15.07.2022 - 07:06

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

Question:

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, 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.

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

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.

b) Interpret the coefficients in the regression equation.

c) Develop a regression equation including an interaction term. Is there a significant interaction between the amount of the bill and the number of diners? You must show your creation of the interaction variable and explain the meaning of the interaction.