For this model, 75 months of data from January 2012 to March 2018 was available. From this, only data up until September 2017 was used for modeling. Data from October 2017 to March 2018 was used as a hold-out sample to validate the forecasts generated. Regression modeling was done as part of the effort to build a multivariate model. To refer to details about pros and cons of regression models and other details, please refer to Chapter 2, Forecasting Stock Prices and Portfolio Decisions Using Time Series.

The modelers built three types of regression models: forward selection, backward selection, and maximizing R. The forward selection model starts with the intercept and then finds the best variable that serves as a predictor. It then continues to add other variables until the specified selection criteria is met. The backward selection model starts with the full model; that is, all the independent variables as predictors. It keeps on removing variables deemed not important enough. The maximizing R model, as the name suggests, tries to maximize R² on the introduction of each variable in the model (for details on the R² metric, please refer to Chapter 2, Forecasting Stock Prices and Portfolio Decisions using Time Series, which introduces regression as a concept). The model starts by having a single variable with the maximum R². After the second variable is added, the model analyzes whether adding one variable and dropping one from the existing selection would increase R². This process continues while adding the third, fourth, fifth, and so on variables until the model runs out of independent variables. There is a regression type which is called stepwise regression. At times, some people confuse stepwise regression with maximizing R. In stepwise regression, the variables are added and removed at each step of the regression. However, the dropping of the worst performing variable is done before looking at the alternative variables that can be added to the model to improve the performance.

The following code is for modeling and validating a dataset:

Data Model; 
Set Inflation; 
; 
If Month gt "30Sep2017"d then do; 
CPI=.; 
End; 
Run; 
 

The CPI value in the current dataset has been set to null for the period October 17 to March 18, as we are interested in generating forecasts for this period based on the regression model.

In this multivariate regression code, three models are compared:

Proc Reg Data=Model Plots=(Criteria SBC); 
   Id Month; 
   /*Forward selection*/ 
   Model CPI = Furniture_Home_Improvement Travel_including_Leisure            Eating_out Entertainment Grocery Education                Communication Clothing_and_shopping  
Spend_save_quaterly_ratio 
         / Selection=Forward Details=All; 
    
/*Backward selection*/    
Model CPI = Furniture_Home_Improvement Travel_including_Leisure            Eating_out Entertainment Grocery Education                Communication Clothing_and_shopping  
Spend_save_quaterly_ratio 
         / Selection=Backward Details=All; 
 
   /*Maxr*/ 
   Model CPI = Furniture_Home_Improvement Travel_including_Leisure            Eating_out Entertainment Grocery Education                Communication Clothing_and_shopping  
Spend_save_quaterly_ratio 
         / Selection=Maxr Details=All; 
Run;