A regional 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. These sample observations are given in the file P10_22.xlsx.
a. Estimate a multiple regression equation involving the two given explanatory variables. What do the results in the ANOVA table indicate about this regression?
b. Is it worthwhile to add the terms X21 and X22 to the regression equation in part a? Base your decision here on a partial F test and a 5% significance level.
c. Is it worthwhile to add the term X1X2 to the most appropriate reduced equation determined in part b? Again, perform a partial F test with a 5% significance level.
d. What regression equation should this company use in predicting the cost of shipping a package? Defend your recommendation.