# Multiple Regression & Variety of Characteristics Worksheet

Multiple regression

Data for this exercise set can be found in the worksheet “Week 7 – Data.xlsx”.

Q1. A researcher wants to determine car prices based on a variety of characteristics such as mileage, model, engine size (number of cylinders and volume (or displacement, in litres)), cruise control etc. The data were collected from Kelly Blue Book for several hundred 2005 used General Motors (GM) cars. (Data are in the Excel file “Week 7 – Data.xlsx”, worksheet “Question 1”.)

1. Using Minitab, determine the estimated regression equation that can be used to predict the price (in \$1000s) given the Mileage, Volume, Cylinders, and CruiseControl. Cruise control is an indicator variable, which is 1 if the car has cruise control, and 0 if itdoes not.
• Use Minitab to perform the F-test to determine the overall significance of the relationship. What is your conclusion at the 0.05 level of significance?
• Use Minitab to perform t-tests to determine the significance of each predictor variable. What is your conclusion at the 0.05 level of significance?
• Remove any predictor variables that are not significant from the estimated regression equation and fit the smaller model. What is your estimated regression equation now? Use R-squared and R-squared (adjusted) to compare this model to the model in part a.
• The data file also contains indicator variables (“dummy variables”) to account for the vehicle type (Sedan, Coupe, Convertible, and Compact). Why is there no indicator variable for SUV? Add these four indicator variables to the model in part d. Use Minitab to develop the multiple linear regression equation. Make sure to select the option

“Sequential sums of squares” when fitting the model. Compare this model to the model in part d. based on R-squared and R-squared (adjusted).

• Carefully interpret the coefficient of the predictor Sedan.
• Do the indicator variables for car type (collectively) add value to the model? (Perform a partial F-test, using a 0.05 level of significance.)

Q2. (Continues Q1 in Week 3) In week 3 you saw a data set that studied the participation rate of 17–24-year-olds in institutions of post-secondary education (universities and colleges). Additionally, the region of the country (Maritimes, Quebec, Ontario, West) was recorded. At the time you developed a one-way analysis of variance to study regional differences.

1. Using Minitab, develop indicator variables to account for the regions. You can do this very conveniently with the menu selection Calc > Make Indicator Variables.
• Develop a multiple linear regression equation that can be used to predict the percentage of 17–24-year-olds who are attending college given the indicator variables you developed in part a. (Your model should only have three predictors; omit the indicator variable for the West.)
• Is the overall model useful to predict participation rates? (Use   =0.05.)
• Carefully interpret the least-squares coefficients returned by Excel, including the intercept.
• Perform t-tests to determine the significance of each indicator variable. What is your conclusion at the 0.05 level of significance? Carefully interpret your findings.

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