The Conch Caf, 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	Number of Diners	Customer	Amount of Tip	Amount of Bill	Number of Diners
1	$ 8.00	$ 48.80	3	16	$ 3.30	$ 23.42	2
2	2.80	28.40	2	17	3.50	22.30	2
3	1.00	10.82	3	18	3.08	32.00	2
4	5.80	19.99	3	19	5.40	50.19	4
5	5.00	28.79	3	20	2.08	17.60	3
6	4.08	25.00	2	21	5.50	44.30	4
7	.50	6.41	1	22	3.00	20.44	2
8	6.00	49.20	4	23	1.08	19.36	2
9	5.00	43.43	3	24	3.08	27.20	3
10	4.58	31.19	4	25	3.00	21.11	2
11	5.08	33.04	4	26	6.76	43.55	1
12	6.00	34.82	3	27	5.60	27.95	4
13	4.00	34.08	4	28	2.50	26.42	2
14	3.18	22.89	2	29	9.08	56.64	5
15	1.09	4.82	1	30	8.08	50.82	5

Click here for the Excel Data File a-1. Compute the following correlation matrix. (Round your answers to 4 decimal places.)

a-2. Which of the independent variables is stronger?

a-3. Do they indicate multicollinearity? multiple choice 1

Yes

No

b-1. Would it be logical to create a multiple regression equation to predict amount of tips? multiple choice 2

Yes

No

c. Compute and report the regression equation that predicts amount of bill with number of diners. (Negative amounts should be indicated by a minus sign. Round "amount of bill" to 3 decimal places and "number of diners" to 4 decimal places.)

d-1. Report the regression equation that predicts amount of tip with amount of bill. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

d-2. Report the coefficient of determination. (Round your answer to 2 decimal places.)

d-3. Interpret the regression coefficient. (Round your answer to 4 decimal places.)

e. Predict the tip based on a bill amount of $100. (Round your answer to 3 decimal places.)

f. Choose the right option from the following graph.

multiple choice 3

The residuals look random.

The residuals do not look random.

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