Question

The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico.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		$6.30		$43.74		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		35.40		3
7		0.50		6.24		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		5.01		38.16		5		25		3.00		21.28		2
11		5.24		53.46		3		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		3.36		56.88		1
15		0.75		4.65		1		30		8.36		71.89		3

Complete the table. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Predictor	Coef	SE Coef	T	P
Constant
Bill
Diners

(a-2)

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. 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 on 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
Regression
Residual Error
Total

(b-2)

What is your decision regarding the null-hypothesis

  (Click to select)Do not rejectReject null hypothesis. At least one coefficient is (Click to select)not differentdifferent from 0.

(c-1)

Conduct an individual test on each of the variables. What is the decision rule? Hint: Use 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

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

(c-2)

Which variable should be deleted?

  (Click to select)Bill onlyDiner onlyNeither should be deleted.

(d)	Use the equation developed in requirement 3 to determine the coefficient of determination. (Round your answer to 2 decimal places.)

The coefficient of determination is

Answer 1

applying multiple regression on above data:

	Coefficients	Standard Error	t Stat	P-value
Constant	-0.327	0.451	-0.725	0.475
bill	0.078	0.012	6.598	0.000
Diners	0.680	0.167	4.080	0.000

a-2)

Tip = -0.327+0.078* Bill + 0.680* Diners

a-3)

  Another diner on average adds $ 0.68 to the tip.

b-1)

	df	SS	MS	F	p value
Regression	2	81.267	40.633	56.68	0.000
Residual	27	19.355	0.717
Total	29	100.622

b-2)

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

c-1)

  It would be rejected if t is less than -2.052 or more than .2.052

c-2)

Neither should be deleted.

d)

The coefficient of determination is =0.81