The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a
ID: 3174159 • Letter: T
Question
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.
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. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Conduct an individual test on each of the variables. What is the decision rule at the .05 level of significance? (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Use the equation developed in part (c) to determine the coefficient of determination. (Round your answer to 2 decimal places.)
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.
Explanation / Answer
Using Minitab:
Regression Analysis: Amount of tip versus Number of Diners, Amount of Bill
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 85.990 42.995 23.16 0.000
Number of Diners 1 1.928 1.928 1.04 0.317
Amount of Bill 1 69.954 69.954 37.67 0.000
Error 27 50.134 1.857
Total 29 136.124
Model Summary
S R-sq R-sq(adj) R-sq(pred)
1.36265 63.17% 60.44% 46.39%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 0.653 0.658 0.99 0.330
Number of Diners 0.201 0.197 1.02 0.317 1.09
Amount of Bill 0.0922 0.0150 6.14 0.000 1.09
Regression Equation
Amount of tip = 0.653 + 0.201 Number of Diners + 0.0922 Amount of Bill
Thus, an additional diner adds 0.201$ to the tip.
Hope this will helpful you. Thanks :-)
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