In the backward selection model, our step 0, as shown in the following diagram, includes all the variables that have been included as independent variables. We have calculated the parameter estimates, the F values, and tested for statistical significance of the variable:

The Eating_out variable has the highest p-value in the Figure 5.17 statistics for removal section. In the next section of the output, the Eating_out variable is dropped from the model. New parameter estimates, F values, and test of significance values are generated for the model, as shown in the following diagram:

In Figure 5.18, we can see that Grocery has the highest p-value before being dropped out of the model. As you can see, we started with a full selection of variables but in the backward selection process, we are continuously eliminating the insignificant variables. This process continues until we reach step 6, which generates the summary of the backward selection model:

In the final step, as shown in Figure 5.19, we can see the variables Entertainment, Education, Clothing_and_shopping, and Spend_save_quarterly_ratio have been retained in the model. Incidentally, these are the same variables retained by the forward selection model: Let us see if the maximize R model produces a different set of statistically significant variables for predicting CPI.