Question

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. picture Click here for the Excel Data File a-1. Develop a correlation matrix. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.) Maintenance cost ($) Age (years) Odometer Miles Miles since last Maintenance Maintenance cost ($) Age (years) Odometer Miles Miles since last Maintenance 1 a-2. Which independent variables have strong or weak correlations with the dependent variable? There is a correlation between age and maintenance cost.

Answer 1

Solution:

To develop a correlation matrix using Minitab, go to Stat. Select Basic Statistics and click on correlation. Select the variables and move to the variables box. Click OK. The final screen shot is given below. Correlation: Maintenance cost, Age, Odometer Miles, Miles, Engine Type (O=diesel) Maintenance cost Age Odometer Miles Age Miles 0.708 0.000 Odometer Miles 0.697 0.000 0.991 0.000 Miles -0.156 0.166 -0.154 0.173 -0.136 0.229 Engine Type (Od 0.595 0.000 -0.075 0.511 -0.076 0.501 -0.045 0.694 The dependent variable maintenance cost has a strong correlation with age. Also, two independent variables age and odometer miles are strongly correlated

To determine the regression equation using Minitab, go to Stat, select Regression and click on Fit Regression Model. Move price to the response box and screen to the predictors box. Click ok. The final screen shot is given below. Model Summary S 665.379 R-sq R-sq(adj) R-sq (pred) 92.278 91.86% 90.95% Coefficients VIF Term Constant Age Odometer Miles Miles Engine Type (O=diesel) Coef -637 746 -0.0092 -0.035 3186 SE Coef T-Value 1431 -0.44 203 3.68 0.0178 -0.52 0.124 -0.28 158 20.16 P-Value 0.658 0.000 0.608 0.779 0.000 54.85 54.56 1.04 1.01 Regression Equation 0.035 Miles Maintenance cost = -637 + 746 Age - 0.0092 Odometer Miles - + 3186 Engine Type (O=diesel) The regression equation is Maintenance cost=-637+746Age-0.00920dometer miles-0.035 miles+3186 engine type The value of correlation coefficient R = 0.9227. Hence, 92.27% of the variation in maintenance cost is explained by the dependent variables.

A histogram on the residuals is drawn using Minitab. The screen shot is given below. Residual Histogram for Maintenance cost X Histogram (response is Maintenance cost) 25 20 15 Frequency 10 0 -1600 -800 800 1600 0 Residual The above plot shows that the residuals follow a normal distribution.

Residuals vs Fits for Maintenance cost х Versus Fits (response is Maintenance cost) 2000 1000 Residual ; -1000 -2000 0 1000 2000 6000 7000 8000 9000 3000 4000 5000 Fitted Value There is no apparent relationship in the residuals, but the residual variation may be increasing with larger fitted values.