Question

1. The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Weekly Gross Revenue ($1,000s)	Television Advertising ($1,000s)	Newspaper Advertising ($1,000s)
96	5	1.5
91	2	2
95	4	1.5
93	2.5	2.5
95	3	3.3
94	3.5	2.2
94	2.5	4.1
94	3	2.5

(a) Use α = 0.01 to test the hypotheses

H0:	β1 = β2 = 0
Ha:	β1 and/or β2 is not equal to zero

for the model y = β₀ + β₁x₁ + β₂x₂ + ε, where

x1	=	television advertising ($1,000s)
x2	=	newspaper advertising ($1,000s).

Find the value of the test statistic. (Round your answer to two decimal places.)

_______

Find the p-value. (Round your answer to three decimal places.)

p-value = ______

(b) Use α = 0.05 to test the significance of β₁.

Find the value of the test statistic. (Round your answer to two decimal places.)

_______

Find the p-value. (Round your answer to three decimal places.)

p-value = _______

(c) Use α = 0.05 to test the significance of β₂.

Find the value of the test statistic. (Round your answer to two decimal places.)

_______

Find the p-value. (Round your answer to three decimal places.)

p-value = ______

2. Data for two variables, x and y, follow.

xi	1	2	3	4	5
yi	5	9	7	13	16

(a) Develop the estimated regression equation for these data. (Round your numerical values to two decimal places.)

ŷ = ______

(b) Compute the studentized deleted residuals for these data. (Round your answers to two decimal places.)

xi	yi	Studentized Deleted Residual
1	5
2	9
3	7
4	13
5	16

Answer 1

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Regression Analysis
	R²	0.925
	Adjusted R²	0.896	n	8
	R	0.962	k	2
	Std. Error	0.488	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	14.8070	2	7.4035	31.03	.0015
Residual	1.1930	5	0.2386
Total	16.0000	7
Regression output				confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper	std. coeff.
Intercept	85.7635						0.000
x1	1.8231	0.2321	7.854	.0005	1.2264	2.4198	1.159
x2	0.9849	0.2522	3.905	.0114	0.3365	1.6333	0.576

(a)

Test statistic, F = 31.03

p- value = 0.002

(b)

Option (e)

Test statistic = 7.85

p- value = 0.001

No

(c)

Test statistic = 3.91

p- value = 0.011

Option (a)

No.