Data set MPG presents the gasoline mileage performance for 32 automobiles.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Use SAS programming to answer the following questions. Submit related SAS codes and outputs. Explain the results in your own words to answer each problem.

Data set MPG presents the gasoline mileage performance for 32 automobiles. The variables in the study are:

Dependent variable: Miles per gallon (y)

Independent variables:

x1: displacement (cubic in.) x2: horsepower (ft-lb)

x3: torque (ft-lb)

x4: horsepower + torque (ft-lb) x5: carburetor (barrels)

x6: weight (lbs.)

x7: type of transmission (1=automatic; 0=manual) x8: no. of transmission speeds (3, 4, or 5)

 

 

 

1. Build a multiple linear regression model relating the response variable Miles per gallon to these predictors. (Hint: x7 and x8 are qualitative variables).

Use SAS program to find the least square regression equation.

 2. Construct the ANOVA table. Test for significance of regression. State the null and alternative hypotheses; report the F statistic and p- value. What conclusions can you draw? (Use 𝛼= .05)

3. Find the coefficient of determination, R^2 and Adjusted-R^2for the linear model you constructed. Discuss your results

4. Find a 95 % CI for the regression coefficient for x2.

5. Fit a reduced regression model using x1-x4 and x7-x8 as the regressors. Give the least squares equation for reduced model.

6. Report the partial F statistic and p-value and make a conclusion whether or not to drop both carburetor and weight have a significant relationship with the gasoline mileage.

7. Find a 95 % CI for the regression coefficient for x3 in reduced model and compare it to the one from full model.

8. (Test for the qualitative variable) Test the hypothesis that no. of transmission speeds level will have impact on Miles per gallon. Set up the null and alternative hypotheses; Report the P- value and make your conclusion from SAS result.

9. (Interaction effect) Test the hypothesis that the type of transmission effect is the same for all three levels of no. of transmission speeds. Set up appropriate model, hypotheses and report your results.

 

Attachments:

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