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).

A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?

Short answer

The best predicted value of the city fuel consumption is 26.3 mi/gal.

Step-by-step solution

Given information

The table represents the model with different predictor variables along with the respective P-values,\({R^2}\), Adjusted\({R^2}\)and the regression equations.

A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal.

State the best regression equation

The city fuel consumption is predicted using seven different models as stated in the table. With reference to exercise 11, the best regression equation is:

\(CITY = - 3.15 + 0.819\;HWY\), as it has maximum value for R-squared and adjusted R-squared measure and there is no significant increase in the measure with the additional variable in the study.

Compute the best predicted value of city fuel consumption

The best predicted value of city fuel consumption is given as,

\(\begin{array}{c}{\rm{CITY}} = - 3.15 + 0.819\left( {36} \right)\\ = 26.334\end{array}\)

Thus, the best predicted value of city fuel consumption is 26.3 mi/gal.

State if the predicted value is a good estimate and accurate

A predicted value is a good estimate as the model chosen for prediction has a high value of R-squared and adjusted R-squared measurement.

Thus, the predicted value is likely to be a good estimate because of lower P-value (0.0000) and optimal adjusted\({R^2}\)value (0.920).

The predicted value may not be accurate as the number of observations taken for prediction is only 21, which is relatively low.