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.

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 picture Amount of Tip $ 7.60 4.50 1.00 2.40 5.00 4.25 0.50 6.00 5.00 5.50 6.25 6.00 4.00 3.35 0.75 Amount of Bill $ 56.77 28.23 10.65 19.82 28.62 24.83 6.25 49.20 43.26 59.32 51.87 34.99 33.91 23.06 4.65 Number of Diners 2 4 1 3 3 2 1 4 3 7 5 3 4 2 1 Customer 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Amount of Tip $ 3.30 3.50 3.25 5.40 2.25 1.40 3.00 1.25 3.25 3.00 6.25 5.60 2.50 5.45 5.40 Amount of Bill $ 23.59 22.30 32.00 50.02 17.60 49.52 20.27 19.53 27.03 21.28 43.38 28.12 26.25 80.76 93.28 Number of Diners 2 2 2 4 3 1 2 2 3 2 4 4 2 2 7 Click here for the Excel Data File a-1. 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 and complete the table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Predictor Coefficient SE Coefficient t p-value Constant Bill Diners a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Tip = + Bill + Diners a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.) Another diner on average adds to the tip. b-1. Complete the ANOVA table. (Leave no cells blank - be certain to enter "0" wherever required. Round "SS, MS" to 3 decimal places and "F" to 2 decimal places.) Source DF SS MS F p-value Regression Residual Error Total b-2. What is your decision regarding the null-hypothesis? null hypothesis. At least one coefficient is from 0. c-1. Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of significance? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) It would be rejected if t is less than or more than . c-2. Which variable should be deleted? should be deleted. d. Use the equation developed in part (c) to determine the coefficient of determination. (Round your answer to 2 decimal places.) The coefficient of determination e. State true or false. From the graph the residuals appear normally distributed. True False f. Choose the right option from the following graph. The residuals look random. The residuals do not look random. References Worksheet Difficulty: 2 Medium Learning Objective: 14-07 Apply multiple regression techniques to develop a linear model