An engineer wants to determine how the weight of a? car, x, affects gas? mileage
ID: 3366790 • Letter: A
Question
An engineer wants to determine how the weight of a? car, x, affects gas? mileage, y. The following data represent the weights of various cars and their miles per gallon.
Car
A
B
C
D
E
Weight? (pounds), x
25452545
31003100
34103410
37703770
40404040
Miles per? Gallon, y
25.225.2
23.923.9
19.619.6
18.518.5
14.314.3
?(a) Find the? least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
Write the equation for the? least-squares regression line.
ModifyingAbove y with caretyequals=negative 0.00717?0.00717xplus+44.544.5
?(Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as? needed.)
?(b) Interpret the slope and? intercept, if appropriate.
Choose the best interpretation for the slope.
A.
The slope indicates the mean weight.
B.
The slope indicates the ratio between the mean weight and the mean miles per gallon.
C.
The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight.
Your answer is correct.
D.
The slope indicates the mean miles per gallon.
E.
It is not appropriate to interpret the slope because it is not equal to zero.
Choose the best interpretation for the? y-intercept.
A.
The? y-intercept indicates the miles per gallon of the lightest car in the population.
B.
The? y-intercept indicates the mean miles for a car that weighs 0 pounds.
C.
The? y-intercept indicates the mean miles per gallon for a car that weighs 0 pounds.
D.
The? y-intercept indicates the miles per gallon for a new car.
E.
It is not appropriate to interpret the? y-intercept because it does not make sense to talk about a car that weighs 0 pounds.
Car
A
B
C
D
E
Weight? (pounds), x
25452545
31003100
34103410
37703770
40404040
Miles per? Gallon, y
25.225.2
23.923.9
19.619.6
18.518.5
14.314.3
Explanation / Answer
y - intercept will represent the car where the weight is 0 pound which is not practically possible. Hence,
It is not appropriate to interpret the? y-intercept because it does not make sense to talk about a car that weighs 0 pounds.
Option E is correct.