The U.S. Department of Energy and the Environmental Protection Agency are actively trying to promote fuel economy.To that end, their Web site www.fueleconomy.gov reports engine efficiency data on all vehicles available in the U.S. market.Sport Utility Vehicles (SUVs) have been accused of consuming more gasoline than ordinary passenger cars.In order to test this argument, a sample of 26 sedans and 27 SUVs was compiled and their "city" Miles per Gallon (MPG), engine Capacity (size) in liters, Hybrid type (1 if hybrid, 0 if not), and SUV type ( 1 if SUV, 0 if sedan) were recorded.Looking at the data table below we see that a Honda Insight yields 40 MPG, whereas a Ford Expedition only 14.But is this an effect of the Expedition being an SUV, or is it simply a consequence of its larger (5.4 L) engine size?Partial results of the regression of MPG, using Capacity, Hybrid, and SUV as predictors, follow. All figures are real and refer to 2010 models. Twelve selected models are shown below.

Model

MPG

Capacity

Hybrid

SUV

Toyota Prius

51

1.8

1

0

Ford Fusion Hybr

41

2.5

1

0

Mercury Milan Hybr

41

2.5

1

0

Honda Insight

40

1.3

1

0

Ford Fusion S

23

2.5

0

0

Mercury Milan S

23

2.5

0

0

Ford Escape Hybr

34

2.5

1

1

Mazda Tribute Hybr

34

2.5

1

1

Ford Explorer

15

4.6

0

1

Nissan Xterra

15

4

0

1

Ford Expedition 8 cyl

14

5.4

0

1

BMW X6 8 cyl

13

4.4

0

1

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.9269

R Square

XXXX

Adjusted R Square

0.8505

Standard Error

3.27492

Observations

53

ANOVA

df

SS

MS

F

Significance F

Regression

3

3205.4512

1068.484

XXXX

7.36E-21

Residual

49

525.52990

10.7251

Total

52

3730.9811

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

30.0814

1.7200023

17.48916

1.04E-22

26.62492

33.537

Capacity

-3.0978

0.5266734

-5.88194

3.56E-07

-4.156249

-2.0394

Hybrid

13.3300

1.109567

12.0137

3.24E-16

11.1002

15.559

SUV

XXXX

0.9377317

-2.64495

0.010948

-4.364691

-0.5958

Which set of independent variables are found to be significant predictors of Gas Mileage (MPG) at the 0.01 significance level?

SUV only

Capacity only

Capacity and SUV

Capacity and Hybrid

Capacity, Hybrid, and SUV

What is the calculated value of the test statistic to test the full regression model (i.e., for the Ho: 1 = 2 = 3 = 0)?

99.6

6.099

0.859

7.36

17.48

At the 1% level of significance, what is your conclusion about the test of the regression model?

The independent variables do not explain MPG.

The dependent variables do not explain MPG.

The group of independent variables has the same coefficients.

Inconclusive since the group of variables appears to be homogeneous.

The group of independent variables explain MPG.

According to the least squares regression from this sample, for a fixed hybrid type (e.g. hybrid) and engine size (e.g. 3L), how will gas mileage of an SUV compare to that of a sedan?

The gas mileage of the SUV is expected to be lower by 3.1 MPG.

The sedan is expected to yield 32.03 MPG and the SUV 21.39 MPG.

Both are expected to yield 30.08 miles per gallon of gas.

The gas mileage of the SUV is expected to be higher by 2.48 MPG.

The gas mileage of the SUV is expected to be lower by 2.48 MPG.

What percentage of the variation in MPG is explained by its regression on Capacity, Hybrid, and SUV?

There is no way to tell based on this output.

85.05%

92.69%

99.63%

85.91%

Using the complete model, what is the predicted MPG of a hybrid vehicle that is a SUV with a 4-liter engine?

30.08

15.21

28.54

31.02

37.83