The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= -0.973. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=-0.0069x +44.5679 Complete parts (a) through (c) below (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is% (Round to one decimal place as needed) (b) Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below O A A Residual 28+ 22- 16 2500 3250 4000 Weight (pounds) Q B. % of the variance in Vis (Round to one decimal place as needed) 24 Residual 0+.. 2500 3250 4000 Weight (pounds) Q Q (c) Interpret the coefficient of determination and comment on the adequacy of the linear model. O C. A Residual 2- 0 by the linear model. The least-squares regression model appears to be " . -2¹ 2500 3250 Weight (pounds) 3250 4000 Q Q G based on the residual plot. OD. AResidual 2- -2 2500 3250 4000 Weight (pounds) Q Q G
The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= -0.973. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=-0.0069x +44.5679 Complete parts (a) through (c) below (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is% (Round to one decimal place as needed) (b) Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below O A A Residual 28+ 22- 16 2500 3250 4000 Weight (pounds) Q B. % of the variance in Vis (Round to one decimal place as needed) 24 Residual 0+.. 2500 3250 4000 Weight (pounds) Q Q (c) Interpret the coefficient of determination and comment on the adequacy of the linear model. O C. A Residual 2- 0 by the linear model. The least-squares regression model appears to be " . -2¹ 2500 3250 Weight (pounds) 3250 4000 Q Q G based on the residual plot. OD. AResidual 2- -2 2500 3250 4000 Weight (pounds) Q Q G
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 88CR
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Transcribed Image Text:The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= -0.973. The least-squares regression
line treating weight as the explanatory variable and miles per gallon as the response variable is y = -0.0069x +44.5679. Complete parts (a) through (c) below.
(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon?
The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is ■%.
(Round to one decimal place as needed.)
(b) Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below.
O A.
A Residual
28
22-
16
2500 3250
4000
Weight (pounds)
Q
B.
IS
2+
0
Residual
2500 3250
Weight (pounds)
4000
(c) Interpret the coefficient of determination and comment on the adequacy of the linear model.
% of the variance in
(Round to one decimal place as needed.)
O C.
A Residual
2-
0-
-2
2500
by the linear model. The least-squares regression model appears to be
•
●
3250
Weight (pounds)
4000
Q
based on the residual plot
D.
A Residual
2+
0-
-2-
●
●
3250
Weight (pounds)
2500
4000
Transcribed Image Text:Data Table
Car
Car 1
Car 2
Car 3
Car 4
Car 5
Car 6
Weight (pounds),
X
3,765
3,984
3,530
3,175
2,580
3,730
Miles
per Gallon, Car
y
19
18
20
22
27
18
Car 7
Car 8
Car 9
Car 10
Car 11
Weight (pounds),
X
2,605
3,772
3,310
2,991
2,752
Miles
per Gallon,
y
26
18
20
25
26
Full data
set D
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