CA_house_price_prediction


California house price prediction

Load the data and explore it


In [4]:
import pandas as pd
housing = pd.read_csv(r"E:\GIS_Data\file_formats\CSV\housing.csv")
housing.head()


Out[4]:
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value ocean_proximity
0 -122.23 37.88 41.0 880.0 129.0 322.0 126.0 8.3252 452600.0 NEAR BAY
1 -122.22 37.86 21.0 7099.0 1106.0 2401.0 1138.0 8.3014 358500.0 NEAR BAY
2 -122.24 37.85 52.0 1467.0 190.0 496.0 177.0 7.2574 352100.0 NEAR BAY
3 -122.25 37.85 52.0 1274.0 235.0 558.0 219.0 5.6431 341300.0 NEAR BAY
4 -122.25 37.85 52.0 1627.0 280.0 565.0 259.0 3.8462 342200.0 NEAR BAY

In [5]:
housing.info()


<class 'pandas.core.frame.DataFrame'>
RangeIndex: 20640 entries, 0 to 20639
Data columns (total 10 columns):
longitude             20640 non-null float64
latitude              20640 non-null float64
housing_median_age    20640 non-null float64
total_rooms           20640 non-null float64
total_bedrooms        20433 non-null float64
population            20640 non-null float64
households            20640 non-null float64
median_income         20640 non-null float64
median_house_value    20640 non-null float64
ocean_proximity       20640 non-null object
dtypes: float64(9), object(1)
memory usage: 1.6+ MB

In [6]:
# find unique values in ocean proximity column
housing.ocean_proximity.value_counts()


Out[6]:
<1H OCEAN     9136
INLAND        6551
NEAR OCEAN    2658
NEAR BAY      2290
ISLAND           5
Name: ocean_proximity, dtype: int64

In [7]:
#describe all numerical rows - basic stats
housing.describe()


Out[7]:
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value
count 20640.000000 20640.000000 20640.000000 20640.000000 20433.000000 20640.000000 20640.000000 20640.000000 20640.000000
mean -119.569704 35.631861 28.639486 2635.763081 537.870553 1425.476744 499.539680 3.870671 206855.816909
std 2.003532 2.135952 12.585558 2181.615252 421.385070 1132.462122 382.329753 1.899822 115395.615874
min -124.350000 32.540000 1.000000 2.000000 1.000000 3.000000 1.000000 0.499900 14999.000000
25% -121.800000 33.930000 18.000000 1447.750000 296.000000 787.000000 280.000000 2.563400 119600.000000
50% -118.490000 34.260000 29.000000 2127.000000 435.000000 1166.000000 409.000000 3.534800 179700.000000
75% -118.010000 37.710000 37.000000 3148.000000 647.000000 1725.000000 605.000000 4.743250 264725.000000
max -114.310000 41.950000 52.000000 39320.000000 6445.000000 35682.000000 6082.000000 15.000100 500001.000000

In [9]:
%matplotlib inline
import matplotlib.pyplot as plt
housing.hist(bins=50, figsize=(20,15))


Out[9]:
array([[<matplotlib.axes._subplots.AxesSubplot object at 0x0000004717640F28>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x00000047179E4F98>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x0000004717D702E8>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x0000004716961588>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x00000047169927F0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x0000004716992358>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x0000004717B7BA58>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x0000004717BEE0F0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x0000004717C4A470>]], dtype=object)

Create a test set


In [10]:
from sklearn.model_selection import train_test_split

In [11]:
train_set, test_set = train_test_split(housing, test_size=0.2, random_state=42)
print(train_set.shape)
print(test_set.shape)


(16512, 10)
(4128, 10)

Do stratified sampling

Assuming median_income is an important predictor, we need to categorize it. It is important to build categories such that there are a sufficient number of data points in each strata, else the stratum's importance is biased. To make sure, we need not too many strata (like it is now with median income) and strata are relatively wide.


In [14]:
# scale the median income down by dividing it by 1.5 and rounding up those which are greater than 5 to 5.0
import numpy as np
housing['income_cat'] = np.ceil(housing['median_income'] / 1.5) #up round to integers

#replace those with values > 5 with 5.0, values < 5 remain as is
housing['income_cat'].where(housing['income_cat'] < 5, 5.0, inplace=True)

In [15]:
housing['income_cat'].hist()


Out[15]:
<matplotlib.axes._subplots.AxesSubplot at 0x471aab0a58>

In [16]:
from sklearn.model_selection import StratifiedShuffleSplit

split = StratifiedShuffleSplit(n_splits=1, test_size=0.2, random_state=42)
for train_index, test_index in split.split(housing, housing['income_cat']):
    strat_train_set = housing.loc[train_index]
    strat_test_set = housing.loc[test_index]

Now remove the income_cat field used for this sampling. We will learn on the median_income data instead


In [27]:
for _temp in (strat_test_set, strat_train_set):
    _temp.drop("income_cat", axis=1, inplace=True)

In [38]:
# Write the train and test data to disk
strat_test_set.to_csv('./housing_strat_test.csv')
strat_train_set.to_csv('./housing_strat_train.csv')

Exploratory data analysis


In [37]:
strat_train_set.plot(kind='scatter', x='longitude', y='latitude', alpha=0.4, s=strat_train_set['population']/100,
                    label='population', figsize=(10,7), color=strat_train_set['median_house_value'], 
                     cmap=plt.get_cmap('jet'), colorbar=True)
plt.legend()


C:\Anaconda3\envs\ml\lib\site-packages\pandas\plotting\_core.py:196: UserWarning: 'color' and 'colormap' cannot be used simultaneously. Using 'color'
  warnings.warn("'color' and 'colormap' cannot be used "
Out[37]:
<matplotlib.legend.Legend at 0x471dd17128>

Do pairwise plot to understand how each feature is correlated to each other


In [50]:
import seaborn as sns
sns.pairplot(data=strat_train_set[['median_house_value','median_income','total_rooms','housing_median_age']])


Out[50]:
<seaborn.axisgrid.PairGrid at 0x471df3cef0>

Focussing on relationship between income and house value


In [51]:
strat_train_set.plot(kind='scatter', x='median_income', y='median_house_value', alpha=0.1)


Out[51]:
<matplotlib.axes._subplots.AxesSubplot at 0x471b8f5cf8>

Creating new features that are meaningful and also useful in prediction

Create the number of rooms per household, bedrooms per household, ratio of bedrooms to the rooms, number of people per household. We do this on the whole dataset, then collect the train and test datasets.


In [52]:
housing['rooms_per_household'] = housing['total_rooms'] / housing['households']
housing['bedrooms_per_household'] = housing['total_bedrooms'] / housing['households']
housing['bedrooms_per_rooms'] = housing['total_bedrooms'] / housing['total_rooms']

In [54]:
corr_matrix = housing.corr()
corr_matrix['median_house_value'].sort_values(ascending=False)


Out[54]:
median_house_value        1.000000
median_income             0.688075
income_cat                0.643892
rooms_per_household       0.151948
total_rooms               0.134153
housing_median_age        0.105623
households                0.065843
total_bedrooms            0.049686
population               -0.024650
longitude                -0.045967
bedrooms_per_household   -0.046739
latitude                 -0.144160
bedrooms_per_rooms       -0.255880
Name: median_house_value, dtype: float64

In [59]:
housing.plot(kind='scatter', x='bedrooms_per_household',y='median_house_value', alpha=0.5)


Out[59]:
<matplotlib.axes._subplots.AxesSubplot at 0x471f178c88>

Prepare data for ML


In [60]:
#create a copy without the house value column
housing = strat_train_set.drop('median_house_value', axis=1)
#create a copy of house value column into a new series, which will be the labeled data
housing_labels = strat_test_set['median_house_value'].copy()

Fill missing values using Imputer - using median values


In [61]:
from sklearn.preprocessing import Imputer
housing_imputer = Imputer(strategy='median')

In [62]:
#drop text columns let Imputer learn
housing_numeric = housing.drop('ocean_proximity', axis=1)
housing_imputer.fit(housing_numeric)
housing_imputer.statistics_


Out[62]:
array([ -118.51  ,    34.26  ,    29.    ,  2119.5   ,   433.    ,
        1164.    ,   408.    ,     3.5409])

In [64]:
_x = housing_imputer.transform(housing_numeric)
housing_filled= pd.DataFrame(_x, columns=housing_numeric.columns)

In [66]:
housing_filled['ocean_proximity'] = housing['ocean_proximity']
housing_filled.head()


Out[66]:
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income ocean_proximity
0 -121.89 37.29 38.0 1568.0 351.0 710.0 339.0 2.7042 NEAR BAY
1 -121.93 37.05 14.0 679.0 108.0 306.0 113.0 6.4214 NEAR BAY
2 -117.20 32.77 31.0 1952.0 471.0 936.0 462.0 2.8621 NEAR BAY
3 -119.61 36.31 25.0 1847.0 371.0 1460.0 353.0 1.8839 NEAR BAY
4 -118.59 34.23 17.0 6592.0 1525.0 4459.0 1463.0 3.0347 NEAR BAY

Transform categorical features to numeric - OneHotEncoder

We can use LabelEncoder of scipy to enumerate the ocean_proximity category. However ML algorithm should not associate higher values as desireable or should not think values 1,2 are closer than values 1,4. So we transform the categories into new columns of booleans using OneHotEncoder.

We can do both enumeration then to booleans using LabelBinarizer


In [ ]: