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.

Weight (pounds), x   Miles per Gallon, y
3787   18
3798   17
2725   24
3460   19
3334   20
3028   24
3808   18
2703   25
3570   19
3836   17
3370   18

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

ŷ =−0.00669 x + 42.68

​(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. A weightless car will get __?__miles per​ gallon, on average.

B.

A weightless car will get __?__miles per​ gallon, on average. It is not appropriate to interpret the slope.

C.

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.

D.

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

Answer 1

(a)

From the given data, the following Table is calculated:

X	Y	XY	X2
3787	18	68166	14341369
3798	17	64566	14424804
2725	24	65400	7425625
3460	19	65740	11971600
3334	20	66680	11115556
3028	24	72672	9168784
3808	18	68544	14500864
2703	25	67575	7306209
3570	19	67830	12744900
3836	17	65212	14714896
3370	18	60660	11356900
Total = 37419	219	733045	129071507

So,

Least Square Regression line is:

(b)

Correct option:

C.   For every pound added to the weight of the car, gas mileage in the city will decrease by 0.00669 miles per gallon, on average. It is not appropriate to interpret the y - intercept.

Reason: Weightless car does not exist.