In: Statistics and Probability
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
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.)
a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.)
b. What is your decision regarding the null-hypothesis?
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.)
c-2. Which variable should be deleted?
ev: 10_17_2017_QC_CS-102203
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