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		$	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			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			5.55			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			0.75			4.65		1	30		5.10			40.95		5

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.)

Predictor	Coefficient	SE Coefficient	t	p-value
Constant
Bill
Diners

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

Tip=

+

Bill+

Diners

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

Another diner of average adds

to the tip.

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.)

Source	DF	SS	MS	F	p-value
Regression
Residual Error
Total

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

Reject

null hypothesis. At least one coefficient is

different

from 0.

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.)

It would be rejected if less than

or more than

c-2. Which variable should be deleted?

Diner only

should be deleted.

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

The coefficient of determination

Answer 1

using excel > data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.896991
R Square	0.804592
Adjusted R Square	0.790118
Standard Error	0.824597
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	2	75.59307	37.79654	55.58638	2.68E-10
Residual	27	18.35893	0.67996
Total	29	93.952
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.320451	0.422622	0.758245	0.454872	-0.5467	1.1876
Bill	0.049976	0.012597	3.967376	0.000482	0.024129	0.075822
Diners	0.680855	0.207436	3.282245	0.002846	0.255232	1.106479

a-1)

	Coefficients	Standard Error	t Stat	P-value
Intercept	0.321	0.423	0.758	0.455
Bill	0.050	0.013	3.967	0.001
Diners	0.681	0.207	3.282	0.003

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

Tip=

0.321

+

0.050

Bill+

0.681

Diners

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

Another diner of average adds

0.681

to the tip.

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.)

ANOVA
	df	SS	MS	F	Significance F
Regression	2	75.593	37.797	55.58	0.000
Residual	27	18.359	0.680
Total	29	93.952

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

Reject

null hypothesis. At least one coefficient is

different

from 0.

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.)

It would be rejected if less than

-2.052

or more than

2.052

c-2. Which variable should be deleted?

no variable

should be deleted.

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

The coefficient of determination

0.81