House_Sales_in_King_Count_USA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\"  />\n",
    "    </a>\n",
    "</p>\n",
    "\n",
    "<h1 align=center><font size = 5>Data Analysis with Python</font></h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# House Sales in King County, USA\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset contains house sale prices for King County, which includes Seattle. It includes homes sold between May 2014 and May 2015.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Variable      | Description                                                                                                 |\n",
    "| ------------- | ----------------------------------------------------------------------------------------------------------- |\n",
    "| id            | A notation for a house                                                                                      |\n",
    "| date          | Date house was sold                                                                                         |\n",
    "| price         | Price is prediction target                                                                                  |\n",
    "| bedrooms      | Number of bedrooms                                                                                          |\n",
    "| bathrooms     | Number of bathrooms                                                                                         |\n",
    "| sqft_living   | Square footage of the home                                                                                  |\n",
    "| sqft_lot      | Square footage of the lot                                                                                   |\n",
    "| floors        | Total floors (levels) in house                                                                              |\n",
    "| waterfront    | House which has a view to a waterfront                                                                      |\n",
    "| view          | Has been viewed                                                                                             |\n",
    "| condition     | How good the condition is overall                                                                           |\n",
    "| grade         | overall grade given to the housing unit, based on King County grading system                                |\n",
    "| sqft_above    | Square footage of house apart from basement                                                                 |\n",
    "| sqft_basement | Square footage of the basement                                                                              |\n",
    "| yr_built      | Built Year                                                                                                  |\n",
    "| yr_renovated  | Year when house was renovated                                                                               |\n",
    "| zipcode       | Zip code                                                                                                    |\n",
    "| lat           | Latitude coordinate                                                                                         |\n",
    "| long          | Longitude coordinate                                                                                        |\n",
    "| sqft_living15 | Living room area in 2015(implies-- some renovations) This might or might not have affected the lotsize area |\n",
    "| sqft_lot15    | LotSize area in 2015(implies-- some renovations)                                                            |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will require the following libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler,PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1: Importing Data Sets\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the csv:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "file_name='https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/FinalModule_Coursera/data/kc_house_data_NaN.csv'\n",
    "df=pd.read_csv(file_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the method <code>head</code> to display the first 5 columns of the dataframe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</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>...</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>0</td>\n",
       "      <td>7129300520</td>\n",
       "      <td>20141013T000000</td>\n",
       "      <td>221900.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6414100192</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>538000.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>400</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>5631500400</td>\n",
       "      <td>20150225T000000</td>\n",
       "      <td>180000.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</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>3</td>\n",
       "      <td>2487200875</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>604000.0</td>\n",
       "      <td>4.0</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>...</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>4</td>\n",
       "      <td>1954400510</td>\n",
       "      <td>20150218T000000</td>\n",
       "      <td>510000.0</td>\n",
       "      <td>3.0</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>...</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",
       "<p>5 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0          id             date     price  bedrooms  bathrooms  \\\n",
       "0           0  7129300520  20141013T000000  221900.0       3.0       1.00   \n",
       "1           1  6414100192  20141209T000000  538000.0       3.0       2.25   \n",
       "2           2  5631500400  20150225T000000  180000.0       2.0       1.00   \n",
       "3           3  2487200875  20141209T000000  604000.0       4.0       3.00   \n",
       "4           4  1954400510  20150218T000000  510000.0       3.0       2.00   \n",
       "\n",
       "   sqft_living  sqft_lot  floors  waterfront  ...  grade  sqft_above  \\\n",
       "0         1180      5650     1.0           0  ...      7        1180   \n",
       "1         2570      7242     2.0           0  ...      7        2170   \n",
       "2          770     10000     1.0           0  ...      6         770   \n",
       "3         1960      5000     1.0           0  ...      7        1050   \n",
       "4         1680      8080     1.0           0  ...      8        1680   \n",
       "\n",
       "   sqft_basement  yr_built  yr_renovated  zipcode      lat     long  \\\n",
       "0              0      1955             0    98178  47.5112 -122.257   \n",
       "1            400      1951          1991    98125  47.7210 -122.319   \n",
       "2              0      1933             0    98028  47.7379 -122.233   \n",
       "3            910      1965             0    98136  47.5208 -122.393   \n",
       "4              0      1987             0    98074  47.6168 -122.045   \n",
       "\n",
       "   sqft_living15  sqft_lot15  \n",
       "0           1340        5650  \n",
       "1           1690        7639  \n",
       "2           2720        8062  \n",
       "3           1360        5000  \n",
       "4           1800        7503  \n",
       "\n",
       "[5 rows x 22 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We display the data types of each column using the function dtypes, then take a screenshot and submit it, include your code in the image.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0         int64\n",
       "id                 int64\n",
       "date              object\n",
       "price            float64\n",
       "bedrooms         float64\n",
       "bathrooms        float64\n",
       "sqft_living        int64\n",
       "sqft_lot           int64\n",
       "floors           float64\n",
       "waterfront         int64\n",
       "view               int64\n",
       "condition          int64\n",
       "grade              int64\n",
       "sqft_above         int64\n",
       "sqft_basement      int64\n",
       "yr_built           int64\n",
       "yr_renovated       int64\n",
       "zipcode            int64\n",
       "lat              float64\n",
       "long             float64\n",
       "sqft_living15      int64\n",
       "sqft_lot15         int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the method describe to obtain a statistical summary of the dataframe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "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",
       "        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>Unnamed: 0</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>...</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>21613.00000</td>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>21600.000000</td>\n",
       "      <td>21603.000000</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>...</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>10806.00000</td>\n",
       "      <td>4.580302e+09</td>\n",
       "      <td>5.400881e+05</td>\n",
       "      <td>3.372870</td>\n",
       "      <td>2.115736</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>...</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>6239.28002</td>\n",
       "      <td>2.876566e+09</td>\n",
       "      <td>3.671272e+05</td>\n",
       "      <td>0.926657</td>\n",
       "      <td>0.768996</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>...</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>0.00000</td>\n",
       "      <td>1.000102e+06</td>\n",
       "      <td>7.500000e+04</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.500000</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>...</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>5403.00000</td>\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>...</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>10806.00000</td>\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>...</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>16209.00000</td>\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>...</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>21612.00000</td>\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>...</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",
       "<p>8 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Unnamed: 0            id         price      bedrooms     bathrooms  \\\n",
       "count  21613.00000  2.161300e+04  2.161300e+04  21600.000000  21603.000000   \n",
       "mean   10806.00000  4.580302e+09  5.400881e+05      3.372870      2.115736   \n",
       "std     6239.28002  2.876566e+09  3.671272e+05      0.926657      0.768996   \n",
       "min        0.00000  1.000102e+06  7.500000e+04      1.000000      0.500000   \n",
       "25%     5403.00000  2.123049e+09  3.219500e+05      3.000000      1.750000   \n",
       "50%    10806.00000  3.904930e+09  4.500000e+05      3.000000      2.250000   \n",
       "75%    16209.00000  7.308900e+09  6.450000e+05      4.000000      2.500000   \n",
       "max    21612.00000  9.900000e+09  7.700000e+06     33.000000      8.000000   \n",
       "\n",
       "        sqft_living      sqft_lot        floors    waterfront          view  \\\n",
       "count  21613.000000  2.161300e+04  21613.000000  21613.000000  21613.000000   \n",
       "mean    2079.899736  1.510697e+04      1.494309      0.007542      0.234303   \n",
       "std      918.440897  4.142051e+04      0.539989      0.086517      0.766318   \n",
       "min      290.000000  5.200000e+02      1.000000      0.000000      0.000000   \n",
       "25%     1427.000000  5.040000e+03      1.000000      0.000000      0.000000   \n",
       "50%     1910.000000  7.618000e+03      1.500000      0.000000      0.000000   \n",
       "75%     2550.000000  1.068800e+04      2.000000      0.000000      0.000000   \n",
       "max    13540.000000  1.651359e+06      3.500000      1.000000      4.000000   \n",
       "\n",
       "       ...         grade    sqft_above  sqft_basement      yr_built  \\\n",
       "count  ...  21613.000000  21613.000000   21613.000000  21613.000000   \n",
       "mean   ...      7.656873   1788.390691     291.509045   1971.005136   \n",
       "std    ...      1.175459    828.090978     442.575043     29.373411   \n",
       "min    ...      1.000000    290.000000       0.000000   1900.000000   \n",
       "25%    ...      7.000000   1190.000000       0.000000   1951.000000   \n",
       "50%    ...      7.000000   1560.000000       0.000000   1975.000000   \n",
       "75%    ...      8.000000   2210.000000     560.000000   1997.000000   \n",
       "max    ...     13.000000   9410.000000    4820.000000   2015.000000   \n",
       "\n",
       "       yr_renovated       zipcode           lat          long  sqft_living15  \\\n",
       "count  21613.000000  21613.000000  21613.000000  21613.000000   21613.000000   \n",
       "mean      84.402258  98077.939805     47.560053   -122.213896    1986.552492   \n",
       "std      401.679240     53.505026      0.138564      0.140828     685.391304   \n",
       "min        0.000000  98001.000000     47.155900   -122.519000     399.000000   \n",
       "25%        0.000000  98033.000000     47.471000   -122.328000    1490.000000   \n",
       "50%        0.000000  98065.000000     47.571800   -122.230000    1840.000000   \n",
       "75%        0.000000  98118.000000     47.678000   -122.125000    2360.000000   \n",
       "max     2015.000000  98199.000000     47.777600   -121.315000    6210.000000   \n",
       "\n",
       "          sqft_lot15  \n",
       "count   21613.000000  \n",
       "mean    12768.455652  \n",
       "std     27304.179631  \n",
       "min       651.000000  \n",
       "25%      5100.000000  \n",
       "50%      7620.000000  \n",
       "75%     10083.000000  \n",
       "max    871200.000000  \n",
       "\n",
       "[8 rows x 21 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 2: Data Wrangling\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We drop the columns <code>\"id\"</code>  and <code>\"Unnamed: 0\"</code> from axis 1 using the method <code>drop()</code>, then use the method <code>describe()</code> to obtain a statistical summary of the data. Take a screenshot and submit it, make sure the <code>inplace</code> parameter is set to <code>True</code>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>21600.000000</td>\n",
       "      <td>21603.000000</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>5.400881e+05</td>\n",
       "      <td>3.372870</td>\n",
       "      <td>2.115736</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>3.671272e+05</td>\n",
       "      <td>0.926657</td>\n",
       "      <td>0.768996</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>7.500000e+04</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.500000</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>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>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>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>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": [
       "              price      bedrooms     bathrooms   sqft_living      sqft_lot  \\\n",
       "count  2.161300e+04  21600.000000  21603.000000  21613.000000  2.161300e+04   \n",
       "mean   5.400881e+05      3.372870      2.115736   2079.899736  1.510697e+04   \n",
       "std    3.671272e+05      0.926657      0.768996    918.440897  4.142051e+04   \n",
       "min    7.500000e+04      1.000000      0.500000    290.000000  5.200000e+02   \n",
       "25%    3.219500e+05      3.000000      1.750000   1427.000000  5.040000e+03   \n",
       "50%    4.500000e+05      3.000000      2.250000   1910.000000  7.618000e+03   \n",
       "75%    6.450000e+05      4.000000      2.500000   2550.000000  1.068800e+04   \n",
       "max    7.700000e+06     33.000000      8.000000  13540.000000  1.651359e+06   \n",
       "\n",
       "             floors    waterfront          view     condition         grade  \\\n",
       "count  21613.000000  21613.000000  21613.000000  21613.000000  21613.000000   \n",
       "mean       1.494309      0.007542      0.234303      3.409430      7.656873   \n",
       "std        0.539989      0.086517      0.766318      0.650743      1.175459   \n",
       "min        1.000000      0.000000      0.000000      1.000000      1.000000   \n",
       "25%        1.000000      0.000000      0.000000      3.000000      7.000000   \n",
       "50%        1.500000      0.000000      0.000000      3.000000      7.000000   \n",
       "75%        2.000000      0.000000      0.000000      4.000000      8.000000   \n",
       "max        3.500000      1.000000      4.000000      5.000000     13.000000   \n",
       "\n",
       "         sqft_above  sqft_basement      yr_built  yr_renovated       zipcode  \\\n",
       "count  21613.000000   21613.000000  21613.000000  21613.000000  21613.000000   \n",
       "mean    1788.390691     291.509045   1971.005136     84.402258  98077.939805   \n",
       "std      828.090978     442.575043     29.373411    401.679240     53.505026   \n",
       "min      290.000000       0.000000   1900.000000      0.000000  98001.000000   \n",
       "25%     1190.000000       0.000000   1951.000000      0.000000  98033.000000   \n",
       "50%     1560.000000       0.000000   1975.000000      0.000000  98065.000000   \n",
       "75%     2210.000000     560.000000   1997.000000      0.000000  98118.000000   \n",
       "max     9410.000000    4820.000000   2015.000000   2015.000000  98199.000000   \n",
       "\n",
       "                lat          long  sqft_living15     sqft_lot15  \n",
       "count  21613.000000  21613.000000   21613.000000   21613.000000  \n",
       "mean      47.560053   -122.213896    1986.552492   12768.455652  \n",
       "std        0.138564      0.140828     685.391304   27304.179631  \n",
       "min       47.155900   -122.519000     399.000000     651.000000  \n",
       "25%       47.471000   -122.328000    1490.000000    5100.000000  \n",
       "50%       47.571800   -122.230000    1840.000000    7620.000000  \n",
       "75%       47.678000   -122.125000    2360.000000   10083.000000  \n",
       "max       47.777600   -121.315000    6210.000000  871200.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop(['Unnamed: 0','id'], axis=1, inplace=True)\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see we have missing values for the columns <code> bedrooms</code>  and <code> bathrooms </code>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of NaN values for the column bedrooms : 13\n",
      "number of NaN values for the column bathrooms : 10\n"
     ]
    }
   ],
   "source": [
    "print(\"number of NaN values for the column bedrooms :\", df['bedrooms'].isnull().sum())\n",
    "print(\"number of NaN values for the column bathrooms :\", df['bathrooms'].isnull().sum())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can replace the missing values of the column <code>'bedrooms'</code> with the mean of the column  <code>'bedrooms' </code> using the method <code>replace()</code>. Don't forget to set the <code>inplace</code> parameter to <code>True</code>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean=df['bedrooms'].mean()\n",
    "df['bedrooms'].replace(np.nan,mean, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also replace the missing values of the column <code>'bathrooms'</code> with the mean of the column  <code>'bathrooms' </code> using the method <code>replace()</code>. Don't forget to set the <code> inplace </code>  parameter top <code> True </code>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean=df['bathrooms'].mean()\n",
    "df['bathrooms'].replace(np.nan,mean, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of NaN values for the column bedrooms : 0\n",
      "number of NaN values for the column bathrooms : 0\n"
     ]
    }
   ],
   "source": [
    "print(\"number of NaN values for the column bedrooms :\", df['bedrooms'].isnull().sum())\n",
    "print(\"number of NaN values for the column bathrooms :\", df['bathrooms'].isnull().sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3: Exploratory Data Analysis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the method <code>value_counts</code> to count the number of houses with unique floor values, use the method <code>.to_frame()</code> to convert it to a dataframe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>floors</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>10680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>8241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.5</th>\n",
       "      <td>1910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.5</th>\n",
       "      <td>161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.5</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     floors\n",
       "1.0   10680\n",
       "2.0    8241\n",
       "1.5    1910\n",
       "3.0     613\n",
       "2.5     161\n",
       "3.5       8"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['floors'].value_counts().to_frame()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the function <code>boxplot</code> in the seaborn library  to  determine whether houses with a waterfront view or without a waterfront view have more price outliers.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='waterfront', ylabel='price'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x='waterfront',y='price', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the function <code>regplot</code>  in the seaborn library  to  determine if the feature <code>sqft_above</code> is negatively or positively correlated with price.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='sqft_above', ylabel='price'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x='sqft_above', y='price', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the Pandas method <code>corr()</code>  to find the feature other than price that is most correlated with price.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "zipcode         -0.053203\n",
       "long             0.021626\n",
       "condition        0.036362\n",
       "yr_built         0.054012\n",
       "sqft_lot15       0.082447\n",
       "sqft_lot         0.089661\n",
       "yr_renovated     0.126434\n",
       "floors           0.256794\n",
       "waterfront       0.266369\n",
       "lat              0.307003\n",
       "bedrooms         0.308797\n",
       "sqft_basement    0.323816\n",
       "view             0.397293\n",
       "bathrooms        0.525738\n",
       "sqft_living15    0.585379\n",
       "sqft_above       0.605567\n",
       "grade            0.667434\n",
       "sqft_living      0.702035\n",
       "price            1.000000\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()['price'].sort_values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 4: Model Development\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can Fit a linear regression model using the  longitude feature <code>'long'</code> and  caculate the R^2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00046769430149007363"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[['long']]\n",
    "Y = df['price']\n",
    "lm = LinearRegression()\n",
    "lm.fit(X,Y)\n",
    "lm.score(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit a linear regression model to predict the <code>'price'</code> using the feature <code>'sqft_living'</code> then calculate the R^2. Take a screenshot of your code and the value of the R^2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4928532179037931"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_6 = df[['sqft_living']]\n",
    "Y = df['price']\n",
    "lm6 = LinearRegression()\n",
    "lm6.fit(X_6, Y)\n",
    "lm6.score(X_6, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit a linear regression model to predict the <code>'price'</code> using the list of features:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "features =[\"floors\", \"waterfront\",\"lat\" ,\"bedrooms\" ,\"sqft_basement\" ,\"view\" ,\"bathrooms\",\"sqft_living15\",\"sqft_above\",\"grade\",\"sqft_living\"]     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then calculate the R^2. Take a screenshot of your code.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6576951666037502"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_7 = df[features]\n",
    "Y = df[['price']]\n",
    "lm7 = LinearRegression()\n",
    "lm7.fit(X_7, Y)\n",
    "lm7.score(X_7, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create a list of tuples, the first element in the tuple contains the name of the estimator:\n",
    "\n",
    "<code>'scale'</code>\n",
    "\n",
    "<code>'polynomial'</code>\n",
    "\n",
    "<code>'model'</code>\n",
    "\n",
    "The second element in the tuple  contains the model constructor\n",
    "\n",
    "<code>StandardScaler()</code>\n",
    "\n",
    "<code>PolynomialFeatures(include_bias=False)</code>\n",
    "\n",
    "<code>LinearRegression()</code>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()),('polynomial', PolynomialFeatures(include_bias=False)),('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the list to create a pipeline object to predict the 'price', fit the object using the features in the list <code>features</code>, and calculate the R^2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7513404101380663"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = Pipeline(Input)\n",
    "pipe\n",
    "\n",
    "X_8 = df[features]\n",
    "Y = df[['price']]\n",
    "\n",
    "X_8 = X_8.astype(float)\n",
    "\n",
    "pipe.fit(X_8, Y)\n",
    "\n",
    "pipe.score(X_8, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 5: Model Evaluation and Refinement\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the necessary modules:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will split the data into training and testing sets:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples: 3242\n",
      "number of training samples: 18371\n"
     ]
    }
   ],
   "source": [
    "features =[\"floors\", \"waterfront\",\"lat\" ,\"bedrooms\" ,\"sqft_basement\" ,\"view\" ,\"bathrooms\",\"sqft_living15\",\"sqft_above\",\"grade\",\"sqft_living\"]    \n",
    "X = df[features]\n",
    "Y = df['price']\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(X, Y, test_size=0.15, random_state=1)\n",
    "\n",
    "\n",
    "print(\"number of test samples:\", x_test.shape[0])\n",
    "print(\"number of training samples:\",x_train.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create and fit a Ridge regression object using the training data, set the regularization parameter to 0.1, and calculate the R^2 using the test data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6478759163939112"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RidgeModel = Ridge(alpha=0.1)\n",
    "RidgeModel.fit(x_train, y_train)\n",
    "RidgeModel.score(x_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We perform a second order polynomial transform on both the training data and testing data. Create and fit a Ridge regression object using the training data, set the regularisation parameter to 0.1, and calculate the R^2 utilising the test data provided. Take a screenshot of your code and the R^2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7002744259992868"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr = PolynomialFeatures(degree=2)\n",
    "\n",
    "x_train_pr = pr.fit_transform(x_train)\n",
    "x_test_pr = pr.fit_transform(x_test)\n",
    "\n",
    "RidgeModel = Ridge(alpha=0.1)\n",
    "RidgeModel.fit(x_train_pr, y_train)\n",
    "RidgeModel.score(x_test_pr, y_test)"
   ]
  }
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