Question

In: Statistics and Probability

The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of...

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 $ 7.35 $ 60.83 4 16 $ 3.30 $ 23.59 2
2 4.50 28.23 4 17 3.50 22.30 2
3 1.00 10.65 1 18 3.25 32.00 2
4 2.40 19.82 3 19 5.40 50.02 4
5 5.00 28.62 3 20 2.25 17.60 3
6 4.25 24.83 2 21 1.25 45.60 1
7 .50 6.25 1 22 3.00 20.27 2
8 6.00 49.20 4 23 1.25 19.53 2
9 5.00 43.26 3 24 3.25 27.03 3
10 3.80 65.45 1 25 3.00 21.28 2
11 6.10 71.61 1 26 6.25 43.38 4
12 6.00 34.99 3 27 5.60 28.12 4
13 4.00 33.91 4 28 2.50 26.25 2
14 3.35 23.06 2 29 8.60 63.90 3
15 .75 4.65 1 30 9.30 62.63 6

  Click here for the Excel Data File

  1. 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.)

  1. a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

  1. a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.)

  1. b. What is your decision regarding the null-hypothesis?

  1. 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.)

  1. c-2. Which variable should be deleted?

  1. Use the equation developed in part (c) to determine the coefficient of determination. (Round your answer to 2 decimal places.)

ev: 10_17_2017_QC_CS-102203

Solutions

Expert Solution

usig excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.906549
R Square 0.82183
Adjusted R Square 0.808633
Standard Error 0.974187
Observations 30
ANOVA
df SS MS F Significance F
Regression 2 118.1946 59.09728 62.27053 7.7E-11
Residual 27 25.6241 0.949041
Total 29 143.8187
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.78676 0.473669 -1.66099 0.108286 -1.75865 0.185131
Amount of Bill 0.073437 0.010681 6.875521 2.18E-07 0.051522 0.095353
Number of Diners 0.901452 0.155207 5.808061 3.51E-06 0.582993 1.21991

1) 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 is

amount of tips =-0.787 +0.073 * Amount of Bill ($) +0.902*Diners

2) 0.902 $ increase the amount of the tips for every add in dinner.

3) ANOVA table is

ANOVA
df SS MS F
Regression 2 118.1946 59.0973 62.27
Residual 27 25.6241 0.9490
Total 29 143.8187

4) we will reject the null hypothesis

5) if p value of individual variable is greater then 0.05 then we say that variable is not significant

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.78676 0.473669 -1.66099 0.108286 -1.75865 0.185131
Amount of Bill 0.073437 0.010681 6.875521 2.18E-07 0.051522 0.095353
Number of Diners 0.901452 0.155207 5.808061 3.51E-06 0.582993 1.21991

p value for Dinners is less then 0.05 so that is significant variable

p value for Amount of Bill ($) is less then 0.05 so that is also significant variable

6) No any variable should be deleted

7) the coefficient of determination is 0.82


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