Chapter 3.2, Problem 37E

(a)

To determine

To find: The slope of the line

Answer to Problem 37E

The slope is b = 1.109

Explanation of Solution

Given:

Regression line = $4.62+1.109$ (city mpg)

Calculation:

On comparing our equation to general equation of regression we get, the slope is: b = 1.109

This tells us that the highway mpg is predicted to go up by 1.109 mpg for each added city mpg.

Conclusion:

Hence, the slope is: b = 1.109.

(b)

To determine

To find: The intercept and explain why the interpret value is not statistically meaningful

Answer to Problem 37E

The intercept is: a = 4.62

Explanation of Solution

Calculation:

On comparing our equation to general equation of regression we get, the intercept is: a = 4.62

The value of the Y intercept is meaningful only when the explanatory variable can actually take values close to zero.

Conclusion:

Hence, the intercept is: a = 4.62

(c)

To determine

To find: The predicted highway mileage for a car

Answer to Problem 37E

Predicted highway mileage for a car that gets mileage 28 mpg will be 35.672

Explanation of Solution

Calculation:

The regression line is:

(Predicted) highway mpg = $4.62+1.109$ (city mpg)

When city mpg = 16 mpg then

(Predicted) highway mpg= $4.62+1.109(16)=22.364$

Predicted highway mileage for a car that gets mileage 16 mpg will be 22.364

When city mpg = 28mpg then

(Predicted) highway mpg = $4.62+1.109(28)=35.672$

Predicted highway mileage for a car that gets mileage 28 mpg will be 35.672.

Conclusion:

Hence, the predicted highway mileage for a car will be 35.672.