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. Develop a 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. Write out the regression equation.
How much does another diner add to the amount of the tips?

b. Conduct a global test of hypothesis to determine if at least one of the independent variables is significant. What is your conclusion?

c. Conduct an individual test on each of the variables. Should one or the other be deleted?

d. Use the equation developed in part

(c) to determine the coefficient of determination. Interpret the value.

e. Plot the residuals. Is it reasonable to assume they follow the normal distribution?

f. Plot the residuals against the fitted values. Is it reasonable to conclude they are random?

Transcribed Image Text:

Amount Amount Number of Amount Amount Customer of Tip of Bill Diners Customer of Tip of Bill Number of Diners 1 $7.00 $48.97 5 16 $3.30 $23.59 2 4.50 28.23 4 17 3.50 22.30 3 1.00 10.65 1 18 3.25 32.00 4 2.40 19.82 3 19 5.40 50.02 5 5.00 28.62 3 20 2.25 17.60 6 4.25 24.83 2 21 5.50 44.47 7 0.50 6.24 1 22 3.00 20.27 8 6.00 49.20 4 23 1.25 19.53 9 5.00 43.26 3. 24 3.25 27.03 10 4.75 31.36 4 25 3.00 21.28 222432232 11 5.25 32.87 26 6.25 43.38 12 6.00 34.99 3 27 5.60 28.12 13 4.00 33.91 4 28 2.50 26.25 14 3.35 23.06 2 29 9.25 56.81 15 0.75 4.65 1 30 8.25 50.65 255