Chapter 10.6, Problem 49E

To determine

If the prediction equation gives a better prediction for car 1 or car 2.

Explanation of Solution

Given information: The prediction equation is,

  $\begin{array}{l}y=-0.13x+37.8\\ x\to \text{ Horse power}\\ \text{y}\to \text{Fuel economy}\text{.}\end{array}$

Car 1 has $135\text{ horse power and average of 19 miles per gallon}\text{.}$

Car 2 has $\text{245 horse power and average of 16 miles per gallon}\text{.}$

Calculations:

The prediction equation is,

  $y=-0.13x+37.8$

Now for car 1 has $135\text{ horse power}$ .

Therefore as per prediction equation,

  $y=-0.13\times 135+37.8=20.25$

But it is given average is $\text{19 miles per gallon}$ .

Therefore deviation is $19-20.25=-1.25$

Now for car 2 has $245\text{ horse power}$ .

Therefore as per prediction equation,

  $y=-0.13\times 245+37.8=5.95$

But it is given average is $\text{16 miles per gallon}$ .

Therefore deviation is $16-5.25=10.75$

Therefore the prediction equation gives a better prediction for car 1.