Chapter 8, Problem 8E

To determine

To find out what fraction of the variability in fuel economy is accounted for by the horsepower.

Answer to Problem 8E

  $75.5\%$ .

Explanation of Solution

It is given in the previous question that, we examined in previous exercise about the relationship between the fuel economy in mpg and horsepower for models of cars. Thus, the analysis produced the regression model for the same:

  $\text{<mover accent="true"><mo>m</mo><mo>^</mo></mover> pg}=46.87-0.084\text{HP}$

And it is also given that the correlation between a car’s horsepower and its fuel economy in mpg is $r=-0.869$ . Thus, the variability in fuel economy is accounted for by the horsepower can be calculated as:

  $\begin{array}{l}{R}^2=r^2\\ $ ={(-0.869)}^2$=0.7552\\ =75.5\%\end{array}$

Thus, $75.5\%$ of the variability in fuel economy is accounted for by the horsepower.