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 Amount Number of Amount of Bill S23.59 22.30 32.00 50.02 17.60 65.08 20.27 19.53 27.03 21.28 43.38 28.12 26.25 57.35 84.29 Number of of Bill S86.55 28.23 10.65 19.82 28.62 24.83 6.25 49.20 43.26 53.00 72.29 34.99 33.91 23.06 4.65 Arnut Diners Customer of Tip $3.30 3.50 3.25 5.40 2.25 3.40 3.00 1.25 3.25 3.00 6.25 Customer of Tip 4.50 1.00 241 5.00 4.25 4 4 4 20 21 6 4 23 5.00 3.60 5.95 6.00 25 26 27 28 29 30 4 4 4 3.35 0.75 2.50 9.25 5.20

Explanation / Answer

a-1. Ans:

Predictor Coef SE Coef T P
Constant 2.5891 0.5632 4.60 0.000
Bill 0.07568 0.01499 5.05 0.000
Dinner -0.3661 0.1895 -1.93 0.064

a-2: Ans:

The regression equation is
Tip = 2.59 + 0.0757 Bill - 0.366 Dinner

a-3. Ans: Another diner on average adds $ -0.366 to the tip.

b-1. Ans:

Analysis of Variance

Source DF SS MS F P
Regression 2 52.602 26.301 13.52 0.000
Residual Error 27 52.524 1.945
Total 29 105.125

b-2. Ans:

Reject the null hypothesis. At least one coefficient is different from 0.

C_1. Ans: It would be rejected if t is less than 2.373 or more than -2.373.

c-2. Ans: Dinner should be deleted.

d) The coefficient of the determinant is 0.50.

e) Ans: From this histogram to say true or false is difficult. When I check the normality of the residual, the residual is follow a normal distribution.

TRUE.

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