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

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

b. Use a statistical software package to determine the multiple regression equation. How did you select the variables to include in the equation? How did you use the information from the correlation analysis? Show that your regression equation shows a significant relationship. Write out the regression equation and interpret its practical application. Report and interpret the R-square.

c. Develop a histogram of the residuals from the final regression equation developed in part (b). Is it reasonable to conclude that the normality assumption has been met?

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