Test: 4-3 MyMathLab Exam: Chapters 3 and 4 14 of 15 (9 complete) This Question:

Question

Test: 4-3 MyMathLab Exam: Chapters 3 and 4 14 of 15 (9 complete) This Question: 1 pt An engineer wants to determine how the weight of a carxaffects gas mileage, y. The folowing data represent the weights of various cars and their miles per gallon. C Weight (pounds). x 2665 3010 3395 3790 4220 25.6 24.6 15.8 14.1 Miles per Gallon, y (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. y x+ (Round to four decimal places as needed.) (b) Interpret the slope and intercept, if appropriate. Choose the best interpretation for the slope. O A. The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. O B. The slope indicates the ratio between the mean weight and the mean miles per gallon. O C. The slope indicates the mean miles per gallon. O D. The slope indicates the mean weight. Click to select your answer(s). O Type here to search a a

Explanation / Answer

Answer:

a).

y=(-0.0082)x +48.4355

b).

A. the slope indicates the mean change in miles per gallon for an increase of 1 pound in weight.

E. it is not appropriate to interpret the y intercept.

c).

predicted value =17.35

residual = 15.8-17.35 = -1.55

it is below average

d).

Graph C

Regression Analysis

r²

0.943

n

5

r

-0.971

k

1

Std. Error

1.432

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

101.9385

1  

101.9385

49.73

.0059

Residual

6.1495

3  

2.0498

Total

108.0880

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

48.4355

4.0240

12.037

.0012

35.6294

61.2417

x

-0.0082

0.0012

-7.052

.0059

-0.0119

-0.0045

Regression Analysis

r²

0.943

n

5

r

-0.971

k

1

Std. Error

1.432

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

101.9385

1  

101.9385

49.73

.0059

Residual

6.1495

3  

2.0498

Total

108.0880

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

48.4355

4.0240

12.037

.0012

35.6294

61.2417

x

-0.0082

0.0012

-7.052

.0059

-0.0119

-0.0045

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