Question

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
90	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 =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables

Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.    

Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b)

Use α = 0.05 to test the significance of

β₁.

State the null and alternative hypotheses.

H0: β1 = 0

Ha: β1 > 0

H0: β1 = 0

Ha: β1 < 0

    

H0: β1 = 0

Ha: β1 ≠ 0

H0: β1 < 0

Ha: β1 = 0

H0: β1 ≠ 0

Ha: β1 = 0

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 =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that β₁ is significant.

Reject H₀. There is sufficient evidence to conclude that β₁ is significant.  

Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.

Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

Should x₁ be dropped from the model? Yes or No?

(c)

Use α = 0.05 to test the significance of

β₂.

State the null and alternative hypotheses.

H0: β2 < 0

Ha: β2 = 0

H0: β2 = 0

Ha: β2 < 0

    

H0: β2 = 0

Ha: β2 ≠ 0

H0: β2 ≠ 0

Ha: β2 = 0

H0: β2 = 0

Ha: β2 > 0

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 =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.    

Reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.

Should x₂ be dropped from the model?Yes or No ?  

Answer 1

from excel: data-data analysis: regression:

	df	SS	MS	F	Significance F
Regression	2	20.64804	10.32402	23.17958	0.002957
Residual	5	2.226964	0.445393
Total	7	22.875
	Coefficients	Standard Error	t Stat	P-value
Intercept	83.84478	1.661211	50.47208	0.0000
x1	2.164392	0.317971	6.806889	0.001042
x2	1.278048	0.344214	3.71295	0.013813

a)

value of the test statistic=23.18

p-value =0.003

Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.

b)

H0: β1 = 0Ha: β1 ≠ 0

value of the test statistic =6.81

p-value =0.001

Reject H0. There is sufficient evidence to conclude that β1 is significant

no ,x1 should not be dropped

c)

H0: β2 = 0

Ha: β2 ≠ 0

value of the test statistic. =3.71

p value =0.014

Reject H0. There is sufficient evidence to conclude that β2 is significant.   

no ,x 2 should not be dropped