Predicting_Home_Prices_Using_Linear,_Multi_Linear,_Polynomial_Regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Predicting Home Prices Using Linear, Multi-Linear, Polynomial Regression.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMiI1RiGqQrYkqyRswG8RYN",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Augusta02/Machine-Learning-Projects/blob/main/Predicting_Home_Prices_Using_Linear%2C_Multi_Linear%2C_Polynomial_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### The aim of this project is to compare the best regression model for this dataset. I would be using the Linear, Multi-Linear and Polynomial Regression models. At the end of the exercise we should be able to determine the best regression model."
      ],
      "metadata": {
        "id": "9qovcF9WRKX_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# first import libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "\n",
        "# import your dataset\n",
        "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": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "id": "L8B4AvHjCj7G",
        "outputId": "75ff6574-e8fe-4f2f-f7ed-542bbd239d08"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-3d1b52c7-d5ee-41ad-9dd1-9e901f009956\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-3d1b52c7-d5ee-41ad-9dd1-9e901f009956\">\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": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving house_data .csv to house_data  (1).csv\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# read_csv file \n",
        "import io \n",
        "home_data= pd.read_csv(io.BytesIO(uploaded[\"house_data .csv\"]))"
      ],
      "metadata": {
        "id": "3QDhyWwgAEaT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "home_data.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 226
        },
        "id": "tmNerlkIDJjS",
        "outputId": "7129cb5a-36cd-4c10-d6d0-a486678bc0f2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "\n",
              "    .dataframe thead th {\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>date</th>\n",
              "      <th>price</th>\n",
              "      <th>bedrooms</th>\n",
              "      <th>bathrooms</th>\n",
              "      <th>sqft_living</th>\n",
              "      <th>sqft_lot</th>\n",
              "      <th>floors</th>\n",
              "      <th>waterfront</th>\n",
              "      <th>view</th>\n",
              "      <th>condition</th>\n",
              "      <th>grade</th>\n",
              "      <th>sqft_above</th>\n",
              "      <th>sqft_basement</th>\n",
              "      <th>yr_built</th>\n",
              "      <th>yr_renovated</th>\n",
              "      <th>zipcode</th>\n",
              "      <th>lat</th>\n",
              "      <th>long</th>\n",
              "      <th>sqft_living15</th>\n",
              "      <th>sqft_lot15</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>7129300520</td>\n",
              "      <td>20141013T000000</td>\n",
              "      <td>221900.0</td>\n",
              "      <td>3</td>\n",
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              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
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              "      <td>1340</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>6414100192</td>\n",
              "      <td>20141209T000000</td>\n",
              "      <td>538000.0</td>\n",
              "      <td>3</td>\n",
              "      <td>2.25</td>\n",
              "      <td>2570</td>\n",
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              "      <td>2.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>2170</td>\n",
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              "      <td>1951</td>\n",
              "      <td>1991</td>\n",
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              "      <td>47.7210</td>\n",
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              "      <td>1690</td>\n",
              "      <td>7639</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
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              "      <td>20150225T000000</td>\n",
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              "      <td>1.0</td>\n",
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              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>6</td>\n",
              "      <td>770</td>\n",
              "      <td>0</td>\n",
              "      <td>1933</td>\n",
              "      <td>0</td>\n",
              "      <td>98028</td>\n",
              "      <td>47.7379</td>\n",
              "      <td>-122.233</td>\n",
              "      <td>2720</td>\n",
              "      <td>8062</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2487200875</td>\n",
              "      <td>20141209T000000</td>\n",
              "      <td>604000.0</td>\n",
              "      <td>4</td>\n",
              "      <td>3.00</td>\n",
              "      <td>1960</td>\n",
              "      <td>5000</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>7</td>\n",
              "      <td>1050</td>\n",
              "      <td>910</td>\n",
              "      <td>1965</td>\n",
              "      <td>0</td>\n",
              "      <td>98136</td>\n",
              "      <td>47.5208</td>\n",
              "      <td>-122.393</td>\n",
              "      <td>1360</td>\n",
              "      <td>5000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1954400510</td>\n",
              "      <td>20150218T000000</td>\n",
              "      <td>510000.0</td>\n",
              "      <td>3</td>\n",
              "      <td>2.00</td>\n",
              "      <td>1680</td>\n",
              "      <td>8080</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>8</td>\n",
              "      <td>1680</td>\n",
              "      <td>0</td>\n",
              "      <td>1987</td>\n",
              "      <td>0</td>\n",
              "      <td>98074</td>\n",
              "      <td>47.6168</td>\n",
              "      <td>-122.045</td>\n",
              "      <td>1800</td>\n",
              "      <td>7503</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           id             date     price  ...     long  sqft_living15  sqft_lot15\n",
              "0  7129300520  20141013T000000  221900.0  ... -122.257           1340        5650\n",
              "1  6414100192  20141209T000000  538000.0  ... -122.319           1690        7639\n",
              "2  5631500400  20150225T000000  180000.0  ... -122.233           2720        8062\n",
              "3  2487200875  20141209T000000  604000.0  ... -122.393           1360        5000\n",
              "4  1954400510  20150218T000000  510000.0  ... -122.045           1800        7503\n",
              "\n",
              "[5 rows x 21 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#using the describe() to understand the dataset better. \n",
        "home_data.describe()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "j6h528MmEU7l",
        "outputId": "6c194e77-5125-4ace-ce5e-6348ce0b0f2c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>price</th>\n",
              "      <th>bedrooms</th>\n",
              "      <th>bathrooms</th>\n",
              "      <th>sqft_living</th>\n",
              "      <th>sqft_lot</th>\n",
              "      <th>floors</th>\n",
              "      <th>waterfront</th>\n",
              "      <th>view</th>\n",
              "      <th>condition</th>\n",
              "      <th>grade</th>\n",
              "      <th>sqft_above</th>\n",
              "      <th>sqft_basement</th>\n",
              "      <th>yr_built</th>\n",
              "      <th>yr_renovated</th>\n",
              "      <th>zipcode</th>\n",
              "      <th>lat</th>\n",
              "      <th>long</th>\n",
              "      <th>sqft_living15</th>\n",
              "      <th>sqft_lot15</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>2.161300e+04</td>\n",
              "      <td>2.161300e+04</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>2.161300e+04</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "      <td>21613.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>4.580302e+09</td>\n",
              "      <td>5.401822e+05</td>\n",
              "      <td>3.370842</td>\n",
              "      <td>2.114757</td>\n",
              "      <td>2079.899736</td>\n",
              "      <td>1.510697e+04</td>\n",
              "      <td>1.494309</td>\n",
              "      <td>0.007542</td>\n",
              "      <td>0.234303</td>\n",
              "      <td>3.409430</td>\n",
              "      <td>7.656873</td>\n",
              "      <td>1788.390691</td>\n",
              "      <td>291.509045</td>\n",
              "      <td>1971.005136</td>\n",
              "      <td>84.402258</td>\n",
              "      <td>98077.939805</td>\n",
              "      <td>47.560053</td>\n",
              "      <td>-122.213896</td>\n",
              "      <td>1986.552492</td>\n",
              "      <td>12768.455652</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>2.876566e+09</td>\n",
              "      <td>3.673622e+05</td>\n",
              "      <td>0.930062</td>\n",
              "      <td>0.770163</td>\n",
              "      <td>918.440897</td>\n",
              "      <td>4.142051e+04</td>\n",
              "      <td>0.539989</td>\n",
              "      <td>0.086517</td>\n",
              "      <td>0.766318</td>\n",
              "      <td>0.650743</td>\n",
              "      <td>1.175459</td>\n",
              "      <td>828.090978</td>\n",
              "      <td>442.575043</td>\n",
              "      <td>29.373411</td>\n",
              "      <td>401.679240</td>\n",
              "      <td>53.505026</td>\n",
              "      <td>0.138564</td>\n",
              "      <td>0.140828</td>\n",
              "      <td>685.391304</td>\n",
              "      <td>27304.179631</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1.000102e+06</td>\n",
              "      <td>7.500000e+04</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>290.000000</td>\n",
              "      <td>5.200000e+02</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>290.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1900.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>98001.000000</td>\n",
              "      <td>47.155900</td>\n",
              "      <td>-122.519000</td>\n",
              "      <td>399.000000</td>\n",
              "      <td>651.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>2.123049e+09</td>\n",
              "      <td>3.219500e+05</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>1.750000</td>\n",
              "      <td>1427.000000</td>\n",
              "      <td>5.040000e+03</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>1190.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1951.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>98033.000000</td>\n",
              "      <td>47.471000</td>\n",
              "      <td>-122.328000</td>\n",
              "      <td>1490.000000</td>\n",
              "      <td>5100.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>3.904930e+09</td>\n",
              "      <td>4.500000e+05</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>2.250000</td>\n",
              "      <td>1910.000000</td>\n",
              "      <td>7.618000e+03</td>\n",
              "      <td>1.500000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>1560.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1975.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>98065.000000</td>\n",
              "      <td>47.571800</td>\n",
              "      <td>-122.230000</td>\n",
              "      <td>1840.000000</td>\n",
              "      <td>7620.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>7.308900e+09</td>\n",
              "      <td>6.450000e+05</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>2.500000</td>\n",
              "      <td>2550.000000</td>\n",
              "      <td>1.068800e+04</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>8.000000</td>\n",
              "      <td>2210.000000</td>\n",
              "      <td>560.000000</td>\n",
              "      <td>1997.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>98118.000000</td>\n",
              "      <td>47.678000</td>\n",
              "      <td>-122.125000</td>\n",
              "      <td>2360.000000</td>\n",
              "      <td>10083.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>9.900000e+09</td>\n",
              "      <td>7.700000e+06</td>\n",
              "      <td>33.000000</td>\n",
              "      <td>8.000000</td>\n",
              "      <td>13540.000000</td>\n",
              "      <td>1.651359e+06</td>\n",
              "      <td>3.500000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>13.000000</td>\n",
              "      <td>9410.000000</td>\n",
              "      <td>4820.000000</td>\n",
              "      <td>2015.000000</td>\n",
              "      <td>2015.000000</td>\n",
              "      <td>98199.000000</td>\n",
              "      <td>47.777600</td>\n",
              "      <td>-121.315000</td>\n",
              "      <td>6210.000000</td>\n",
              "      <td>871200.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                 id         price  ...  sqft_living15     sqft_lot15\n",
              "count  2.161300e+04  2.161300e+04  ...   21613.000000   21613.000000\n",
              "mean   4.580302e+09  5.401822e+05  ...    1986.552492   12768.455652\n",
              "std    2.876566e+09  3.673622e+05  ...     685.391304   27304.179631\n",
              "min    1.000102e+06  7.500000e+04  ...     399.000000     651.000000\n",
              "25%    2.123049e+09  3.219500e+05  ...    1490.000000    5100.000000\n",
              "50%    3.904930e+09  4.500000e+05  ...    1840.000000    7620.000000\n",
              "75%    7.308900e+09  6.450000e+05  ...    2360.000000   10083.000000\n",
              "max    9.900000e+09  7.700000e+06  ...    6210.000000  871200.000000\n",
              "\n",
              "[8 rows x 20 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# using the corr() to find out values that correlate with each other, especially values that correlate with prices\n",
        "home_data.corr()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 697
        },
        "id": "QaR5OUYtElJN",
        "outputId": "ba357f38-9a5b-4d56-d2e9-231220699be8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>price</th>\n",
              "      <th>bedrooms</th>\n",
              "      <th>bathrooms</th>\n",
              "      <th>sqft_living</th>\n",
              "      <th>sqft_lot</th>\n",
              "      <th>floors</th>\n",
              "      <th>waterfront</th>\n",
              "      <th>view</th>\n",
              "      <th>condition</th>\n",
              "      <th>grade</th>\n",
              "      <th>sqft_above</th>\n",
              "      <th>sqft_basement</th>\n",
              "      <th>yr_built</th>\n",
              "      <th>yr_renovated</th>\n",
              "      <th>zipcode</th>\n",
              "      <th>lat</th>\n",
              "      <th>long</th>\n",
              "      <th>sqft_living15</th>\n",
              "      <th>sqft_lot15</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>id</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.016797</td>\n",
              "      <td>0.001286</td>\n",
              "      <td>0.005160</td>\n",
              "      <td>-0.012258</td>\n",
              "      <td>-0.132109</td>\n",
              "      <td>0.018525</td>\n",
              "      <td>-0.002721</td>\n",
              "      <td>0.011592</td>\n",
              "      <td>-0.023783</td>\n",
              "      <td>0.008130</td>\n",
              "      <td>-0.010842</td>\n",
              "      <td>-0.005151</td>\n",
              "      <td>0.021380</td>\n",
              "      <td>-0.016907</td>\n",
              "      <td>-0.008224</td>\n",
              "      <td>-0.001891</td>\n",
              "      <td>0.020799</td>\n",
              "      <td>-0.002901</td>\n",
              "      <td>-0.138798</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>price</th>\n",
              "      <td>-0.016797</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.308338</td>\n",
              "      <td>0.525134</td>\n",
              "      <td>0.702044</td>\n",
              "      <td>0.089655</td>\n",
              "      <td>0.256786</td>\n",
              "      <td>0.266331</td>\n",
              "      <td>0.397346</td>\n",
              "      <td>0.036392</td>\n",
              "      <td>0.667463</td>\n",
              "      <td>0.605566</td>\n",
              "      <td>0.323837</td>\n",
              "      <td>0.053982</td>\n",
              "      <td>0.126442</td>\n",
              "      <td>-0.053168</td>\n",
              "      <td>0.306919</td>\n",
              "      <td>0.021571</td>\n",
              "      <td>0.585374</td>\n",
              "      <td>0.082456</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>bedrooms</th>\n",
              "      <td>0.001286</td>\n",
              "      <td>0.308338</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.515884</td>\n",
              "      <td>0.576671</td>\n",
              "      <td>0.031703</td>\n",
              "      <td>0.175429</td>\n",
              "      <td>-0.006582</td>\n",
              "      <td>0.079532</td>\n",
              "      <td>0.028472</td>\n",
              "      <td>0.356967</td>\n",
              "      <td>0.477600</td>\n",
              "      <td>0.303093</td>\n",
              "      <td>0.154178</td>\n",
              "      <td>0.018841</td>\n",
              "      <td>-0.152668</td>\n",
              "      <td>-0.008931</td>\n",
              "      <td>0.129473</td>\n",
              "      <td>0.391638</td>\n",
              "      <td>0.029244</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>bathrooms</th>\n",
              "      <td>0.005160</td>\n",
              "      <td>0.525134</td>\n",
              "      <td>0.515884</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.754665</td>\n",
              "      <td>0.087740</td>\n",
              "      <td>0.500653</td>\n",
              "      <td>0.063744</td>\n",
              "      <td>0.187737</td>\n",
              "      <td>-0.124982</td>\n",
              "      <td>0.664983</td>\n",
              "      <td>0.685342</td>\n",
              "      <td>0.283770</td>\n",
              "      <td>0.506019</td>\n",
              "      <td>0.050739</td>\n",
              "      <td>-0.203866</td>\n",
              "      <td>0.024573</td>\n",
              "      <td>0.223042</td>\n",
              "      <td>0.568634</td>\n",
              "      <td>0.087175</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_living</th>\n",
              "      <td>-0.012258</td>\n",
              "      <td>0.702044</td>\n",
              "      <td>0.576671</td>\n",
              "      <td>0.754665</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.172826</td>\n",
              "      <td>0.353949</td>\n",
              "      <td>0.103818</td>\n",
              "      <td>0.284611</td>\n",
              "      <td>-0.058753</td>\n",
              "      <td>0.762704</td>\n",
              "      <td>0.876597</td>\n",
              "      <td>0.435043</td>\n",
              "      <td>0.318049</td>\n",
              "      <td>0.055363</td>\n",
              "      <td>-0.199430</td>\n",
              "      <td>0.052529</td>\n",
              "      <td>0.240223</td>\n",
              "      <td>0.756420</td>\n",
              "      <td>0.183286</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_lot</th>\n",
              "      <td>-0.132109</td>\n",
              "      <td>0.089655</td>\n",
              "      <td>0.031703</td>\n",
              "      <td>0.087740</td>\n",
              "      <td>0.172826</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.005201</td>\n",
              "      <td>0.021604</td>\n",
              "      <td>0.074710</td>\n",
              "      <td>-0.008958</td>\n",
              "      <td>0.113621</td>\n",
              "      <td>0.183512</td>\n",
              "      <td>0.015286</td>\n",
              "      <td>0.053080</td>\n",
              "      <td>0.007644</td>\n",
              "      <td>-0.129574</td>\n",
              "      <td>-0.085683</td>\n",
              "      <td>0.229521</td>\n",
              "      <td>0.144608</td>\n",
              "      <td>0.718557</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>floors</th>\n",
              "      <td>0.018525</td>\n",
              "      <td>0.256786</td>\n",
              "      <td>0.175429</td>\n",
              "      <td>0.500653</td>\n",
              "      <td>0.353949</td>\n",
              "      <td>-0.005201</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.023698</td>\n",
              "      <td>0.029444</td>\n",
              "      <td>-0.263768</td>\n",
              "      <td>0.458183</td>\n",
              "      <td>0.523885</td>\n",
              "      <td>-0.245705</td>\n",
              "      <td>0.489319</td>\n",
              "      <td>0.006338</td>\n",
              "      <td>-0.059121</td>\n",
              "      <td>0.049614</td>\n",
              "      <td>0.125419</td>\n",
              "      <td>0.279885</td>\n",
              "      <td>-0.011269</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>waterfront</th>\n",
              "      <td>-0.002721</td>\n",
              "      <td>0.266331</td>\n",
              "      <td>-0.006582</td>\n",
              "      <td>0.063744</td>\n",
              "      <td>0.103818</td>\n",
              "      <td>0.021604</td>\n",
              "      <td>0.023698</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.401857</td>\n",
              "      <td>0.016653</td>\n",
              "      <td>0.082775</td>\n",
              "      <td>0.072075</td>\n",
              "      <td>0.080588</td>\n",
              "      <td>-0.026161</td>\n",
              "      <td>0.092885</td>\n",
              "      <td>0.030285</td>\n",
              "      <td>-0.014274</td>\n",
              "      <td>-0.041910</td>\n",
              "      <td>0.086463</td>\n",
              "      <td>0.030703</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>view</th>\n",
              "      <td>0.011592</td>\n",
              "      <td>0.397346</td>\n",
              "      <td>0.079532</td>\n",
              "      <td>0.187737</td>\n",
              "      <td>0.284611</td>\n",
              "      <td>0.074710</td>\n",
              "      <td>0.029444</td>\n",
              "      <td>0.401857</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.045990</td>\n",
              "      <td>0.251321</td>\n",
              "      <td>0.167649</td>\n",
              "      <td>0.276947</td>\n",
              "      <td>-0.053440</td>\n",
              "      <td>0.103917</td>\n",
              "      <td>0.084827</td>\n",
              "      <td>0.006157</td>\n",
              "      <td>-0.078400</td>\n",
              "      <td>0.280439</td>\n",
              "      <td>0.072575</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>condition</th>\n",
              "      <td>-0.023783</td>\n",
              "      <td>0.036392</td>\n",
              "      <td>0.028472</td>\n",
              "      <td>-0.124982</td>\n",
              "      <td>-0.058753</td>\n",
              "      <td>-0.008958</td>\n",
              "      <td>-0.263768</td>\n",
              "      <td>0.016653</td>\n",
              "      <td>0.045990</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.144674</td>\n",
              "      <td>-0.158214</td>\n",
              "      <td>0.174105</td>\n",
              "      <td>-0.361417</td>\n",
              "      <td>-0.060618</td>\n",
              "      <td>0.003026</td>\n",
              "      <td>-0.014941</td>\n",
              "      <td>-0.106500</td>\n",
              "      <td>-0.092824</td>\n",
              "      <td>-0.003406</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>grade</th>\n",
              "      <td>0.008130</td>\n",
              "      <td>0.667463</td>\n",
              "      <td>0.356967</td>\n",
              "      <td>0.664983</td>\n",
              "      <td>0.762704</td>\n",
              "      <td>0.113621</td>\n",
              "      <td>0.458183</td>\n",
              "      <td>0.082775</td>\n",
              "      <td>0.251321</td>\n",
              "      <td>-0.144674</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.755923</td>\n",
              "      <td>0.168392</td>\n",
              "      <td>0.446963</td>\n",
              "      <td>0.014414</td>\n",
              "      <td>-0.184862</td>\n",
              "      <td>0.114084</td>\n",
              "      <td>0.198372</td>\n",
              "      <td>0.713202</td>\n",
              "      <td>0.119248</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_above</th>\n",
              "      <td>-0.010842</td>\n",
              "      <td>0.605566</td>\n",
              "      <td>0.477600</td>\n",
              "      <td>0.685342</td>\n",
              "      <td>0.876597</td>\n",
              "      <td>0.183512</td>\n",
              "      <td>0.523885</td>\n",
              "      <td>0.072075</td>\n",
              "      <td>0.167649</td>\n",
              "      <td>-0.158214</td>\n",
              "      <td>0.755923</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.051943</td>\n",
              "      <td>0.423898</td>\n",
              "      <td>0.023285</td>\n",
              "      <td>-0.261190</td>\n",
              "      <td>-0.000816</td>\n",
              "      <td>0.343803</td>\n",
              "      <td>0.731870</td>\n",
              "      <td>0.194050</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_basement</th>\n",
              "      <td>-0.005151</td>\n",
              "      <td>0.323837</td>\n",
              "      <td>0.303093</td>\n",
              "      <td>0.283770</td>\n",
              "      <td>0.435043</td>\n",
              "      <td>0.015286</td>\n",
              "      <td>-0.245705</td>\n",
              "      <td>0.080588</td>\n",
              "      <td>0.276947</td>\n",
              "      <td>0.174105</td>\n",
              "      <td>0.168392</td>\n",
              "      <td>-0.051943</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.133124</td>\n",
              "      <td>0.071323</td>\n",
              "      <td>0.074845</td>\n",
              "      <td>0.110538</td>\n",
              "      <td>-0.144765</td>\n",
              "      <td>0.200355</td>\n",
              "      <td>0.017276</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>yr_built</th>\n",
              "      <td>0.021380</td>\n",
              "      <td>0.053982</td>\n",
              "      <td>0.154178</td>\n",
              "      <td>0.506019</td>\n",
              "      <td>0.318049</td>\n",
              "      <td>0.053080</td>\n",
              "      <td>0.489319</td>\n",
              "      <td>-0.026161</td>\n",
              "      <td>-0.053440</td>\n",
              "      <td>-0.361417</td>\n",
              "      <td>0.446963</td>\n",
              "      <td>0.423898</td>\n",
              "      <td>-0.133124</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.224874</td>\n",
              "      <td>-0.346869</td>\n",
              "      <td>-0.148122</td>\n",
              "      <td>0.409356</td>\n",
              "      <td>0.326229</td>\n",
              "      <td>0.070958</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>yr_renovated</th>\n",
              "      <td>-0.016907</td>\n",
              "      <td>0.126442</td>\n",
              "      <td>0.018841</td>\n",
              "      <td>0.050739</td>\n",
              "      <td>0.055363</td>\n",
              "      <td>0.007644</td>\n",
              "      <td>0.006338</td>\n",
              "      <td>0.092885</td>\n",
              "      <td>0.103917</td>\n",
              "      <td>-0.060618</td>\n",
              "      <td>0.014414</td>\n",
              "      <td>0.023285</td>\n",
              "      <td>0.071323</td>\n",
              "      <td>-0.224874</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.064357</td>\n",
              "      <td>0.029398</td>\n",
              "      <td>-0.068372</td>\n",
              "      <td>-0.002673</td>\n",
              "      <td>0.007854</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>zipcode</th>\n",
              "      <td>-0.008224</td>\n",
              "      <td>-0.053168</td>\n",
              "      <td>-0.152668</td>\n",
              "      <td>-0.203866</td>\n",
              "      <td>-0.199430</td>\n",
              "      <td>-0.129574</td>\n",
              "      <td>-0.059121</td>\n",
              "      <td>0.030285</td>\n",
              "      <td>0.084827</td>\n",
              "      <td>0.003026</td>\n",
              "      <td>-0.184862</td>\n",
              "      <td>-0.261190</td>\n",
              "      <td>0.074845</td>\n",
              "      <td>-0.346869</td>\n",
              "      <td>0.064357</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.267048</td>\n",
              "      <td>-0.564072</td>\n",
              "      <td>-0.279033</td>\n",
              "      <td>-0.147221</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>lat</th>\n",
              "      <td>-0.001891</td>\n",
              "      <td>0.306919</td>\n",
              "      <td>-0.008931</td>\n",
              "      <td>0.024573</td>\n",
              "      <td>0.052529</td>\n",
              "      <td>-0.085683</td>\n",
              "      <td>0.049614</td>\n",
              "      <td>-0.014274</td>\n",
              "      <td>0.006157</td>\n",
              "      <td>-0.014941</td>\n",
              "      <td>0.114084</td>\n",
              "      <td>-0.000816</td>\n",
              "      <td>0.110538</td>\n",
              "      <td>-0.148122</td>\n",
              "      <td>0.029398</td>\n",
              "      <td>0.267048</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.135512</td>\n",
              "      <td>0.048858</td>\n",
              "      <td>-0.086419</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>long</th>\n",
              "      <td>0.020799</td>\n",
              "      <td>0.021571</td>\n",
              "      <td>0.129473</td>\n",
              "      <td>0.223042</td>\n",
              "      <td>0.240223</td>\n",
              "      <td>0.229521</td>\n",
              "      <td>0.125419</td>\n",
              "      <td>-0.041910</td>\n",
              "      <td>-0.078400</td>\n",
              "      <td>-0.106500</td>\n",
              "      <td>0.198372</td>\n",
              "      <td>0.343803</td>\n",
              "      <td>-0.144765</td>\n",
              "      <td>0.409356</td>\n",
              "      <td>-0.068372</td>\n",
              "      <td>-0.564072</td>\n",
              "      <td>-0.135512</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.334605</td>\n",
              "      <td>0.254451</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_living15</th>\n",
              "      <td>-0.002901</td>\n",
              "      <td>0.585374</td>\n",
              "      <td>0.391638</td>\n",
              "      <td>0.568634</td>\n",
              "      <td>0.756420</td>\n",
              "      <td>0.144608</td>\n",
              "      <td>0.279885</td>\n",
              "      <td>0.086463</td>\n",
              "      <td>0.280439</td>\n",
              "      <td>-0.092824</td>\n",
              "      <td>0.713202</td>\n",
              "      <td>0.731870</td>\n",
              "      <td>0.200355</td>\n",
              "      <td>0.326229</td>\n",
              "      <td>-0.002673</td>\n",
              "      <td>-0.279033</td>\n",
              "      <td>0.048858</td>\n",
              "      <td>0.334605</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.183192</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sqft_lot15</th>\n",
              "      <td>-0.138798</td>\n",
              "      <td>0.082456</td>\n",
              "      <td>0.029244</td>\n",
              "      <td>0.087175</td>\n",
              "      <td>0.183286</td>\n",
              "      <td>0.718557</td>\n",
              "      <td>-0.011269</td>\n",
              "      <td>0.030703</td>\n",
              "      <td>0.072575</td>\n",
              "      <td>-0.003406</td>\n",
              "      <td>0.119248</td>\n",
              "      <td>0.194050</td>\n",
              "      <td>0.017276</td>\n",
              "      <td>0.070958</td>\n",
              "      <td>0.007854</td>\n",
              "      <td>-0.147221</td>\n",
              "      <td>-0.086419</td>\n",
              "      <td>0.254451</td>\n",
              "      <td>0.183192</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                     id     price  ...  sqft_living15  sqft_lot15\n",
              "id             1.000000 -0.016797  ...      -0.002901   -0.138798\n",
              "price         -0.016797  1.000000  ...       0.585374    0.082456\n",
              "bedrooms       0.001286  0.308338  ...       0.391638    0.029244\n",
              "bathrooms      0.005160  0.525134  ...       0.568634    0.087175\n",
              "sqft_living   -0.012258  0.702044  ...       0.756420    0.183286\n",
              "sqft_lot      -0.132109  0.089655  ...       0.144608    0.718557\n",
              "floors         0.018525  0.256786  ...       0.279885   -0.011269\n",
              "waterfront    -0.002721  0.266331  ...       0.086463    0.030703\n",
              "view           0.011592  0.397346  ...       0.280439    0.072575\n",
              "condition     -0.023783  0.036392  ...      -0.092824   -0.003406\n",
              "grade          0.008130  0.667463  ...       0.713202    0.119248\n",
              "sqft_above    -0.010842  0.605566  ...       0.731870    0.194050\n",
              "sqft_basement -0.005151  0.323837  ...       0.200355    0.017276\n",
              "yr_built       0.021380  0.053982  ...       0.326229    0.070958\n",
              "yr_renovated  -0.016907  0.126442  ...      -0.002673    0.007854\n",
              "zipcode       -0.008224 -0.053168  ...      -0.279033   -0.147221\n",
              "lat           -0.001891  0.306919  ...       0.048858   -0.086419\n",
              "long           0.020799  0.021571  ...       0.334605    0.254451\n",
              "sqft_living15 -0.002901  0.585374  ...       1.000000    0.183192\n",
              "sqft_lot15    -0.138798  0.082456  ...       0.183192    1.000000\n",
              "\n",
              "[20 rows x 20 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# using scatter plot to visualize the relationship between price and sqft_living\n",
        "plt.scatter(home_data[\"price\"], home_data[\"sqft_living\"], color=\"r\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "571EWRdqE24a",
        "outputId": "b429ebef-76c8-4f1f-e489-f95a76c78efa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f5ed7ee6f50>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "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",
      "source": [
        "# using scatter plot to visualize the relationship between price and bathrooms\n",
        "plt.scatter(home_data[\"price\"], home_data[\"bathrooms\"], color=\"r\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "lAscjbdBFccQ",
        "outputId": "2b9afb7e-d792-4195-9c93-4a789a969ee5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f5ed7964710>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "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",
      "source": [
        "# using scatter plot to visualize the relationship between price and grade\n",
        "plt.scatter(home_data[\"price\"], home_data[\"grade\"], color=\"r\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "nnjgHjArFxVd",
        "outputId": "5b70a915-e2f2-4e5d-aa42-8dffc5e177de"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f861a0e39d0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "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",
      "source": [
        "# need to be sure i have no missing values\n",
        "home_data.isnull().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f-Jd48oiK0LS",
        "outputId": "1de17e84-dd0b-4b18-d78e-18d76ebdcd23"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "id               0\n",
              "date             0\n",
              "price            0\n",
              "bedrooms         0\n",
              "bathrooms        0\n",
              "sqft_living      0\n",
              "sqft_lot         0\n",
              "floors           0\n",
              "waterfront       0\n",
              "view             0\n",
              "condition        0\n",
              "grade            0\n",
              "sqft_above       0\n",
              "sqft_basement    0\n",
              "yr_built         0\n",
              "yr_renovated     0\n",
              "zipcode          0\n",
              "lat              0\n",
              "long             0\n",
              "sqft_living15    0\n",
              "sqft_lot15       0\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "home_data.info()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xoKnch7UQSJh",
        "outputId": "498738c3-dc1c-49a7-c8bb-fb7fd5e826bc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 21613 entries, 0 to 21612\n",
            "Data columns (total 21 columns):\n",
            " #   Column         Non-Null Count  Dtype  \n",
            "---  ------         --------------  -----  \n",
            " 0   id             21613 non-null  int64  \n",
            " 1   date           21613 non-null  object \n",
            " 2   price          21613 non-null  float64\n",
            " 3   bedrooms       21613 non-null  int64  \n",
            " 4   bathrooms      21613 non-null  float64\n",
            " 5   sqft_living    21613 non-null  int64  \n",
            " 6   sqft_lot       21613 non-null  int64  \n",
            " 7   floors         21613 non-null  float64\n",
            " 8   waterfront     21613 non-null  int64  \n",
            " 9   view           21613 non-null  int64  \n",
            " 10  condition      21613 non-null  int64  \n",
            " 11  grade          21613 non-null  int64  \n",
            " 12  sqft_above     21613 non-null  int64  \n",
            " 13  sqft_basement  21613 non-null  int64  \n",
            " 14  yr_built       21613 non-null  int64  \n",
            " 15  yr_renovated   21613 non-null  int64  \n",
            " 16  zipcode        21613 non-null  int64  \n",
            " 17  lat            21613 non-null  float64\n",
            " 18  long           21613 non-null  float64\n",
            " 19  sqft_living15  21613 non-null  int64  \n",
            " 20  sqft_lot15     21613 non-null  int64  \n",
            "dtypes: float64(5), int64(15), object(1)\n",
            "memory usage: 3.5+ MB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# time to train my data \n",
        "# first import libraries\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn import metrics\n",
        "\n",
        "\n",
        "# input input/feature(x) and output/target(y)\n",
        "# dropping the data(price,id,date) leaves all other column to be trained as inputted data\n",
        "x= home_data.drop(['price','id','date'], axis=1)\n",
        "y= home_data['price']\n",
        "\n",
        "# using the train_test_split method to train my x and y\n",
        "x_train,x_test,y_train,y_test= train_test_split(x,y,test_size=0.20,random_state=40)\n",
        "lg_reg = LinearRegression()\n",
        "\n",
        "# fit my data and test the data\n",
        "lg_reg.fit(x_train,y_train)\n",
        "predicted= lg_reg.predict(x_test)\n",
        "\n",
        "print(\"MSE\", mean_squared_error(y_test,predicted))\n",
        "print(\"R_squared\", metrics.r2_score(y_test,predicted))\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "10YZIIgFITkx",
        "outputId": "722ab334-f99f-4e35-8120-66ddc091c773"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE 37915305038.86295\n",
            "R_squared 0.698989620237105\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# using the score() to find out the Linear regression model score\n",
        "lg_reg.score(x_test,y_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gxP8TilpS6uP",
        "outputId": "2382b91b-faa5-47da-9f14-025270509d1a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.698989620237105"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear Regression model score is 70%\n"
      ],
      "metadata": {
        "id": "dOQYs67nVORX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sns.regplot(home_data[\"sqft_living\"], home_data[\"price\"])"
      ],
      "metadata": {
        "id": "U4m-x4jjQXEf",
        "outputId": "1271de48-d15d-462a-c8aa-b112c2973e2a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f5ebc277a10>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "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",
      "source": [
        "lg_reg.coef_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zmZWS-ASTNkz",
        "outputId": "14889047-eae8-4e2a-e7a5-ca3cc9cd1a79"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-3.74326945e+04,  4.30778079e+04,  1.10846450e+02,  1.13273748e-01,\n",
              "        5.70052968e+03,  6.07244174e+05,  5.38928855e+04,  2.57288732e+04,\n",
              "        9.55276590e+04,  7.14550483e+01,  3.93914013e+01, -2.63400896e+03,\n",
              "        2.25048072e+01, -5.94979292e+02,  6.04119613e+05, -2.16480007e+05,\n",
              "        2.33019635e+01, -3.66055155e-01])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "BnyQrRq1QW4x"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# MUlti_linear Regression. Another value have been assigned to x\n",
        "x= home_data[[\"sqft_living\", \"bathrooms\"]]\n",
        "y= home_data['price']\n",
        "\n",
        "x_train,x_test,y_train,y_test= train_test_split(x,y,test_size=0.20,random_state=40)\n",
        "\n",
        "lg_= LinearRegression()\n",
        "lg_.fit(x_train,y_train)\n",
        "predicted = lg_.predict(x_test)\n",
        "\n",
        "print(\"MSE\",mean_squared_error(y_test,predicted))\n",
        "print(\"R_squared\", metrics.r2_score(y_test, predicted))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rPTYq6yMWk_N",
        "outputId": "27cd95a2-baf9-4fb3-fa30-1eab8b7a1aaa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE 62515982341.22817\n",
            "R_squared 0.503684341547688\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Multi_linear regression score\n",
        "lg_.score(x_test,y_test)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yPv9KYLoYNle",
        "outputId": "50b21b7f-c02f-42f5-c410-e0b0f0525152"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.503684341547688"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Multi-Linear Regression score 50%\n"
      ],
      "metadata": {
        "id": "8UQpgiwAVJkb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lg_.coef_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "npH3W_OIYzJS",
        "outputId": "459ad0c1-77ae-4137-b62e-0d428af60bbd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  285.29168351, -4218.80882791])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lg_.intercept_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tHOIhQsqY7ep",
        "outputId": "a94192b9-6048-4c35-9691-33f24aabc527"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-44304.42134521296"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn import metrics\n",
        "x= home_data[['sqft_living', 'bathrooms']]\n",
        "y= home_data['price']\n",
        "\n",
        "x_train,x_test,y_train,y_test= train_test_split(x,y,test_size=0.2,random_state=40)\n",
        "\n",
        "lin_reg= LinearRegression()\n",
        "reg= PolynomialFeatures(degree=4)\n",
        "\n",
        "x_train_fit= reg.fit_transform(x_train)\n",
        "lin_reg.fit(x_train,y_train)\n",
        "\n",
        "x_test_fit= reg.fit_transform(x_test)\n",
        "predicted = lin_reg.predict(x_test)\n",
        "\n",
        "print(\"MSE\", metrics.mean_squared_error(y_test, predicted))\n",
        "print(\"R_squared\", metrics.r2_score(y_test, predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S5Fmc5WWZN4l",
        "outputId": "07aacc97-29f3-497f-e086-0eb5d5543956"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE 62515982341.22817\n",
            "R_squared 0.503684341547688\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lin_reg.score(x_test,y_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Se2tWIaSemSw",
        "outputId": "ff4507a1-ea18-459f-9db2-ad991d2ac5ea"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5445800081187551"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Linear Regression model has a higher score (70%), compared to the Multi-Linear Regression and Polynominal Regression."
      ],
      "metadata": {
        "id": "NONrUxh_fC0f"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x= home_data[\"bathrooms\"].values.reshape(-1, 1)\n",
        "y= home_data['price']\n",
        "\n",
        "poly= PolynomialFeatures(degree=2)\n",
        "x_poly= poly.fit_transform(x)\n",
        "poly.fit(x_poly,y)\n",
        "lg= LinearRegression()\n",
        "lg.fit(x_poly,y)\n",
        "\n",
        "plt.scatter(x,y,color=\"r\")\n",
        "plt.title(\"Polynomial Regression\")\n",
        "plt.ylabel(\"price\")\n",
        "plt.xlabel(\"bathrooms\")\n",
        "plt.plot(x,lg.predict(poly.fit_transform(x)),color=\"k\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "XdXcL-PIin6Z",
        "outputId": "a1f6de8b-2196-4465-e4f3-75e10bfc2ccc"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f5eb6e95450>]"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}