Question

An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below

​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

Weight (pounds), x	Miles per Gallon, y
3748	16
3834	16
2794	25
3562	20
3350	20
3016	24
3770	17
2699	25
3487	18
3870	16
3292	18

​(Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as​ needed.)

​(b) Interpret the slope and​ y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. ​(Use the answer from part a to find this​ answer.)

A. For every pound added to the weight of the​ car, gas mileage in the city will decrease by ___ ​mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept.

B. For every pound added to the weight of the​ car, gas mileage in the city will decrease by ___ ​mile(s) per​ gallon, on average. A weightless car will get ___ miles per​ gallon, on average.

C. A weightless car will get ___ miles per​ gallon, on average. It is not appropriate to interpret the slope.

D. It is not appropriate to interpret the slope or the​ y-intercept.

​(c) A certain​ gas-powered car weighs 3700 pounds and gets 19 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight?

A. Below

B. Above

(d) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not?

A. ​No, because the hybrid is a different type of car.

B. Yes, because the hybrid is partially powered by gas.

C. ​No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n = 11.

D.​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 11.

Answer 1

a)

y =47.49+(-0.00821)*x

b)

A. For every pound added to the weight of the​ car, gas mileage in the city will decrease by 0.00821 mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept.

c)

predicted val=47.486+3700*-0.008=

17.10

since above value is below actual value

B. Above

d)

A. ​No, because the hybrid is a different type of car.