The owner of Soffritto Italian Grill would like to predict the amount of the tip a server receives from dinner customers. From randomly selected tables, the owner has collected the data shown in the Excel file Sofrittos.xlsx. The data show the tip, the food bill for the table, the number of diners at the table, the number of minutes the diners were in the restaurant, and whether the meal was on a weekday (Monday through Thursday) or a weekend (Friday through Sunday).

a. Check for the presence of multicollinearity between the independent variables. If it is present, take the necessary steps to eliminate it.

b. Construct a regression model using all the independent variables remaining after part a.

c. Interpret the meaning of the regression coefficients.

d. Test the significance of the overall regression model using α = 0.02.

e. Using the p values, identify which independent variables are significant with α = 0.02.

f. Construct a 98% confidence interval for the regression coefficients for the bill variable from part b. Be sure to interpret the meaning of this confidence interval.

g. Construct a regression model using a best subsets regression that predicts the average tip from a table of diners using the independent variables from part b.

h. With the model from part g, predict the average tip for a table of four weekend diners with a total bill of $ 125 who spent 95 minutes at the table.