1) A consumer organization wants to develop a regression model to predict gasoline mileage(as measured by miles pergallon) based on the horsepower of thecar's engine and the weight of the car(in pounds). A sample of 20

20 recent car models wasselected, with the results recorded in the accompanying table.

a. State the multiple regression equation.

Est. Mean Mileage= ___+(__)+(__)Weight

(Round to five decimal places asneeded.)

b. Interpret the meaning of theslopes,bH and bW, that you entered above

Each increase of one unit in horsepower is estimated to result in a

decrease in the mean gasoline mileage of ___units, holding weight constant.

Each increase of one unit in weight is estimated to result in the decrease in the mean gasoline mileage of __units, holding horsepower constant

c. Explain why the regressioncoefficient,

b0, has no practical meaning in the context of this problem.

A.

The interpretation of b0 has no practical meaning here because it would correspond to the estimated mean weight when a car has 0 gasoline mileage and 0 horsepower.

B.

The interpretation of b0 has no practical meaning here because it would correspond to the estimated mean gasoline mileage when a car has 0 horsepower and 0 weight.

C.

The interpretation of b0 has no practical meaning here because it would correspond to the estimated mean horsepower when a car has 0 gasoline mileage and 0 weight.

d. Predict the miles per gallon for a car that has 60 horsepower and weighs 2000 pounds.

The gasoline mileage(as measured by miles pergallon) prediction for a car that has 60 horsepower and weighs 2000 pounds is ____

miles per gallon.

(Round to three decimal places asneeded.)

2)A consumer organization wants to develop a regression model to predict gasolinemileage (as measured by milesper gallon) based on the horsepower ofthe car's engine and the weight of thecar (inpounds). A sample of 20 recent car modelswas selected, with the results recorded in the accompanying table.

The resulting ANOVA table is below. Complete parts(a) through(c).

Regression

Statistics

Multiple R

0.9770

R Square

0.9546

n

8

Source

Regression

Degreesof

Freedom

2

Sumof

Squares

16.94097

Mean Square

8.47049

F

52.56

p-value

0.0004

Error

Degreesof

Freedom

5

Sumof

Squares

0.80575

Mean Square

0.16115

total

Degreesof

Freedom

7

Sumof

Squares

17.74672

a. Determine whether the model is significant(overall) at the

0.05 level of significance. Choose the correct answer below.

A.

Donotreject H0. There is insufficient evidence to prove that at least one slope is not zero.Wecannotprovethatthere is a linear relationship between mileage and at least one of the horsepower and weight.

B. Reject H0. There is insufficient evidence to prove that at least one slope is not zero. We cannot prove that there is a linear relationship between mileage and at least one of horsepower and weight.

C. Reject H0. There is sufficient evidence to prove that at least one slope is not zero.There is a linear relationship between mileage and at least one of horsepower and weight.

D. Do not reject H0. There is sufficient evidence to prove that at least one slope is not zero.There is a linear relationship between mileage and at least one of horsepower and weight.

b. What is the value coefficient of multipledetermination, R2, and interpret its meaning.

R2=

(Round to four decimal places asneeded.)

c. Interpret the meaning of R2.

It indicates that ___% of the variation in mileage in the sample can be explained by its linear relationship with horsepower and weight.

(Round to two decimal places asneeded.)

3)A consumer organization wants to develop a regression model to predict gasolinemileage (as measured by milesper gallon) based on the horsepower ofthe car's engine and the weight of thecar (inpounds). A sample of 25 recent car modelswas selected, with the results recorded in the accompanying table.

Variable Coefficient Std Error tstat p-value Lower95%Upper95%

Intercept 0.00282 0.05667 0.05 0.9608 -0.11471 0.12035

Horsepower-0.71635 0.03717 -19.27 0.0000 -0.79344 -0.63926

Weight -0.11854 0.08734 -1.36 0.1885 -0.29968 0.0626

At the 0.05 level ofsignificance, determine whether each independent variable makes a significant contribution(individually) to the regression model.

Can we prove that there a relationship between mileage andhorsepower?

*No.Donotreject the null. There is insufficient enough evidence to conclude that the slope of horsepower is not 0.

Yes. Reject the null. There is enough evidence to conclude that the slope of horsepower is not 0.

Can we prove that there a relationship between mileage andweight?

No. Do not reject the null. There is insufficient enough evidence to conclude that the slope of weight is not 0.

Yes.Reject the null. There is enough evidence to conclude that the slope of weight is not 0.