Regression OLS with Python

Data analysis and coding are part of the skill set of a UX researcher – especially when working with quantitative data. There are so many sources of information to learn from – but in my experience, they are not equally useful, or functional. This is the first Jupyter notebook where I use Python to run some multivariate regression analysis. The data is publicly available so that anyone can follow along.

Data: Taiwan real estate prices https://www.kaggle.com/datasets/smitisinghal/real-estate-dataset

In [44]:

import seaborn as sns
import pandas as pd
csv_file = "C:\\Users\\UXpix\\Downloads\\Real estate.csv"
taiwan_real_estate=pd.read_csv(csv_file)
#print(taiwan_real_estate)

In [45]:

list(taiwan_real_estate)  #list the variables in the dataset. We can see that some of these variables are not relevant

Out[45]:

['No',
 'house age',
 'distance to the nearest MRT station',
 'number of convenience stores',
 'latitude',
 'longitude',
 'house price of unit area']

In [48]:

taiwan_real_estate = taiwan_real_estate.drop(['No', 'latitude', 'longitude'],  axis=1)
list(taiwan_real_estate)

Out[48]:

['house age',
 'distance to the nearest MRT station',
 'number of convenience stores',
 'house price of unit area']

In [49]:

# Import matplotlib.pyplot with alias plt
import matplotlib.pyplot as plt

# Draw the scatter plot
sns.scatterplot(x="distance to the nearest MRT station",
                y="house price of unit area",
                data=taiwan_real_estate)

# Show the plot
plt.show()

No description has been provided for this image

The scatterplot clearly shows that the relationship between price and distance to the closest metro station is non-linear, so we cannot use a linear regression model. One commonly used way of transforming the variables is to use the square root function, which happened to be effective in this case.

In [50]:

import numpy as np   #I imported the numpy library so that I can perform mathematical transformation
taiwan_real_estate['distance_Sqrt'] = np.sqrt(taiwan_real_estate['distance to the nearest MRT station'])
taiwan_real_estate['price_Sqrt'] = np.sqrt(taiwan_real_estate["house price of unit area"])
sns.scatterplot(x="distance_Sqrt", y="price_Sqrt",
                data=taiwan_real_estate)
# Show the plot
plt.show()

In [52]:

sns.regplot    (x="distance_Sqrt",
                y="price_Sqrt",
                data=taiwan_real_estate, 
                ci=95,  #this gives me the 95% confidence interval in the plot 
                scatter_kws={"s": 2}, line_kws={"lw":1, 'linestyle':'--'}) #s means the nodes - how big should they be,
                #whereas line_kws refers to the line - lw - linewidth
                #scatter_kws={'alpha':0.35})       
# Show the plot
plt.show()

In [18]:

from statsmodels.formula.api import ols

sns.regplot (x=”distance_Sqrt”, y=”price_Sqrt”, data=taiwan_real_estate, ).resid plt.show()

In [39]:

mdl_priceSq_vs_distanceSq= ols('price_Sqrt ~ distance_Sqrt', data = taiwan_real_estate)
mdl_priceSq_vs_distanceSq = mdl_priceSq_vs_distanceSq.fit()
print(mdl_priceSq_vs_distanceSq.params)

Intercept        7.557101
distance_Sqrt   -0.052459
dtype: float64

In [56]:

taiwan_real_estate = taiwan_real_estate.rename(columns={'house age': 'house_age', 'number of convenience stores': 'stores'})
list(taiwan_real_estate)

Out[56]:

['house_age',
 'distance to the nearest MRT station',
 'stores',
 'house price of unit area',
 'distance_Sqrt',
 'price_Sqrt']

In [57]:

# import packages and libraries 
import numpy as np 
import pandas as pd 
import matplotlib.pyplot as plt 
import statsmodels.api as sm 
from statsmodels.formula.api import ols 

# fit linear regression model 

linear_model = ols('price_Sqrt ~ house_age + stores + distance_Sqrt + stores*distance_Sqrt + house_age * distance_Sqrt ', 
				data=taiwan_real_estate).fit() 
# display model summary 
print(linear_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:             price_Sqrt   R-squared:                       0.641
Model:                            OLS   Adj. R-squared:                  0.636
Method:                 Least Squares   F-statistic:                     145.5
Date:                Thu, 26 Sep 2024   Prob (F-statistic):           2.35e-88
Time:                        15:17:03   Log-Likelihood:                -422.86
No. Observations:                 414   AIC:                             857.7
Df Residuals:                     408   BIC:                             881.9
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
===========================================================================================
                              coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------------
Intercept                   7.4002      0.169     43.827      0.000       7.068       7.732
house_age                  -0.0227      0.006     -3.817      0.000      -0.034      -0.011
stores                      0.0931      0.024      3.816      0.000       0.045       0.141
distance_Sqrt              -0.0452      0.005     -8.721      0.000      -0.055      -0.035
stores:distance_Sqrt       -0.0014      0.001     -1.379      0.169      -0.003       0.001
house_age:distance_Sqrt     0.0002      0.000      0.785      0.433      -0.000       0.001
==============================================================================
Omnibus:                       96.960   Durbin-Watson:                   2.113
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              908.951
Skew:                           0.690   Prob(JB):                    4.20e-198
Kurtosis:                      10.127   Cond. No.                     3.41e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.41e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

In [58]:

sns.histplot(linear_model.resid);

In [62]:

linear_model = ols('price_Sqrt ~ house_age + stores + distance_Sqrt', 
				data=taiwan_real_estate).fit() 
# display model summary 
print(linear_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:             price_Sqrt   R-squared:                       0.638
Model:                            OLS   Adj. R-squared:                  0.636
Method:                 Least Squares   F-statistic:                     241.1
Date:                Thu, 26 Sep 2024   Prob (F-statistic):           4.01e-90
Time:                        15:23:12   Log-Likelihood:                -424.31
No. Observations:                 414   AIC:                             856.6
Df Residuals:                     410   BIC:                             872.7
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
Intercept         7.3787      0.138     53.643      0.000       7.108       7.649
house_age        -0.0187      0.003     -6.357      0.000      -0.024      -0.013
stores            0.0664      0.015      4.357      0.000       0.036       0.096
distance_Sqrt    -0.0441      0.003    -16.172      0.000      -0.049      -0.039
==============================================================================
Omnibus:                       99.008   Durbin-Watson:                   2.107
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              906.752
Skew:                           0.721   Prob(JB):                    1.26e-197
Kurtosis:                      10.105   Cond. No.                         154.
==============================================================================

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

In [67]:

taiwan_RE_core_varr = taiwan_real_estate[['house_age', 'stores', 'distance_Sqrt', 'price_Sqrt']]
list(taiwan_RE_core_varr)

Out[67]:

['house_age', 'stores', 'distance_Sqrt', 'price_Sqrt']

# Plotting correlation heatmap import seaborn as sb import matplotlib.pyplot as mp dataplot = sb.heatmap(taiwan_RE_core_varr.corr(numeric_only=True), cmap=”YlGnBu”, annot=True) # Displaying heatmap mp.show()

In [71]:

import seaborn as sb
import matplotlib.pyplot as mp
dataplot=sb.heatmap(taiwan_RE_core_varr.corr(numeric_only=True), cmap='YlGnBu', annot = True)
mp.show()

In [ ]:

Features	List	Tuple	Dictionary	Set	Series (pandas)	Dataframes (pandas)
Ideal for	Sequential, mutable data	Sequential, immutable data	Mapping data	Removing duplicates, set operations	Time series, single variable analysis	Multi-variable analysis, data manipulation
Main Use case	Storing ordered collections	Immutable sequences	Key-value pairs	Unique elements	Single column data	Tabular data
Data type	Any	Any	Any (for values)	Immutable types only	Homogeneous	Heterogeneous (by column)
Ordered	Yes	Yes	Yes	No	Yes	Yes
Mutable*	Yes	No	Yes	Yes	Yes	Yes
Access by	Index	Index	Key	N/A	Index or label	Row/column index or label
Allows duplicates	Yes	Yes	No	No	Yes	Yes

Tag: Python

Python Data structures

Standard Linear Regression with Python