Question

In Exercises 9–12, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 20 “Car Measurements” in Appendix B. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal).

Which regression equation is best for predicting city fuel consumption? Why?

Short answer

The best regression equation is \({\rm{CITY}} = - 3.15 + 0.819{\rm{HWY}}\)to predict the city fuel consumption.

Step-by-step solution

Given information

The table representing the predictor variables, P-value, \({R^2}\) , Adjusted \({R^2}\)and the regression equations are provided.

Criteria for selecting the best model

The model with the highest measure of R-square and adjusted R-square is a good fit. Also, the number of predictors in the model should not be large to avoid overfitting. Thus, a two-predictor model is better if there is a significant increase in the measures of R-squared measure from the one-predictor model.

Determine the regression equation for the best model

It is alwaysbetter to use one predictor variable instead of twoin a regression equation.

It can be observed that all models have a P-value of 0.0000, which indicates a significant model.

The highest adjusted\({R^2}\)value in one predictor model is 0.920 for the HWY predictor variable. As the WT or DISP variable is added in the analysis, the adjusted\({R^2}\)measure increases to 0.935 and 0.928, which is not significant increase.

Therefore, the best predictor variable to predict the city’s fuel consumption is HWY, and the best regression equation is \({\rm{CITY}} = - 3.15 + 0.819{\rm{HWY}}\)