The initial regression model given in this chapter was Price = 24,765 – 0.1725 (Mileage).
a. Give a practical explanation of the coefficient, b1 = 0.1725, in the context of the Cars data.
b. The coefficient, b1 = 0.1725, is a fairly small number. However, the p-value for the corresponding hypothesis test caused us to reject H0: b1 = 0. How could such a small value cause us to reject the null hypothesis?
c. The p-value caused us to conclude that mileage is important in predicting the retail price. However, the R2 value seemed to indicate that the regression model was not very useful in estimating the retail price. These results may originally appear somewhat contradictory. Explain how these statistics are measuring different aspects of the same regression model, and thus the results do not really contradict each other.