Multiple Linear Regression Analysis for Philippines’ Revenue

This study case is a simplified methodology to deal with the problem and data described in the article "Modelling the Philippines’ Revenue Collection Performance: A Study Using Multiple Linear Regression Analysis" and can be seen at:  

https://ijrpr.com/uploads/V3ISSUE11/IJRPR8001.pdf

To build the linear regression model the dataset has five independent variables: inflation rate, forex rate, import value, export value, and stock price index. These variables can be used to predict the Philippines’ revenue value.

Extracting data statistics

Since the data set had been cleaned, it is time to extract statistics to better understand how to model the multiple linear regression. The first step is to compute the Pearson correlation between variables.

pearsoncorr = df2.corr(method='pearson')

pearsoncorr

The Pearson correlation could be visualized using a heat map graphic.

# import required libraries

import seaborn as sns

# Displaying dataframe as an heatmap

# with diverging colourmap as RdYlGn

sns.heatmap(pearsoncorr, cmap ='RdYlGn', linewidths = 0.30, annot = True);

A dispersion graphic is another way to visualize patterns of correlation between independent and dependent variables as done in the next commands.

import seaborn as sns

X = df2[list(df2.columns)]

sns.pairplot(X);

And define the columns that will be the independent variables of the model.

# X 5 predictor variables

x = df2[['Inflation Rate(x1)',

       'Forex Rate Average (x2)',

       'Import (FOB Value in Million USD) (x3)',

       'Export (FOB Value in Million USD) (x4)',

       'Stock Price Index (x5)']]

x

Another possibility is to select only the columns that showed  higher values of Pearson correlation or dispersion graphic linear pattern, i.e., variables x3 and x5,

 Now it is possible to build a multiple linear model with all variables and only the selected variables and print a detailed report about it.

# Obtain multiple linear regression using statsmodels

import statsmodels.api as sm

# Employing multiple linear regression and return its results.

def get_model(x, y):

  xm = sm.add_constant(x) # adding a constant

  model = sm.OLS(y, xm).fit()

  return model, xm

# Printing a report about the model.

def print_model(model, name='None'):

  summary = model.summary()

  print('--------------------------------------')

  print(name,'model')

  print(summary)

  print('--------------------------------------')

# Multiple linear regression using statsmodels

model_revenue, xm_import = get_model(x, y_revenue)

print_model(model_revenue,'Revenue - All five')

model_revenue_selected, xm_import_selected = get_model(x_selected, y_revenue)

print_model(model_revenue_selected,'Revenue - x3 and x5')

Finally, it is possible to use both models to predict the dependent variable and use graphics to verify the quality of the model's prediction.

import matplotlib.pyplot as plt

def model_predict(model, xm):

   y_hat = model.predict(xm)

   return y_hat

def draw_model(model, y, yname, y_hat):

  xp = list(range(1,len(x)+1))

  plt.plot(xp,y,'ob',label='Data')

  plt.plot(xp,y,'-r')

  plt.plot(xp,y_hat,'--g',label='Prediction')

  plt.title('Prediction on ' + str(yname))

  plt.xlabel('Time')

  plt.ylabel(yname)

  plt.legend()

  plt.grid()

  plt.show()

# Predict the values used to build the model with all coefficients.

y_hat = model_predict(model_revenue, xm_import)

#print(y_hat)

# Drawing to compare data x prediction in score data.

draw_model(model_revenue, y_revenue, 'Revenue', y_hat)

# Predict the values used to build the model with x3 and x5 coefficients.

y_hat_selected = model_predict(model_revenue_selected, xm_import_selected)

#print(y_hat_selected)

# Drawing to compare data x prediction in score data.

draw_model(model_revenue_selected, y_revenue, 'Selected Revenue', y_hat_selected)