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).

If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?

Short answer

The model with predictors HWY and WT are the best 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.

Discuss the measures stated in the table

The three measures stated in the table are:

• P-value: to decide the significance of the model
• \({R^2}:\)to indicate the accuracy of the model and the fitness of the regression model
• Adjusted \({R^2}:\)to measure the accuracy of the model by evaluating the counts of independent variables

Identify the best model

From the table, the two variable model that has the smallest P-value (0.0000), t highest\({R^2}\)and adjusted\({R^2}\)values (0.942 and 0.935 respectively) correspond to the WT/HWY predictor variable.

This implies that the HWY and WT predictor models are the best to predict the city’s fuel consumption.