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.

Customer		Amount of Tip			Amount of Bill			Number of Diners	Customer	Amount of Tip			Amount of Bill			Number of Diners
1		$	6.05		$	73.22		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		1.40			41.80		5
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			5.60			38.99		5	25		3.00			21.28		2
11			6.00			84.48		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		5.80			44.52		6
15			0.75			4.65		1	30		5.40			89.01		5

1. 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.)

1. a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

1. a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.)

1. 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.)

1. b-2. What is your decision regarding the null-hypothesis?
   
   

2. Use the equation developed in part (c) to determine the coefficient of determination. (Round your answer to 2 decimal places.)

Answer 1

applying multiple regression"

	Coefficients	Standard Error	t Stat	P-value
Intercept	1.027	0.575	1.786	0.085
bill	0.056	0.012	4.642	0.000
diners	0.331	0.175	1.892	0.069

a-2)

regression equation: Tip =1.027+0.056*Bill+0.331*Diner

a-3)

another diner adds $ 0.33

b-1)

	df	SS	MS	F	p value
Regression	2	52.655	26.328	17.41	0.0000
Residual	27	40.837	1.512
Total	29	93.492

b-2_

since p value <0.05 , we reject the null hypothesis

coefficient of determination =0.56