House Price Prediction

Second

Let's start by importing libraries we will be using.

%matplotlib inline

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression

plt.style.use('ggplot')

Collecting Data

For this simple case study, we are going to use the California Housing Prices dataset from the StatLib repository; you can download this dataset from here.

df = pd.read_csv('./data/data.csv')

# let's quickly check the meta-data
df.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

df.head()

	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

As we can see from the above, the dataset contains 9 numerical variables and one categorical variable. Each row in the dataset represent a district in CA.

Summary Statistics

For numerical variables, Tukey's five-number summary statistics (minimum, first quartile, median, third quartile, maximum) can provide quick information about the dataset.

df.describe()

	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

For categorical variables, we can simply check the count of each category.

df['ocean_proximity'].value_counts()

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

Histograms

df.hist(bins=50, figsize=(20, 15))

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA2A13EB8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA74A1DD8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA74D42B0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA74FA7F0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA7521D68>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA7552320>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA7577898>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA759FE48>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001DEA759FE80>]],
      dtype=object)

Visualization

df.plot(kind="scatter",
       x="longitude", 
       y="latitude",
       alpha=0.1)

<matplotlib.axes._subplots.AxesSubplot at 0xfe59668>

df.plot(kind="scatter", x="longitude", y="latitude", alpha=0.4,
        s=df["population"]/100, 
        label="population", figsize=(10,7),
        c="median_house_value", 
        cmap=plt.get_cmap("jet"), 
        colorbar=True,
        sharex=False)
plt.legend()
plt.tight_layout(pad=0.1)
plt.savefig('00_scatter_prices.png')

from matplotlib.image import imread

ca_img = imread('http://www.cs.uga.edu/~jwlee/images/00_california.png')

df.plot(kind="scatter", x="longitude", y="latitude", figsize=(10,7),
        s=df['population']/100, label="Population",
        c="median_house_value", cmap=plt.get_cmap("jet"),
        colorbar=True, alpha=0.4)
plt.imshow(ca_img, 
           extent=[-124.55, -113.80, 32.45, 42.05], 
           alpha=0.5)

plt.ylabel("Latitude", fontsize=14)
plt.xlabel("Longitude", fontsize=14)

prices = df["median_house_value"]
tick_values = np.linspace(prices.min(), prices.max(), 11)
#cbar = plt.colorbar()
cbar_ax = plt.gcf().get_axes()[1]
cbar_ax.set_yticklabels(["$%dk"%(round(v/1000)) for v in tick_values], 
                        fontsize=14)
#cbar_ax.set_label('Median House Value', fontsize=16)

plt.legend(fontsize=16)
plt.tight_layout(pad=0.1)
plt.savefig("00_ca_housing_prices.png")
plt.show()

Data Exploration

Feature-Target Relationship

from pandas.plotting import scatter_matrix
attrs = ['median_house_value', 'median_income', 'housing_median_age', 
         'total_rooms']
scatter_matrix(df[attrs],
               alpha=0.1, figsize=(10, 10), diagonal='kde')

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x000001F25979BC50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25AB05CC0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A000320>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A02C8D0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A05BE80>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A093470>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A0C2A20>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A0F4FD0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A103080>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25A164B70>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25AB73160>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25ABA2710>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x000001F25ABD6CC0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25B2B12B0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25B2E3860>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x000001F25B316E10>]],
      dtype=object)

Correlation Analysis

corr_mat = df[attrs].corr()
corr_mat

	median_house_value	median_income	housing_median_age	total_rooms
median_house_value	1.000000	0.688075	0.105623	0.134153
median_income	0.688075	1.000000	-0.119034	0.198050
housing_median_age	0.105623	-0.119034	1.000000	-0.361262
total_rooms	0.134153	0.198050	-0.361262	1.000000

corr_mat['median_house_value'].sort_values(ascending=False)

median_house_value    1.000000
median_income         0.688075
total_rooms           0.134153
housing_median_age    0.105623
Name: median_house_value, dtype: float64

corr_mat = df.corr()

fig, ax = plt.subplots(figsize=(10, 10))

cmap = sns.diverging_palette(220, 10, as_cmap=True)
sns.heatmap(corr_mat, cmap=cmap, linewidth=.5, square=True, annot=True)

<matplotlib.axes._subplots.AxesSubplot at 0x14de5f60>

Data Processing

• handling missing values
• Transforming categorical attributes
• feature scaling

rows_with_missing_values = df[df.isnull().any(axis=1)].head()
rows_with_missing_values

	longitude	latitude	housing_median_age	total_rooms	total_bedrooms	population	households	median_income	median_house_value	ocean_proximity
290	-122.16	37.77	47.0	1256.0	NaN	570.0	218.0	4.3750	161900.0	NEAR BAY
341	-122.17	37.75	38.0	992.0	NaN	732.0	259.0	1.6196	85100.0	NEAR BAY
538	-122.28	37.78	29.0	5154.0	NaN	3741.0	1273.0	2.5762	173400.0	NEAR BAY
563	-122.24	37.75	45.0	891.0	NaN	384.0	146.0	4.9489	247100.0	NEAR BAY
696	-122.10	37.69	41.0	746.0	NaN	387.0	161.0	3.9063	178400.0	NEAR BAY

from sklearn.impute import SimpleImputer

imputer = SimpleImputer(strategy="mean")
housing_num = df.drop('ocean_proximity', axis=1)

imputer.fit(housing_num)
X= imputer.transform(housing_num)

housing_tr = pd.DataFrame(X, columns=housing_num.columns,
                          index=list(df.index.values))
housing_tr.loc[rows_with_missing_values.index.values]

	longitude	latitude	housing_median_age	total_rooms	total_bedrooms	population	households	median_income	median_house_value
290	-122.16	37.77	47.0	1256.0	537.870553	570.0	218.0	4.3750	161900.0
341	-122.17	37.75	38.0	992.0	537.870553	732.0	259.0	1.6196	85100.0
538	-122.28	37.78	29.0	5154.0	537.870553	3741.0	1273.0	2.5762	173400.0
563	-122.24	37.75	45.0	891.0	537.870553	384.0	146.0	4.9489	247100.0
696	-122.10	37.69	41.0	746.0	537.870553	387.0	161.0	3.9063	178400.0

Handling categorical variables

from sklearn.preprocessing import OneHotEncoder

housing_cat = df[['ocean_proximity']]
cat_encoder = OneHotEncoder(sparse=False)                                      # Instantiating the OneHot Encoder class.
housing_cat_onehot = cat_encoder.fit_transform(housing_cat)                    # Encoding the Text.
print(housing_cat_onehot[:10])                                                 # Converting into numpy arrays.
print("\n")
print(cat_encoder.categories_) 

[[0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0.]]


[array(['<1H OCEAN', 'INLAND', 'ISLAND', 'NEAR BAY', 'NEAR OCEAN'],
      dtype=object)]

Data Normalization

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

#@ Pipeline for Numerical attributes:
num_pipeline = Pipeline([
    ("imputer", SimpleImputer(strategy="mean")),
    ("std_scaler", StandardScaler())    
])

housing_num_tr = num_pipeline.fit_transform(housing_num)
housing_num_tr.shape

(20640, 9)

from sklearn.compose import ColumnTransformer

num_attrs = list(housing_num)                          # List of numerical attributes.
cat_attrs = ["ocean_proximity"]                        # List of categorical attributes. 
pipeline = ColumnTransformer([
    ("num", num_pipeline, num_attrs),
    ("cat", OneHotEncoder(), cat_attrs)
])

housing_data = pipeline.fit_transform(df)
housing_label = df["median_house_value"].copy()
housing_data[:5]

array([[-1.32783522,  1.05254828,  0.98214266, -0.8048191 , -0.97522785,
        -0.9744286 , -0.97703285,  2.34476576,  2.12963148,  0.        ,
         0.        ,  0.        ,  1.        ,  0.        ],
       [-1.32284391,  1.04318455, -0.60701891,  2.0458901 ,  1.3550882 ,
         0.86143887,  1.66996103,  2.33223796,  1.31415614,  0.        ,
         0.        ,  0.        ,  1.        ,  0.        ],
       [-1.33282653,  1.03850269,  1.85618152, -0.53574589, -0.82973217,
        -0.82077735, -0.84363692,  1.7826994 ,  1.25869341,  0.        ,
         0.        ,  0.        ,  1.        ,  0.        ],
       [-1.33781784,  1.03850269,  1.85618152, -0.62421459, -0.72239929,
        -0.76602806, -0.73378144,  0.93296751,  1.16510007,  0.        ,
         0.        ,  0.        ,  1.        ,  0.        ],
       [-1.33781784,  1.03850269,  1.85618152, -0.46240395, -0.61506641,
        -0.75984669, -0.62915718, -0.012881  ,  1.17289952,  0.        ,
         0.        ,  0.        ,  1.        ,  0.        ]])

Splitting Data into train and test

#df_tr = pd.get_dummies(df, columns=['ocean_proximity'], drop_first=True)
#df_tr.head()

X_train, X_test, Y_train, Y_test  = train_test_split(housing_data, housing_label, test_size=0.3, random_state=10)
print(X_train.shape)
print(X_test.shape)
print(Y_train.shape)
print(Y_test.shape)

(14448, 14)
(6192, 14)
(14448,)
(6192,)

Linear regression

# Create an object lm for the LinearRegression model
lm = LinearRegression()
# Fit the model on the training data
lm.fit(X_train, Y_train)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,
         normalize=False)

# regression coefficients
lm.coef_

array([ 8.12986216e-11,  1.68671119e-10,  2.15467161e-11,  3.88705838e-11,
       -8.99805034e-12, -2.16932722e-11,  3.18490569e-11, -3.68252413e-11,
        1.15392820e+05, -3.19482215e-11,  4.19977728e-11,  5.19945705e-14,
        8.58398092e-12, -2.92190990e-11])

# predict
Y_pred = lm.predict(X_test)
mse = (Y_pred - Y_test).mean()
print(f"MSE={mse}")

MSE=415.0572620847688

Decision Trees

from sklearn.tree import DecisionTreeRegressor
from sklearn.metrics import mean_squared_error, mean_absolute_error

tree_reg = DecisionTreeRegressor()                                   # Instantiating the Model.
tree_reg.fit(X_train, Y_train)
housing_predictions = tree_reg.predict(X_test)
tree_mse = mean_squared_error(Y_test, housing_predictions)
tree_rmse = np.sqrt(tree_mse)
print(tree_rmse) 

95.35395776254865

data = {'alg': ['LinReg', 'DecTree', 'RF'],
       'RMSE': [68628.198198489219, 71436.9531067, 52789.3237327]}

df

	alg	RMSE
0	LinReg	68628.198198
1	DecTree	71436.953107
2	RF	52789.323733

df.plot(kind='bar', x="alg", y="RMSE")

<matplotlib.axes._subplots.AxesSubplot at 0x1f2597e8550>