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.
D.
The slope indicates the mean miles per gallon.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Miles per gallon, y
Independent Variable: Weight, x
Miles per gallon, y = 44.491244 - 0.007172026 Weight, x
Sample size: 5
R (correlation coefficient) = -0.95641895
R-sq = 0.91473721
Estimate of error standard deviation: 1.4764435

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	44.491244	4.3149362	? 0	3	10.310985	0.0019
Slope	-0.007172026	0.0012641914	? 0	3	-5.6732123	0.0108

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	70.160344	70.160344	32.185338	0.0108
Error	3	6.5396558	2.1798853
Total	4	76.7

Hence,

a) Regression line:

y = 44.5 - 0.00717 x

Best interpretation of slope: The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. Option C is correct.