Refer to the Buena School District bus data. First, add a variable to change the type of bus (diesel or gasoline) to a qualitative variable. If the bus type is diesel, then set the qualitative variable to 0. If the bus type is gasoline, then set the qualitative variable to 1. Develop a regression equation using statistical software with maintenance as the dependent variable and age, miles, and bus type as the independent variables.

a. Write out the multiple regression equation analysis. Discuss each of the variables.

b. Determine the value of R2. Interpret.

c. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?

d. Conduct the global test on the set of independent variables. Interpret.

e. Conduct a test of hypothesis on each of the independent variables. Would you consider deleting any of the variables? If so, which ones?

f. Rerun the analysis until only significant regression coefficients remain in the analysis. Identify these variables.

g. Develop a histogram or a stem-and-leaf display of the residuals from the final regression equation developed in part (f). Is it reasonable to conclude that the normality assumption has been met?

h. Plot the residuals against the fitted values from the final regression equation developed in part (f) against the fitted values of Y. Plot the residuals on the vertical axis and the fitted values on the horizontal axis.