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# Data Sales 1.

"The marketing manager of a large supermarket chainwould like to determine the eﬀect of shelf space and whether the product wasplaced at the front (= 1) or back (= 0) of the aisle on the sales of pet food. Arandom sample of 12 equal-sized stores is selected, with the results stored in theﬁle PETFOOD.i) State the multiple regression equation that predicts sales based on shelfspace and location, perform the the regression.ii) Interpret the regression coeﬃcients you computed in part i).iii) Predict the weekly sales of pet food for a store with 8 feet of shelf spacesituated at the back of the aisle.iv) Perform a residual analysis on the results and determine if the regressionassumptions are valid.v) Is there a signiﬁcant relationship between sales and two independentvariables (shelf space and aisle position) at the 0.05 level of signiﬁcance?vi) At the 0.05 level of signiﬁcance, determine whether each independentvariable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.vii) Construct and interpret a 95% conﬁdence interval estimates for therelationship between sales and shelf space and between sales and aisle location.viii) Someone already did a preliminary simple linear regression using onlyweekly sales and shelf space. The regression results were b0 = 1.45 and b1 =0.074. Compare the slope you computed in part (i) against the slope for thesimple linear regression. Explain the diﬀerence in the results.ix) Report R2and adjusted R2.Interpret their meaning .x) What assumption about the slope of shelf space with sales do you needto make in this problem?xi) Add an interaction term to the model and, at the 0.05 level of signiﬁ-cance, determine whether it makes a signiﬁcant contribution to the model.xii) On the basis of your answers, which model is most appropriate? Explain."