\fA 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). Several 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.xisx. The estimated multiple regression equation is Y = -4.6728 + 1.2924X1 + 0.0369X2, R-square = 0.916. Suppose that one of the managers of this regional express delivery service company is trying to decide whether to add an interaction term involving the package weight and the distance shipped in the previous multiple regression equation. a. Why would the manager want to add such a term to the regression equation? The manager might want to add an interaction term if she/her believes that the rate of increase of the cost of shipment v with the package weight may be affected by the shipping distance v b. Estimate the revised equation. Let X3 represent the interaction (package weight, distance shipped). Round your answers to four decimal places, if necessary. If your answer is negative number, enter "minus" sign. Y = X x1 + * x2 + x X3 c. Interpret each of the estimated coefficients in your revised equation. Round your answers to four decimal places, if necessary. As the package weight increases by 1 pound, the shipment cost typically Increases v by X dollars v plus the product of X dollars v and the current distance shipped v , while holding the distance shipped v constant. As the shipment distance increases by 1 mile, the shipment cost v typically increases v by dollars v plus the product of dollars and the current package weight v while holding the package weight constant. d. Does this revised equation fit the data better than the original multiple regression equation? Yes the revised model yields a higher |R-square and thus fits the given data better v than the original model. The interaction term appears to add significantly to the overall explanatory power of the model