Refer to Market share data set in Appendix C.3. Company executives want to be able to predict market share of their product (Y) based on merchandise price (X d, the gross Nielsen rating pOints (Xl, an index of the amount of advertising exposure that the product received); the presence or absence of a wholesale pticing discount (X3 = I if discount present: otherwise X3 = 0); the presence or absence ofa package promotion dmingthe period (X4 = I if promotion present: otherwise X4 = 0): and year (X,). Code year as a nominal level variable and lise 2000 as the referent year.

a. Fit a first-order regression model. Plot the residuals against the fitted values. How well does the first-order model appear to Ilt the data?

b. Re-fitthe model in parr (a). after adding all second-orderterrns involving only the quantitative predictors. Test whether or not all quadratic and interaction terms can be dropped from the regression model: use CI = .05. State the alternatives. decision rule, and conclusion.

c. In part (a), test whetheradvettising index (X2) and year (X,) can be dropped from the model; use (){ = .05. State the alternatives, decision rule, and conclusion.

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