The Conch Caf, located in Gulf Shores, Alabama, features casual lunches with a great view of the

The Conch Café, 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, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.

a. Compute and report the correlation matrix. Review the correlation coefficients for the independent variables. Do they indicate multicollinearity? Why?

b. Based on the results in part (a), would it be logical to create a multiple regression equation to predict “amount of tips”? Why?

c. Compute and report the regression equation that predicts “amount of bill” with “number of diners.”

d. Report the regression equation that predicts “amount of tip” with “amount of bill.” Report the coefficient of determination. Interpret the regression coefficient.

e. Using the regression equations from parts (c) and (d), predict the tip based on a bill amount of $100.

f. Plot the residuals versus the fitted values. Do the plot satisfy the assumption of randomness?

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Amount Amount Number of Customer of Tip of Bill Diners 1 $7.00 $48.97 2 4.50 28.23 4 3 1.00 10.65 1 28 2.50 26.25 2 29 9.25 56.81 30 8.25 50.65 ...