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.)

  Diners

Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

  Tip =  +  Bill +  Diners

  Another diner on average adds $  to the tip.

  Total

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.)

  It would be rejected if t is less than  or more than

  

  

  

Customer Amount
of Tip Amount
of Bill Number of
Diners Customer Amount
of Tip Amount
of Bill Number of
Diners 1 $7.75 $58.38 1 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 3.10 63.78 1 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 3.80 51.97 4 25 3.00 21.28 2 11 5.45 35.45 5 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 5.90 45.88 7 15 0.75 4.65 1 30 8.25 62.25 1

Explanation / Answer

a1)

a2)

Tip^ = 0.33949901 + 0.089668465 * Bill + 0.287715361 * Diner

a3)

b2 = 0.287715361 = 0.29

b1)

c1 ) df = n-k-1 = 27

for alpha = 0.05

t-critical = 2.052

hence if |TS| > t-critical ,the variable is significant

here Bill has t= 6.066 > 2.052 ,hence it is significant

Diner has t = 1.75 < 2.052 . hence insignificant

we can remove Diners

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Thanks and have a good day!

Coefficients Standard Error t Stat P-value Intercept 0.33949901 0.600367228 0.565485579 0.57641305 Bill 0.089668465 0.014780968 6.066481028 1.776E-06 Diners 0.287715361 0.164170233 1.752542811 0.091031053

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