Multiple Regression Analysis The Excel output in Figure 1 be

Multiple Regression Analysis

The Excel output in Figure 1 below estimates the effect the number of occupants and whether the driver wears a seat belts has on driving speed. The variable Seatbelts is a dummy (Seatbelts = 1 if driver is wearing a seat belt, Seatbelts = 0 if he or she is not). Use Figure 1 to answer Questions 1 through 5.

Is the regression equation significant at the .10 level?

Select one:

a. Yes, because the variable Seatbelts is significant at the .10 level.

b. Yes, because the variable Seatbelts is a dummy variable.

c. No, because the significance of F (the 2p value ) = .125 which is greater than .10

Question 2

Using a two-tail test, what is the lowest level of significance for which we would conclude the number of occupants significantly affects driving speed? Choose best answer.

Select one:

a. .18

b. .10

c. .50

d. .025

Question 3

Interpret the effect of wearing seatbelts on driving speed.

Select one:

a. Drivers that wear seatbelts drive wicked slow

b. Drivers that wear seat belts drive roughly 6.63 Miles Per Hour SLOWER than those that do not wear seat belts.

c. Drivers that wear seat belts drive roughly 6.63 miles per hour FASTER than those that do not wear seat belts.

d. If the number of seat belts in the car increases by one, the driving speed decreases by 6.63 miles per hour.

Question 4

Do seat belts significantly affect driving speed at the .10 significance level?

Select one:

a. Yes

b. No

c. More information is needed to answer this question

Question 5

What percentage of the total variation in driving speed is explained by the reqression equation?

Select one:

a. 95%

b. 100%

c. 56.14%

d. 31.5%

Question 6

The Figure below is Excel output that estimates the effect a vehicle\'s length (in inches), width (in inches) and weight (in pounds) has on a its average miles per gallon for city driving.

Which is a correct interpretation of the Joint Hypothesis Test?

Select one:

a. At the 0.05 significance level, the regression equation is no better at predicting CityMPG than the naive model is (i.e., the mean of CityMPG)

b. We fail to reject the null hypothesis at the 0.05 significance level

c. Zero of the coefficients are statistically different from zero at the 0.05 significance level

d. The regression equation is significant at the 0.05 level and is therefore better at predicting CityMPG than the naive model

Question 7

Which variable(s) significantly affect the average miles per gallon for city driving at the .05 level?

Select one:

a. Length, Width and Weight

b. Width and Weight

c. Weight

d. Length and Width

Question 8

What percentage of the variation in miles per gallon is explained by changes in the independent variables?

Select one:

a. 68%

b. 66%

c. 92%

d. 125%

Question 9

Interpret the effect on MPG of increasing a vehicle\'s weight by 1,000 pounds (holding everything else constant).

Select one:

a. The predicted MPG would not change

b. The predicted MPG would decrease by .04 MPGs

c. The predicted MPG would decrease by 4 MPG

d. The predicted MPG would increase by 4 MPG

Question 10

Suppose the variance inflation factor (VIF) for the variable LENGTH was 6.42. This statistic would indicate that

Select one:

a. the value of r^2 (i.e., r squared) is greater than 0.90

b. we should be very concerned about length being highly correlated with the other independent variables

c. we should NOT be very concerned about length being highly correlated with the other independent variables

d. 6.42% of the variation in the dependent variable is explained by changes in length

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.561415721 0.315187612 5.464881981 14 ANOVA df MS Regression Residual Total 151.2 75.6 2.531396765 0.124636098 11 328.5142857 29.86493506 13 479.7142857 t Stat P-value Lower 95% Upper 95% Intercept Occupnts SeatBelt Figure 1: The effect of the number of occupants and whether they were wearing seat belts on driving speed Coefficients Standard Error 67.62857143 5.017157945 13.47945833 3.49148E-08 56.58588125 3.214285714 2.1908267181.467156525 0.17033373 -8.036262805 1.607691377 6.6285714293.199907234 -2.071488622 0.062611837 -13.671519760.414376903 78.6712616

Solution

c. No, because the significance of F (the 2p value ) = .125 which is greater than .10

Using a two-tail test, the lowest level of significance for which we would conclude the number of occupants significantly affects driving speed is 0.10.

b. Drivers that wear seat belts drive roughly 6.63 Miles Per Hour SLOWER than those that do not wear seat belts.

Yes, seat belts significantly affect driving speed at the .10 significance level.