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We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198vehicles in the government's 2008Fuel Economy Guide give the regression line predicted highway mpg=4.62+1.109(city mpg).

(a) What鈥檚 the slope of this line? Interpret this value in context.

(b) What鈥檚 the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted highway mileage for a car that gets 16miles per gallon in the city. Do the same for a car with a city mileage of 28mpg.

Short Answer

Expert verified

a. Per 1mpgincrease in city mileage, there will be a 1.109mpgincrease on the highway.

b. In the city, a car cannot go 0mpg.

Thus the y-intercept is 4.62. This may be viewed as extrapolation.

c. According to the prediction, a car that gets 16mpgin the city and one that gets 28mpgin the city get 22,36mpgand 35.67mpg, respectively, on the highway.

Step by step solution

01

Part (a) Step 1: Given Information

The regression line predicted highway mpg=4.62+1.109(city mpg).

02

Part (a) Step 2: Explanation

A regression line's slope is the indirect relationship between the x- and y-variables.

Slope=1.109

In each of the two variables, x(city mpg) and y(highway mpg) represents the increase in the y-variable.

Note: mpg =miles per gallon

03

Part (b) Step 3: Given Information 

The regression line predicted highway mpg=4.62+1.109(city mpg).

04

Part (b) Step 4: Explanation

Statistics have meaning only when a value is in line with reality.

In these circumstances, the car will get 0miles per gallon in the city since the intercept is4.62highway mpg.

If the explanatory variable is 0, the y-intercept is the value of the response variable.

05

Part (c) Step 5: Given Information

The regression line predicted highway mpg=4.62+1.109(city mpg).

06

Part (c) Step 6: Explanation

Highwaympg=4.62+1.109Highwaympg=4.62+1.109Highwaympg=4.62+17.74=22.36(city mpg)

Using the regression equation for the regression line, we can calculate the predicted highway mileage given the city mileage of the vehicle.

Highwaympg=4.62+1.109Highwaympg=4.62+1.109(28)Highwaympg=4.62+31.05=35.67 (city mpg)

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