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 only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why?

Short answer

HWY is the best predictor in the single variable study for predicting fuel consumption of the city.

Step-by-step solution

Given information

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

State the criteria for best predictor variables

The p-value determines the significance of the variable in regression analysis. The R-squared measure is the coefficient of determination measure, which measures the sum of squares explained by the regression line.The R-squared adjusted measures the accuracy while considering the count of independent variables in the model. A good-fit model gives a better prediction.

The optimum level of each measure defines the best predictor in the regression model.

Identify the best predictor model

From the provided three models with one predictor variable, the model with predictor HWY (highway fuel consumption) has the:

• smallest P-value is 0.000
• highest measures of both\({R^2}\)and adjusted\({R^2}\)value which is 0.924 and 0.920 respectively.

This implies that HWY is the best predictor of the city’s fuel consumption variable.