The Figure below is Excel output that estimates the effect a vehicle\'s length (

Question

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 0.825901596 0.682113446 0.657660634 2.557507153 43 ANOVA Significance F 3 547.3722456 182.4574152 27.89509237 8.35174E-10 df MS Regression Residual Total 39 255.0928707 6.540842839 42 802.4651163 Stat P-value Lower 95% Upper 95% Intercept Length (in) Width (in) Weight (lbs Goefficients Standard Error 39.449209818.167769437 4.829863296 2.13929E-05 22.92833689 55.97008273 0.001574708 0.045396656 -0.034687761 0.972505655 0.093398111 0.090248695 0.046264664 0.137251585 0.337079273 0.737864512 0.323882196 0.231352867 0.004336659 0.00083949 -5.165825432 7.41213E-06 0.006034688 -0.00263863

Explanation / Answer

1st question

d) The regression equation is significant at the 0.05 level and is therefore better at predicting CityMPG than the naive model. Beacuse look at the 2nd table (Anova table ) corresponding to regression the p-value is 8.35174E-10 which is way less than 0.05. Hence the regression model has significant effect, actually better in predicting that the naive model.

2nd question

To answer this look at the last table. Corresponding to variable length p-value is .972505655 >0.05.

For the variable width p-value is .737864512<0.05

For Weight pvalue is 7.41213E-06<0.05

Now we reject the hypothesis that indenpendent variables has no effect on the model if the p-value > level of significance, else conclude that the variables has significant effect. So going by this we find only the variable Weight has significant effect on the model.option c is correct.

3rd question

percentage of the variation in miles per gallon is explained by changes in the independent variables is given by adjusted R square

which is .657660634 or approx. 66%

4th question

Coefficients in the last table gives us an idea keeping other variables intact if we chance one variable by one unit in turn what amount of change we cant expect to see in MPG.

Coefficient corresponding to Weight is -.004336659. This means that if keeping every other variable unchanged we increase weight by 1 unit the MPG would increase by -.004336659 i.e. decrease by .004336659 unit. So if Weight is incresed by 1000 lbs then the decrease in MPG will be 1000*.004336659 approx 4.

c. The predicted MPG would decrease by 4 MPG is the correct answer.

5th question

For VIF we know if VIF>5 then the independent variables are highly correlated. Here VIF for length is 6.42 meaning it is highly correlated with other variables. So,

b. we should be very concerned about length being highly correlated with the other independent variable. This is the correct answer.

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