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.


Customer Amount of Tip Amount of Bill Number of Diners Customer Amount of Tip Amount of Bill Number of Diners
1 $ 7.00 $ 48.85 3 16 $ 3.30 $ 23.47 2
2 3.30 28.35 2 17 3.50 22.30 2
3 1.00 10.77 3 18 3.13 32.00 2
4 4.80 19.94 3 19 5.40 50.14 4
5 5.00 28.74 3 20 2.13 17.60 3
6 4.13 24.95 2 21 5.50 44.35 4
7 .50 6.36 1 22 3.00 20.39 2
8 6.00 49.20 4 23 1.13 19.41 2
9 5.00 43.38 3 24 3.13 27.15 3
10 4.63 31.24 4 25 3.00 21.16 2
11 5.13 32.99 4 26 6.61 43.50 4
12 6.00 34.87 3 27 5.60 28.00 4
13 4.00 34.03 4 28 2.50 26.37 5
14 3.23 22.94 2 29 9.13 56.69 5
15 0.99 4.77 1 30 8.13 50.77 5

picture 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.


A scatterplot titled residuals versus the fitted values (response is tip). The vertical axis plots residuals ranging from -1.0 to 1.5 in increments of 0.5. The horizontal axis plots fitted value ranging from 0 to 8 in increments of 1. The data is scattered.

multiple choice 3
The residuals look random.
The residuals do not look random.