gd</td>\n",
              "      <td>ALQ</td>\n",
              "      <td>978</td>\n",
              "      <td>Unf</td>\n",
              "      <td>0</td>\n",
              "      <td>284</td>\n",
              "      <td>1262</td>\n",
              "      <td>GasA</td>\n",
              "      <td>...</td>\n",
              "      <td>Y</td>\n",
              "      <td>SBrkr</td>\n",
              "      <td>1262</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1262</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>TA</td>\n",
              "      <td>6</td>\n",
              "      <td>Typ</td>\n",
              "      <td>1</td>\n",
              "      <td>TA</td>\n",
              "      <td>Attchd</td>\n",
              "      <td>1976.0</td>\n",
              "      <td>RFn</td>\n",
              "      <td>2</td>\n",
              "      <td>460</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>Y</td>\n",
              "      <td>298</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>2007</td>\n",
              "      <td>WD</td>\n",
              "      <td>Normal</td>\n",
              "      <td>181500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>60</td>\n",
              "      <td>RL</td>\n",
              "      <td>68.0</td>\n",
              "      <td>11250</td>\n",
              "      <td>Pave</td>\n",
              "      <td>NaN</td>\n",
              "      <td>IR1</td>\n",
              "      <td>Lvl</td>\n",
              "      <td>AllPub</td>\n",
              "      <td>Inside</td>\n",
              "      <td>Gtl</td>\n",
              "      <td>CollgCr</td>\n",
              "      <td>Norm</td>\n",
              "      <td>Norm</td>\n",
              "      <td>1Fam</td>\n",
              "      <td>2Story</td>\n",
              "      <td>7</td>\n",
              "      <td>5</td>\n",
              "      <td>2001</td>\n",
              "      <td>2002</td>\n",
              "      <td>Gable</td>\n",
              "      <td>CompShg</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>BrkFace</td>\n",
              "      <td>162.0</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>PConc</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>Mn</td>\n",
              "      <td>GLQ</td>\n",
              "      <td>486</td>\n",
              "      <td>Unf</td>\n",
              "      <td>0</td>\n",
              "      <td>434</td>\n",
              "      <td>920</td>\n",
              "      <td>GasA</td>\n",
              "      <td>...</td>\n",
              "      <td>Y</td>\n",
              "      <td>SBrkr</td>\n",
              "      <td>920</td>\n",
              "      <td>866</td>\n",
              "      <td>0</td>\n",
              "      <td>1786</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>Gd</td>\n",
              "      <td>6</td>\n",
              "      <td>Typ</td>\n",
              "      <td>1</td>\n",
              "      <td>TA</td>\n",
              "      <td>Attchd</td>\n",
              "      <td>2001.0</td>\n",
              "      <td>RFn</td>\n",
              "      <td>2</td>\n",
              "      <td>608</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>Y</td>\n",
              "      <td>0</td>\n",
              "      <td>42</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>9</td>\n",
              "      <td>2008</td>\n",
              "      <td>WD</td>\n",
              "      <td>Normal</td>\n",
              "      <td>223500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>70</td>\n",
              "      <td>RL</td>\n",
              "      <td>60.0</td>\n",
              "      <td>9550</td>\n",
              "      <td>Pave</td>\n",
              "      <td>NaN</td>\n",
              "      <td>IR1</td>\n",
              "      <td>Lvl</td>\n",
              "      <td>AllPub</td>\n",
              "      <td>Corner</td>\n",
              "      <td>Gtl</td>\n",
              "      <td>Crawfor</td>\n",
              "      <td>Norm</td>\n",
              "      <td>Norm</td>\n",
              "      <td>1Fam</td>\n",
              "      <td>2Story</td>\n",
              "      <td>7</td>\n",
              "      <td>5</td>\n",
              "      <td>1915</td>\n",
              "      <td>1970</td>\n",
              "      <td>Gable</td>\n",
              "      <td>CompShg</td>\n",
              "      <td>Wd Sdng</td>\n",
              "      <td>Wd Shng</td>\n",
              "      <td>None</td>\n",
              "      <td>0.0</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>BrkTil</td>\n",
              "      <td>TA</td>\n",
              "      <td>Gd</td>\n",
              "      <td>No</td>\n",
              "      <td>ALQ</td>\n",
              "      <td>216</td>\n",
              "      <td>Unf</td>\n",
              "      <td>0</td>\n",
              "      <td>540</td>\n",
              "      <td>756</td>\n",
              "      <td>GasA</td>\n",
              "      <td>...</td>\n",
              "      <td>Y</td>\n",
              "      <td>SBrkr</td>\n",
              "      <td>961</td>\n",
              "      <td>756</td>\n",
              "      <td>0</td>\n",
              "      <td>1717</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>Gd</td>\n",
              "      <td>7</td>\n",
              "      <td>Typ</td>\n",
              "      <td>1</td>\n",
              "      <td>Gd</td>\n",
              "      <td>Detchd</td>\n",
              "      <td>1998.0</td>\n",
              "      <td>Unf</td>\n",
              "      <td>3</td>\n",
              "      <td>642</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>Y</td>\n",
              "      <td>0</td>\n",
              "      <td>35</td>\n",
              "      <td>272</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2006</td>\n",
              "      <td>WD</td>\n",
              "      <td>Abnorml</td>\n",
              "      <td>140000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>60</td>\n",
              "      <td>RL</td>\n",
              "      <td>84.0</td>\n",
              "      <td>14260</td>\n",
              "      <td>Pave</td>\n",
              "      <td>NaN</td>\n",
              "      <td>IR1</td>\n",
              "      <td>Lvl</td>\n",
              "      <td>AllPub</td>\n",
              "      <td>FR2</td>\n",
              "      <td>Gtl</td>\n",
              "      <td>NoRidge</td>\n",
              "      <td>Norm</td>\n",
              "      <td>Norm</td>\n",
              "      <td>1Fam</td>\n",
              "      <td>2Story</td>\n",
              "      <td>8</td>\n",
              "      <td>5</td>\n",
              "      <td>2000</td>\n",
              "      <td>2000</td>\n",
              "      <td>Gable</td>\n",
              "      <td>CompShg</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>VinylSd</td>\n",
              "      <td>BrkFace</td>\n",
              "      <td>350.0</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>PConc</td>\n",
              "      <td>Gd</td>\n",
              "      <td>TA</td>\n",
              "      <td>Av</td>\n",
              "      <td>GLQ</td>\n",
              "      <td>655</td>\n",
              "      <td>Unf</td>\n",
              "      <td>0</td>\n",
              "      <td>490</td>\n",
              "      <td>1145</td>\n",
              "      <td>GasA</td>\n",
              "      <td>...</td>\n",
              "      <td>Y</td>\n",
              "      <td>SBrkr</td>\n",
              "      <td>1145</td>\n",
              "      <td>1053</td>\n",
              "      <td>0</td>\n",
              "      <td>2198</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>Gd</td>\n",
              "      <td>9</td>\n",
              "      <td>Typ</td>\n",
              "      <td>1</td>\n",
              "      <td>TA</td>\n",
              "      <td>Attchd</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>RFn</td>\n",
              "      <td>3</td>\n",
              "      <td>836</td>\n",
              "      <td>TA</td>\n",
              "      <td>TA</td>\n",
              "      <td>Y</td>\n",
              "      <td>192</td>\n",
              "      <td>84</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>12</td>\n",
              "      <td>2008</td>\n",
              "      <td>WD</td>\n",
              "      <td>Normal</td>\n",
              "      <td>250000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 81 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b8a7534c-c342-4815-bf22-f2ddca1a5a1f')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b8a7534c-c342-4815-bf22-f2ddca1a5a1f button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b8a7534c-c342-4815-bf22-f2ddca1a5a1f');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Id  MSSubClass MSZoning  ...  SaleType  SaleCondition SalePrice\n",
              "0   1          60       RL  ...        WD         Normal    208500\n",
              "1   2          20       RL  ...        WD         Normal    181500\n",
              "2   3          60       RL  ...        WD         Normal    223500\n",
              "3   4          70       RL  ...        WD        Abnorml    140000\n",
              "4   5          60       RL  ...        WD         Normal    250000\n",
              "\n",
              "[5 rows x 81 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "iowa_train_data.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "0bf6c343dd46681dcec16dae4cf3f57e5fb37ecf",
        "id": "6V3pTUlM7ZCs"
      },
      "source": [
        "## Part 2: Building a Random Forest model and handling missing values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "ba33c1a01e204297242c2246572d52e59632c2a3",
        "id": "1b0P4hvh7ZCs"
      },
      "source": [
        "First, we define the prediction features and target. For simplicity, we'll ignore categorical (non-numerical) data for now."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "_uuid": "e146fd6ef49b654dc33611bfd4dd34f5d882605f",
        "id": "eslJ0n207ZCt"
      },
      "outputs": [],
      "source": [
        "iowa_target = iowa_train_data['SalePrice']\n",
        "iowa_predictors = iowa_train_data.drop(['SalePrice'], axis=1)\n",
        "\n",
        "# For the sake of keeping the example simple, we'll use only numeric predictors. \n",
        "iowa_numeric_predictors = iowa_predictors.select_dtypes(exclude=['object'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_cell_guid": "88d1c1c9-91ba-4bef-aee5-f4a19a68e61c",
        "_uuid": "de7bdb4f005022ea45742b5d25f47cba7a6d698d",
        "id": "85a6PkVO7ZCt"
      },
      "source": [
        "Let's also create a function to measure the quality of an approach. This function reports the out-of-sample mean absolute error (MAE) score from a Random Forest. We begin by splitting our training data into a a train and a test portion."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "_cell_guid": "986dbfe4-9386-4a03-b2a4-9e99bf1b08f5",
        "_kg_hide-input": true,
        "_uuid": "6088bfdac20ece9c040e83beb28ff169d17f0666",
        "id": "f7idv6L37ZCt"
      },
      "outputs": [],
      "source": [
        "from sklearn.ensemble import RandomForestRegressor\n",
        "from sklearn.metrics import mean_absolute_error\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(iowa_numeric_predictors, \n",
        "                                                    iowa_target,\n",
        "                                                    train_size=0.7, \n",
        "                                                    test_size=0.3, \n",
        "                                                    random_state=0)\n",
        "\n",
        "def score_dataset(X_train, X_test, y_train, y_test):\n",
        "    model = RandomForestRegressor(random_state=0)\n",
        "    model.fit(X_train, y_train)\n",
        "    preds = model.predict(X_test)\n",
        "    return mean_absolute_error(y_test, preds)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_cell_guid": "7184fc99-e266-4bd7-af0d-0da9c96887f0",
        "_uuid": "df0103056e52ffb3c500f5fc1437bd175a41adad",
        "id": "IYrz1vPX7ZCt"
      },
      "source": [
        "We first try to handle missing values by dropping the entire column containing them and measure the resulting MAE."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "_cell_guid": "64ae7a0a-95aa-47a7-aa29-a1589ebcbd18",
        "_uuid": "2957c4a7c4e6ed990b1406d5c88a9aa4c738b28f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XH6TuI4t7ZCt",
        "outputId": "e6d8011d-851d-4968-b768-5c97e8e33231"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Absolute Error from dropping columns with missing values:\n",
            "18003\n"
          ]
        }
      ],
      "source": [
        "cols_with_missing = [col for col in X_train.columns if X_train[col].isnull().any()]\n",
        "reduced_X_train = X_train.drop(cols_with_missing, axis = 1)\n",
        "reduced_X_test  = X_test.drop(cols_with_missing, axis = 1)\n",
        "print(\"Mean Absolute Error from dropping columns with missing values:\")\n",
        "print(int(score_dataset(reduced_X_train, reduced_X_test, y_train, y_test)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_cell_guid": "b446d3e1-0a5c-4552-8718-e07ab5f4496a",
        "_uuid": "e78f8751db60278737a388a4b85b72bed4d3f45b",
        "id": "ihthYswZ7ZCu"
      },
      "source": [
        "We next try to replace missing values through standard imputation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "_cell_guid": "8cb756dc-9623-43b7-92c7-dfd87c70f450",
        "_uuid": "7f1030b598d08cd586a56d4ab33d1f99f6535784",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JdgBedYy7ZCu",
        "outputId": "5313ce8c-fc44-498b-dcf5-57229eac92b1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Absolute Error from imputation:\n",
            "17868\n"
          ]
        }
      ],
      "source": [
        "from sklearn.impute import SimpleImputer\n",
        "\n",
        "my_imputer = SimpleImputer()\n",
        "imputed_X_train = my_imputer.fit_transform(X_train)\n",
        "imputed_X_test = my_imputer.transform(X_test)\n",
        "print(\"Mean Absolute Error from imputation:\")\n",
        "print(int(score_dataset(imputed_X_train, imputed_X_test, y_train, y_test)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "74d86db6e782a18cfe286f6d55da95e88ac38d23",
        "id": "rg4YmgV07ZCu"
      },
      "source": [
        "Our error seems smaller but the improvement is so little that a different `random_state` could easily make the error bigger. Why haven't we improved? Let's look at how many missing values there actually are."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "_uuid": "56bcb82486d45a9a60975cacea3a560d75e93694",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aY3pt_yE7ZCv",
        "outputId": "4bc4bfd4-6f65-488e-a19d-b0edc701e6ef"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LotFrontage    189\n",
              "MasVnrArea       5\n",
              "GarageYrBlt     54\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "missing = X_train.isnull().sum()\n",
        "missing[missing != 0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "dfe3f8be93897749d36595b96977ffdaab11b64b",
        "id": "2ovnsFyl7ZCv"
      },
      "source": [
        "There are only few missing values (remember, there are 1460 rows) and they are concentrated in only 3 out of 80 features/columns. Replacing these with their mean values (which is what `SimpleImputer` does) is thus no improvement over simply dropping the three columns. Still, let's see if keeping track of which columns have missing values that are replaced improves the situation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "_cell_guid": "39ba8166-9b03-41cb-9403-d728b342d5e7",
        "_uuid": "914b9e57b99d7964013f007537c300fe57e0bf91",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GBn7K0LD7ZCv",
        "outputId": "f5f832a6-1dd8-4bac-84c7-952386ac59b9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Absolute Error from imputation while tracking what was imputed:\n",
            "17859\n"
          ]
        }
      ],
      "source": [
        "imputed_X_train_plus = X_train.copy()\n",
        "imputed_X_test_plus = X_test.copy()\n",
        "\n",
        "cols_with_missing = (col for col in X_train.columns if X_train[col].isnull().any())\n",
        "for col in cols_with_missing:\n",
        "    imputed_X_train_plus[col + '_was_missing'] = imputed_X_train_plus[col].isnull()\n",
        "    imputed_X_test_plus[col + '_was_missing'] = imputed_X_test_plus[col].isnull()\n",
        "\n",
        "# Imputation\n",
        "my_imputer = SimpleImputer()\n",
        "imputed_X_train_plus = my_imputer.fit_transform(imputed_X_train_plus)\n",
        "imputed_X_test_plus = my_imputer.transform(imputed_X_test_plus)\n",
        "\n",
        "print(\"Mean Absolute Error from imputation while tracking what was imputed:\")\n",
        "print(int(score_dataset(imputed_X_train_plus, imputed_X_test_plus, y_train, y_test)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "35888f7d87fa506a07afbb0cb57c5b489bd5f621",
        "id": "yNG5yo1E7ZCw"
      },
      "source": [
        "It does not. Again, the `random_state` variance is greater than the error difference."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "1dc9e6072bad39ead6ba047f7909fbd0eddfe999",
        "id": "qcBBDh0M7ZCw"
      },
      "source": [
        "## Part 3: Converting categorical data to dummy variables"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "49669f889f61347fd132dd983c1dbb2e14fcf740",
        "id": "eQ01tH7Y7ZCw"
      },
      "source": [
        "Let's see if we can improve our model by one-hot encoding our categoricals, i.e. turning them into dummy variables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "_uuid": "873e1270d2b461d39d3816f1c6fe9fa5c2cc8a88",
        "id": "KuuPxgqq7ZCw"
      },
      "outputs": [],
      "source": [
        "one_hot_encoded_iowa_predictors = pd.get_dummies(iowa_predictors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "_uuid": "d68f071944b758f0ffda5b32de7448d3878d1f5f",
        "id": "T0rXt2NC7ZCw"
      },
      "outputs": [],
      "source": [
        "X_train_1hot, X_test_1hot, y_train, y_test = train_test_split(one_hot_encoded_iowa_predictors, \n",
        "                                                    iowa_target,\n",
        "                                                    train_size=0.7, \n",
        "                                                    test_size=0.3, \n",
        "                                                    random_state=0)\n",
        "\n",
        "cols_with_missing = [col for col in X_train_1hot.columns if X_train_1hot[col].isnull().any()]\n",
        "reduced_X_train_1hot = X_train_1hot.drop(cols_with_missing, axis = 1)\n",
        "reduced_X_test_1hot  = X_test_1hot.drop(cols_with_missing, axis = 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "_uuid": "e6406aace1eb4020d5e2552126c4afc757f44634",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5JLgtRmZ7ZCx",
        "outputId": "fd0b2f6e-68f7-4e86-d01c-587f59b28e5b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Absolute Error from including categorical data:\n",
            "17448\n"
          ]
        }
      ],
      "source": [
        "print(\"Mean Absolute Error from including categorical data:\")\n",
        "print(int(score_dataset(reduced_X_train_1hot, reduced_X_test_1hot, y_train, y_test)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "752e00ad53d4e773cf21e3f8b07a7f5bba40262d",
        "id": "oUhyFkDE7ZCy"
      },
      "source": [
        "We have reduced the error by about $400. This should be more than the `random_state` variance and a first small piece of progress."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "96e7cda13c65241facf4ad673ca8001edd966754",
        "id": "6qbMLnoz7ZCy"
      },
      "source": [
        "## Part 4: XGBoost"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "ddd653836a22b5d06e0b42038c3654a9050b144d",
        "id": "uE5wpe_F7ZCy"
      },
      "source": [
        "Let's use the powerful XGBoost regressor and run it on our data set with missing values dropped."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "_uuid": "8e9246c2fd9e486de4cb587a1607647b30d106b6",
        "id": "SHwHFqro7ZCz"
      },
      "outputs": [],
      "source": [
        "from xgboost import XGBRegressor\n",
        "\n",
        "xgb = XGBRegressor()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "_uuid": "363de4bf8ad2f2022c492738585240f486e959a9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K_ExcuSU7ZCz",
        "outputId": "fd91379a-5a29-473d-eb92-65121c56734a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[16:11:23] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "XGBRegressor(base_score=0.5, booster='gbtree', colsample_bylevel=1,\n",
              "             colsample_bynode=1, colsample_bytree=1, gamma=0,\n",
              "             importance_type='gain', learning_rate=0.1, max_delta_step=0,\n",
              "             max_depth=3, min_child_weight=1, missing=None, n_estimators=100,\n",
              "             n_jobs=1, nthread=None, objective='reg:linear', random_state=0,\n",
              "             reg_alpha=0, reg_lambda=1, scale_pos_weight=1, seed=None,\n",
              "             silent=None, subsample=1, verbosity=1)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "xgb.fit(reduced_X_train_1hot, y_train, verbose=False)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "_uuid": "de91420d4dc687e7210cbd6616afef7ae1430425",
        "scrolled": false,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Kz8R5l6U7ZCz",
        "outputId": "5a44fe67-fd3a-432a-ec5f-5e15cb54037b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Absolute Error: 16380\n"
          ]
        }
      ],
      "source": [
        "xgb_preds = xgb.predict(reduced_X_test_1hot)\n",
        "print(\"Mean Absolute Error: \" + str(int(mean_absolute_error(y_test, xgb_preds))))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "729d3186f7f9c11c046918cf216b2fb6833c9c66",
        "id": "M7BUb--X7ZCz"
      },
      "source": [
        "Great! We've reduced our error by another $1000. To further improve, let's find the optimal number of estimators to use in our XGBoost."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "_uuid": "f92134279d906f09def5872fb2fdded4e2ab1542",
        "id": "fPV5rLHf7ZC0"
      },
      "outputs": [],
      "source": [
        "def get_xgb_mae(n_estimators, learning_rate=0.1):\n",
        "    xgb = XGBRegressor(n_estimators=n_estimators, learning_rate=learning_rate)\n",
        "    xgb.fit(reduced_X_train_1hot, y_train, eval_set=[(reduced_X_test_1hot, y_test)], verbose=False)\n",
        "    xgb_preds = xgb.predict(reduced_X_test_1hot)\n",
        "    mae = mean_absolute_error(y_test, xgb_preds)\n",
        "    print(\"Mean Absolute Error from using {} estimators at a learning rate of {}: {}\"\\\n",
        "          .format(str(n_estimators), learning_rate, str(int(mae))))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "_uuid": "f8173d2426eda140279960537521813c518c1ea9",
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JJCATttL7ZC0",
        "outputId": "51b52c31-b0cc-4364-d2e6-ab9bcd937523"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[16:11:24] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 100 estimators at a learning rate of 0.1: 16380\n",
            "[16:11:25] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 200 estimators at a learning rate of 0.1: 16028\n",
            "[16:11:26] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 300 estimators at a learning rate of 0.1: 15967\n",
            "[16:11:29] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 400 estimators at a learning rate of 0.1: 16014\n",
            "[16:11:32] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 500 estimators at a learning rate of 0.1: 16080\n",
            "[16:11:36] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 600 estimators at a learning rate of 0.1: 16082\n",
            "[16:11:40] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 700 estimators at a learning rate of 0.1: 16061\n",
            "[16:11:45] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 800 estimators at a learning rate of 0.1: 16100\n",
            "[16:11:52] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 900 estimators at a learning rate of 0.1: 16159\n",
            "[16:11:59] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 1000 estimators at a learning rate of 0.1: 16176\n"
          ]
        }
      ],
      "source": [
        "for i in range(100, 1100, 100):\n",
        "    get_xgb_mae(i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "09c14b4813e55901f5c0d39c62041f95d102ddf6",
        "id": "-keJlaqx7ZC0"
      },
      "source": [
        "We see that the best number of estimators is 300. By using a slower learning rate we may be able to further improve our results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "_uuid": "7fc3cc5be1676e269f99a873794a3a656f863e91",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9KO8i5N07ZC0",
        "outputId": "b7d5af95-e0c0-4e8d-8744-6963e4129b7e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[16:12:06] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "Mean Absolute Error from using 300 estimators at a learning rate of 0.05: 15935\n"
          ]
        }
      ],
      "source": [
        "get_xgb_mae(300, 0.05)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "ec152d8ee5e035fbd1b15063ad647ae88fde495a",
        "id": "dJkGbiGp7ZC0"
      },
      "source": [
        "## Part 5: Training our model on the whole data set and submitting our work"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "67e48833a4feb0431c1f9a5447b2dbaed6cac326",
        "id": "-1IaNLUK7ZC1"
      },
      "source": [
        "Now that we have determined the best model and parameters, we train our model on the entire data set and submit our work."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "_uuid": "de12bfb39a99c550ca3fde23016a4aa41eebc0fd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ohj-LuQ87ZC1",
        "outputId": "67dd2df6-7dcc-4b96-9352-dec024b564ba"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[16:12:09] WARNING: /workspace/src/objective/regression_obj.cu:152: reg:linear is now deprecated in favor of reg:squarederror.\n",
            "[201790.48 161235.44 205076.22 ... 262795.75 140582.1  147336.23]\n"
          ]
        }
      ],
      "source": [
        "# Starting data\n",
        "iowa_target = iowa_train_data['SalePrice']\n",
        "y_train = iowa_target\n",
        "iowa_predictors = iowa_train_data.drop(['SalePrice'], axis=1)\n",
        "\n",
        "# Drop missing values from training and test data\n",
        "cols_with_missing = [col for col in iowa_predictors.columns if iowa_predictors[col].isnull().any()]\n",
        "reduced_iowa_predictors = iowa_predictors.drop(cols_with_missing, axis = 1)\n",
        "reduced_iowa_test_data = iowa_test_data.drop(cols_with_missing, axis = 1)\n",
        "\n",
        "# Convert categoricals to dummies in training and test data and aligning the columns\n",
        "one_hot_encoded_reduced_iowa_predictors = pd.get_dummies(reduced_iowa_predictors)\n",
        "one_hot_encoded_reduced_iowa_test_data = pd.get_dummies(reduced_iowa_test_data)\n",
        "X_train, X_test = one_hot_encoded_reduced_iowa_predictors.align(one_hot_encoded_reduced_iowa_test_data,\n",
        "                                                                    join='left', \n",
        "                                                                    axis=1)\n",
        "\n",
        "# Build best currently known model and use it to make predictions\n",
        "xgb = XGBRegressor(n_estimators=300, learning_rate=0.05)\n",
        "xgb.fit(X_train, y_train, verbose=False)\n",
        "predicted_prices = xgb.predict(X_test)\n",
        "\n",
        "# Print result\n",
        "print(predicted_prices)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "_uuid": "845384b1ffebe278b3378c696a9a42d3554dbc3c",
        "id": "cjq6HNrL7ZC1"
      },
      "outputs": [],
      "source": [
        "# Prepare data for submission\n",
        "my_submission = pd.DataFrame({'Id': X_test.Id, 'SalePrice': predicted_prices})\n",
        "my_submission.to_csv('submission.csv', index=False)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "7964dbbf6e826fb2dccca64a63bd1b9c3ec7e739",
        "id": "obJ2LoiW7ZC1"
      },
      "source": [
        "## Part 6: Partial dependence plots"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "8c9c47e3bc218a32f68579887e837b0874c6d97c",
        "id": "FoXiChCq7ZC1"
      },
      "source": [
        "Let's see how the predicted price depends on individual features. The plot visualizing this dependence is known as a partial dependence plot. The obvious features to chose from are the following:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "_uuid": "ba84966713348fad755e5aa623c9a12de0dd4324",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "JivsIuhy7ZC2",
        "outputId": "5526260a-2613-4ec2-9859-050847a33525"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Id  MSSubClass  LotArea  OverallQual  ...  PoolArea  MiscVal  MoSold  YrSold\n",
              "0   1          60     8450            7  ...         0        0       2    2008\n",
              "1   2          20     9600            6  ...         0        0       5    2007\n",
              "2   3          60    11250            7  ...         0        0       9    2008\n",
              "3   4          70     9550            7  ...         0        0       2    2006\n",
              "4   5          60    14260            8  ...         0        0      12    2008\n",
              "\n",
              "[5 rows x 34 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "reduced_iowa_predictors.select_dtypes(exclude=['object']).head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "5c23cf71e3834adccd7923e567a89ad0635de900",
        "id": "9krlhqh57ZC2"
      },
      "source": [
        "Let's see how lot area, above ground living area, and the size of the garage affect the price. We hypothesize that prices will rise with increasing number of square footage for these values. We also look at the year the house was built. Again, we expect the price to be higher for more recently built houses."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "ebc00603185c6974149ee71dc70cd1dde40e70fb",
        "id": "GwboLkvs7ZC3"
      },
      "source": [
        " *Note:* The plots are relative to the average price which is centered at 0."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "_uuid": "89528b09fd24e252377dc910eb0f314677ef401d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "F4TnQL5V7ZC3",
        "outputId": "1b342237-1eeb-4237-aec3-b6f565f7b6d3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# We need to load a gradient booster that is compatible with scikit-learn's partial dependence module (not XGBoost).\n",
        "from sklearn.ensemble import GradientBoostingRegressor\n",
        "from sklearn.ensemble.partial_dependence import partial_dependence, plot_partial_dependence\n",
        "\n",
        "my_model = GradientBoostingRegressor()\n",
        "my_model.fit(X_train, y_train)\n",
        "my_plots = plot_partial_dependence(my_model,       \n",
        "                                   features=[X_train.columns.get_loc(\"LotArea\"), X_train.columns.get_loc(\"GrLivArea\")], # column numbers of plots we want to show\n",
        "                                   X=X_train,            # raw predictors data.\n",
        "                                   feature_names=list(X_train.columns.values), # labels on graphs\n",
        "                                   grid_resolution=10) # number of values to plot on x axis\n",
        "my_plots = plot_partial_dependence(my_model,       \n",
        "                                   features=[X_train.columns.get_loc(\"YearBuilt\"), X_train.columns.get_loc(\"GarageArea\")], # column numbers of plots we want to show\n",
        "                                   X=X_train,            # raw predictors data.\n",
        "                                   feature_names=list(X_train.columns.values), # labels on graphs\n",
        "                                   grid_resolution=10) # number of values to plot on x axis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "_uuid": "945592a86e5af9b8da35a8d3ffd071a46469fe51",
        "id": "nMHHrLvN7ZC3"
      },
      "source": [
        "As expected, prices grow with larger available space (lot area, ground floor living area, garage) and more recent year built."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "_uuid": "f02de7dd07e0dd8059be3fb69caad8a11ea5dc44",
        "id": "BQKxWNGJ7ZC3"
      },
      "outputs": [],
      "source": [
        "#!pip install scikit-learn==0.22.2 --user"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "hJJyvPvKDf5t"
      },
      "execution_count": 28,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.1"
    },
    "colab": {
      "name": "Housing price prediction.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}