Reference no: EM131834731
An express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package (Y), the package weight (X1) and the distance shipped (X2).
Twenty packages were randomly selected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package. The sample information is shown in the table here.
(A) Estimate a simple linear regression model involving shipping cost and package weight. Interpret the slope coefficient of the least squares line as well as the computed value of R2.
(B) Add another explanatory variable - distance shipped - to the regression in Part A. Estimate and interpret this expanded model. How does the R2 value for this multiple regression model compare to that of the simple regression model estimated in Part A? Explain any difference between the two R2 values. Compute and interpret the adjusted R2 value for the revised model.
(C) Suppose that one of the managers of this express delivery service company is trying to decide whether to add an interaction term involving the package weight (X1) and the distance shipped (X2) in the multiple regression model developed previously. Why would the manager want to add such a term to the regression equation?
(D) Estimate the revised model using the interaction term suggested in Part C.
(E) Interpret each of the estimated coefficients in your revised model in Part D. In particular, how do you interpret the coefficient for the interaction term in the revised model?
(F) Does this revised model in Part D fit the given data better than the original multiple regression model in Part B? Explain why or why not.