The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a

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.

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-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.)

b-2. 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?

The residuals do not look random.

EXCEL FILE:

Customer Amount of Tip Amount of Bill Number of Diners Customer Amount of Tip Amount of Bill Number of Diners 1 $ 5.70 $ 61.85 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 63.38 3 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 5.55 62.78 4 25 3.00 21.28 2 11 6.25 71.15 4 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 7.00 76.97 5 15 .75 4.65 1 30 5.10 40.95 5

Explanation / Answer

a) Amount_of_Tip^ =b0 + b1*Amount_of_Bill + b2 * Diners

b)  Amount_of_Tip^ = 0.32045 + 0.049975586 *Amount_of_Bill + 0.680855311* Diners

c)

0.680855311

b1)See Table above

b2) sicne significance F is less than 0.05

we reject the null

c1) p-value for both Bill and Diners is less than 0.05 ,hence they are significant

where-as p-value for intercept is more thann 0.05

c2) b0 should be deleted ,

R^2 for model is   

0.804592467

for model without intercept R^2 is

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Feel free to comment on the answer if some part is not clear or you would like to be elaborated upon.
Thanks and have a good day!

SUMMARY OUTPUT Regression Statistics Multiple R 0.896990784 R Square 0.804592467 Adjusted R Square 0.790117835 Standard Error 0.824597063 Observations 30 ANOVA df SS MS F Significance F Regression 2 75.59307148 37.79653574 55.58638477 2.67736E-10 Residual 27 18.35892852 0.679960316 Total 29 93.952 Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.320451183 0.422622168 0.758245089 0.454872335 -0.546697878 Amount of Bill ($) 0.049975586 0.012596634 3.967376116 0.000482431 0.024129427 Diners 0.680855311 0.207435849 3.282245159 0.002845558 0.255232106

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