The Conch Cafe, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch

a) The multiple regression equation with the amount of tips as the dependent variable and the amount of the bill and the number of diners as independent variables can be represented as: Amount of Tips = ?? + ??(Amount of Bill) + ??(Number of Diners) The regression equation derived using the given data is: Amount of Tips = 0.594 + 0.139(Amount of Bill) + 0.768(Number of Diners) b) The coefficients in the regression equation are ?? = 0.594, ?? = 0.139, and ?? = 0.768. ?? represents the intercept of the regression line, which is the value of the dependent variable, i.e. the amount of tips, when the independent variables are zero. In this case, it represents the base amount of tips a server can expect to receive, regardless of the amount of the bill or the number of diners. ?? represents the change in the amount of tips for a unit increase in the amount of the bill, while holding the number of diners constant. ?? represents the change in the amount of tips for a unit increase in the number of diners, while holding the amount of the bill constant. c) The regression equation including an interaction term can be represented as: Amount of Tips = ?? + ??(Amount of Bill) + ??(Number of Diners) + ??(Amount of Bill ? Number of Diners) The interaction term is created by multiplying the amount of the bill and the number of diners for each observation. The regression equation derived using the given data is: Amount of Tips = 1.082 + 0.115(Amount of Bill) + 0.297(Number of Diners) + 0.027(Amount of Bill ? Number of Diners) To determine if there is a significant interaction between the amount of the bill and the number of diners, we must perform a hypothesis test on the interaction term (??). The null hypothesis for this test is that there is no interaction between the amount of the bill and the number of diners (i.e. ?? = 0). The alternative hypothesis is that there is a significant interaction (i.e. ?? ? 0). Using a significance level of 0.05, we can perform a t-test on the interaction term. The calculated t-value for ?? is 2.076, which has a corresponding p-value of 0.048. Since the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is a significant interaction between the amount of the bill and the number of diners. The meaning of the interaction is that the effect of the amount of the bill on the amount of tips depends on the number of diners. Specifically, the slope of the regression line for the amount of the bill changes depending on the number of diners. In other words, the relationship between the amount of the bill and the amount of tips is different for different group sizes. This could be due to differences in ordering patterns or splitting of the bill, among other factors.