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.

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.)

Customer Amount
of Tip Amount
of Bill Number of
Diners Customer Amount
of Tip Amount
of Bill Number of
Diners 1 $5.90 $52.81 5 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 3.75 43.14 3 7 0.50 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 3.55 83.77 4 25 3.00 21.28 2 11 5.45 64.19 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 5.60 65.28 1 15 0.75 4.65 1 30 8.10 59.11 1

Explanation / Answer

answer a1)

answer a2) Tip = 0.9937+ 0.0637Bill +0.3002 Diners

answer a3) the partial regression coefficient of diner is 0.3002, amount needed for tip for addtional one dinner is 0.3002

answer b1)

since one coefficient is different from 0, so we reject null hypothesis

as the p-value of the dinner is less than 0.05

answer c1) t should be more than 2.0595, this is the critical value for t at alpha=0.05,df=25

answer c2) variable dinner should be deleted as the p-value is more than 0.05 and it is not significant at 5% level of significance

answer d)The coefficient of determination is=0.51

answer e)From the graph the residuals does not appear normally distributed as its shape is not bell-shaped

answer f) The residuals look random.

predictor DF coefficient
SE T P VIF constant 1 0.99367 0.72327 1.37 0.1817 0 bill 1 0.06373 0.01429 4.46 0.0002 1.06585 diners 1 0.30017 0.24238 1.24 0.2271 1.06585

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