An assistant in the district sales office of a national cosmetics firm obtained data, shown below, on
Question:
An assistant in the district sales office of a national cosmetics firm obtained data, shown below, on advertising expenditures and sales last year in the district’s 14 territories. X1 denotes expenditures for point-of-sale displays in beauty salons and department stores (in thousand dollars) while X2 and X3 represent the corresponding expenditures for local media advertising and prorated share of national media advertising, respectively. Y denotes sales (in thousand cases). The assistant was instructed to estimate the increase in expected sales when X1 is increased by one thousand dollars and X2 and X3 are held constant, and was told to use an ordinary multiple regression model with linear terms for the independent variables and with independent normal error terms.
a. Compute the variance inflation factor for all the independent variables. What do these suggest about the effects of multicollinearity (if there are any)?
b. The assistant eventually decided to drop variables X2 and X3 from the model “to clear up the picture”. Fit the assistant’s revise model. Is the assistant now in better position to achieve the research objective? Support your answer with appropriate results.
c. Using the model in (b), identify if there are any influential observations using the hat matrix, studentized deleted residuals and Cook’s distance.
Dataset:
Auditing and Assurance services an integrated approach
ISBN: 978-0132575959
14th Edition
Authors: Alvin a. arens, Randal j. elder, Mark s. Beasley