Tipping behavior in restaurants. Can food servers increase their tips by complimenting the customers they are waiting on? To answer this question, researchers collected data on the customer tipping behavior for a sample of 348 dining parties and reported their findings in the Journal of Applied Social Psychology (Vol. 40, 2010). Tip size (y, measured as a percentage of the total food bill) was modeled as a function of size of the dining party (x1) and whether or not the server complimented the customersâ€™ choice of menu items (x2). One theory states that the effect of size of the dining party on tip size is independent of whether or not the server compliments the customersâ€™ menu choices. A second theory hypothesizes that the effect of size of the dining party on tip size is greater when the server compliments the customersâ€™ menu choices as opposed to when the server refrains from complimenting menu choices.
a. Write a model for E(y) as a function of x1 and x2 that corresponds to Theory 1.
b. Write a model for E(y) as a function of x1 and x2 that corresponds to Theory 2.
c. The researchers summarized the results of their analysis with the following graph. Based on the graph, which of the two models would you expect to fit the data better? Explain.