# https://www.kaggle.com/yasserh/housing-prices-dataset

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

#Modelling 
import statsmodels.formula.api as smf

# df_mat = pd.read_csv('/kaggle/input/student-performance/student-mat.csv', delimiter=';')
data = pd.read_csv('C:/Users/Stevie/Data_Analysis/Regressions/Housing.csv')

Data Cleaning

No missing values (na)

data.isna().sum()

price               0
area                0
bedrooms            0
bathrooms           0
stories             0
mainroad            0
guestroom           0
basement            0
hotwaterheating     0
airconditioning     0
parking             0
prefarea            0
furnishingstatus    0
dtype: int64

data.head()

	price	area	bedrooms	bathrooms	stories	mainroad	guestroom	basement	hotwaterheating	airconditioning	parking	prefarea	furnishingstatus
0	13300000	7420	4	2	3	yes	no	no	no	yes	2	yes	furnished
1	12250000	8960	4	4	4	yes	no	no	no	yes	3	no	furnished
2	12250000	9960	3	2	2	yes	no	yes	no	no	2	yes	semi-furnished
3	12215000	7500	4	2	2	yes	no	yes	no	yes	3	yes	furnished
4	11410000	7420	4	1	2	yes	yes	yes	no	yes	2	no	furnished

Distribution of hoses with and without basic amenities (hotwater/airconditioning/basement)

Plot

f = plt.figure(figsize=(14,6))

ax = f.add_subplot(121)
sns.distplot(data['price'],bins=50)
plt.title("Distribution of housing prices")

ax = f.add_subplot(122)
sns.distplot(np.log10(data['price']),bins=50,color='red')
plt.title("Distribution of $log$ housing prices")

C:\Users\Stevie\anaconda3\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\Stevie\anaconda3\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

Text(0.5, 1.0, 'Distribution of $log$ housing prices')

Distribution of the variable seesm to be normally distribution. I will be using this as the dependent variable in my regression analysis

Distribution of housing prices given their number of parking slots

plt.figure(figsize=(14,8))
plt.hist((data[data['parking']==1].price,data[data['parking']==2].price,data[data['parking']==3].price),
        color=['#3f7ea6',"#023059",'#1b6f1b'])

plt.legend(['1 Parking slot','2 Parking slots','3 Parking slots'])
plt.xlabel("Housing Price")
plt.ylabel('Number of obs')
plt.title('Distribution of housing prices given the number of parking slots')

Text(0.5, 1.0, 'Distribution of housing prices given the number of parking slots')

Categorical variables 

columns = ['mainroad','guestroom','basement','airconditioning','hotwaterheating','prefarea','furnishingstatus']
for i in columns: 
    plt.figure(figsize=(3,1))
    data.groupby(i)[i].count().plot(kind="barh")
    plt.title(i)

data.head()

	price	area	bedrooms	bathrooms	stories	mainroad	guestroom	basement	hotwaterheating	airconditioning	parking	prefarea	furnishingstatus
0	13300000	7420	4	2	3	yes	no	no	no	yes	2	yes	furnished
1	12250000	8960	4	4	4	yes	no	no	no	yes	3	no	furnished
2	12250000	9960	3	2	2	yes	no	yes	no	no	2	yes	semi-furnished
3	12215000	7500	4	2	2	yes	no	yes	no	yes	3	yes	furnished
4	11410000	7420	4	1	2	yes	yes	yes	no	yes	2	no	furnished

---

Data Processing

#no = 0
# yes = 1

c = ['mainroad','guestroom','basement','hotwaterheating','airconditioning','prefarea']

for i in c:
    data.loc[data[i]=='yes',i] = 1
    data.loc[data[i]=='no',i] = 0

Dummy variables

df_encode = pd.get_dummies(data,
                           prefix= '',
                           prefix_sep='',
                           columns= ['furnishingstatus'],
                           drop_first=True, #remove if you want 0 to be a true value
                           dtype='int8')

Correlation Heatmap

plt.figure(figsize=(14,8))
sns.heatmap(df_encode.corr(),annot=True)
plt.title('Correlation Heatmap')

Text(0.5, 1.0, 'Correlation Heatmap')

df_encode = df_encode.rename(columns={"semi-furnished":'semifurnished'}) #renaming

---

Data Modelling OLS

df_encode

	price	area	bedrooms	bathrooms	stories	mainroad	guestroom	basement	hotwaterheating	airconditioning	parking	prefarea	semifurnished	unfurnished
0	13300000	7420	4	2	3	1	0	0	0	1	2	1	0	0
1	12250000	8960	4	4	4	1	0	0	0	1	3	0	0	0
2	12250000	9960	3	2	2	1	0	1	0	0	2	1	1	0
3	12215000	7500	4	2	2	1	0	1	0	1	3	1	0	0
4	11410000	7420	4	1	2	1	1	1	0	1	2	0	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
540	1820000	3000	2	1	1	1	0	1	0	0	2	0	0	1
541	1767150	2400	3	1	1	0	0	0	0	0	0	0	1	0
542	1750000	3620	2	1	1	1	0	0	0	0	0	0	0	1
543	1750000	2910	3	1	1	0	0	0	0	0	0	0	0	0
544	1750000	3850	3	1	2	1	0	0	0	0	0	0	0	1

545 rows × 14 columns

sns.distplot(data['area'])

C:\Users\Stevie\anaconda3\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

<AxesSubplot:xlabel='area', ylabel='Density'>

import statsmodels.formula.api as smf
df_encode['price'] = np.log(df_encode['price'])

mod = smf.ols(formula='price~unfurnished+stories+parking+bedrooms+bathrooms+mainroad',data=df_encode)
res = mod.fit()
print(res.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.499
Model:                            OLS   Adj. R-squared:                  0.493
Method:                 Least Squares   F-statistic:                     89.14
Date:                Thu, 20 Jan 2022   Prob (F-statistic):           2.14e-77
Time:                        15:58:28   Log-Likelihood:                -46.057
No. Observations:                 545   AIC:                             106.1
Df Residuals:                     538   BIC:                             136.2
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
Intercept        14.4642      0.059    243.658      0.000      14.348      14.581
mainroad[T.1]     0.2370      0.034      6.999      0.000       0.170       0.304
unfurnished      -0.1591      0.025     -6.393      0.000      -0.208      -0.110
stories           0.0930      0.015      6.274      0.000       0.064       0.122
parking           0.0924      0.014      6.669      0.000       0.065       0.120
bedrooms          0.0594      0.018      3.347      0.001       0.025       0.094
bathrooms         0.2200      0.025      8.721      0.000       0.170       0.270
==============================================================================
Omnibus:                        2.796   Durbin-Watson:                   0.978
Prob(Omnibus):                  0.247   Jarque-Bera (JB):                2.611
Skew:                          -0.130   Prob(JB):                        0.271
Kurtosis:                       3.218   Cond. No.                         23.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

I have excluded area because i believe it is highly correlated with all other amenities. Adding it to the regression model might cause multicollinearities

Results suggests that all my variables except for the intercept are significant at the 95% level. R^2 suggests that the model explains 50% of the data variation.

Variables used:

• Price (dependent)
• mainroad (0/1 dummy)
• unfurnished (0/1 dummy)
• stories (continous)
• parking (continous)
• bedroom (continous)
• bathrooms (continous)

sns.scatterplot(x=res.fittedvalues,y=res.resid)
plt.title('Check for Heteroskedasticity:\n Fitted vs resid')
plt.xlabel('fitted')
plt.ylabel('resid')

Text(0, 0.5, 'resid')

Residuals seems to be scattered randomly when fitted value increases. No signs of heteroskedasticity

Prediction

Parameters

res.params

Intercept        14.464198
mainroad[T.1]     0.236998
unfurnished      -0.159127
stories           0.093023
parking           0.092431
bedrooms          0.059434
bathrooms         0.219987
dtype: float64

plt.figure(figsize=(14,6))
plt.plot(res.predict())
plt.plot(df_encode['price'])
plt.legend(['OLS','Price Distribution'],fontsize=13)
plt.title('Price Fluctuation and OLS prediction')

Text(0.5, 1.0, 'Price Fluctuation and OLS prediction')

import statsmodels.api as sm

fig = plt.figure(figsize=(14, 10))
sm.graphics.plot_ccpr_grid(res,fig=fig)
fig.tight_layout(pad=2.0)

Alternative for single linear regression and plots

Price ~ Area (OLS)

import statsmodels.api as sm
olsmod = sm.OLS(data['price'], data['area'])
olsres = olsmod.fit()
print(olsres.summary())

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                  price   R-squared (uncentered):                   0.872
Model:                            OLS   Adj. R-squared (uncentered):              0.872
Method:                 Least Squares   F-statistic:                              3717.
Date:                Thu, 20 Jan 2022   Prob (F-statistic):                   2.64e-245
Time:                        17:26:02   Log-Likelihood:                         -8632.0
No. Observations:                 545   AIC:                                  1.727e+04
Df Residuals:                     544   BIC:                                  1.727e+04
Df Model:                           1                                                  
Covariance Type:            nonrobust                                                  
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
area         855.7099     14.036     60.967      0.000     828.139     883.281
==============================================================================
Omnibus:                       45.221   Durbin-Watson:                   1.440
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              117.437
Skew:                          -0.411   Prob(JB):                     3.15e-26
Kurtosis:                       5.120   Cond. No.                         1.00
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.

from statsmodels.graphics.regressionplots import abline_plot

plt.figure(figsize=(14,6))
sns.regplot(x='area',y='price',data=data)
plt.plot(data['area'],olsres.predict(data['area']),color='r')
plt.legend(['sns','OLS'],fontsize=10)

<matplotlib.legend.Legend at 0x258c84835e0>