The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico.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 | $6.30 | $43.74 | 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 | 5.40 | 35.40 | 3 | ||||||||
7 | 0.50 | 6.24 | 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 | 5.01 | 38.16 | 5 | 25 | 3.00 | 21.28 | 2 | ||||||||
11 | 5.24 | 53.46 | 3 | 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 | 3.36 | 56.88 | 1 | ||||||||
15 | 0.75 | 4.65 | 1 | 30 | 8.36 | 71.89 | 3 | ||||||||
Complete the table. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) |
Predictor | Coef | SE Coef | T | P | |
Constant | |||||
Bill | |||||
Diners | |||||
(a-2) |
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. 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 |
Regression | |||||
Residual Error | |||||
Total | |||||
(b-2) | What is your decision regarding the null-hypothesis |
(Click to select)Do not rejectReject null hypothesis. At least one coefficient is (Click to select)not differentdifferent from 0. |
(c-1) |
Conduct an individual test on each of the variables. What is the decision rule? Hint: Use 0.05 significance level. (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? |
(Click to select)Bill onlyDiner onlyNeither should be deleted. |
(d) |
Use the equation developed in requirement 3 to determine the coefficient of determination. (Round your answer to 2 decimal places.) |
The coefficient of determination is |
applying multiple regression on above data:
Coefficients | Standard Error | t Stat | P-value | |
Constant | -0.327 | 0.451 | -0.725 | 0.475 |
bill | 0.078 | 0.012 | 6.598 | 0.000 |
Diners | 0.680 | 0.167 | 4.080 | 0.000 |
a-2)
Tip = -0.327+0.078* Bill + 0.680* Diners
a-3)
Another diner on average adds $ 0.68 to the tip.
b-1)
df | SS | MS | F | p value | |
Regression | 2 | 81.267 | 40.633 | 56.68 | 0.000 |
Residual | 27 | 19.355 | 0.717 | ||
Total | 29 | 100.622 |
b-2)
Reject null hypothesis. At least one coefficient is different from 0.
c-1)
It would be rejected if t is less than -2.052 or more than .2.052
c-2)
Neither should be deleted.
d)
The coefficient of determination is =0.81
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