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	2.3
94	2.5	4.1
94	3	2.5

1. 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).

1b. Find the value of the test statistic. (Round your answer to two decimal places.)

1c. Find the p-value. (Round your answer to three decimal places.)

p-value =

1d. State your conclusion.

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

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

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

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

2. Use α = 0.05 to test the significance of β₁.

2a. State the null and alternative hypotheses.

(a) H0: β1 ≠ 0

Ha: β1 = 0

(b) H0: β1 = 0

Ha: β1 ≠ 0

    

(c) H0: β1 = 0

Ha: β1 > 0

(d) H0: β1 = 0

Ha: β1 < 0

(e) H0: β1 < 0

Ha: β1 = 0

2b. Find the value of the test statistic. (Round your answer to two decimal places.)

2c. Find the p-value. (Round your answer to three decimal places.)

p-value =

2d. State your conclusion.

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

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

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

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

2e. Should x₁ be dropped from the model?

Yes

No

3.Use α = 0.05 to test the significance of β₂.

3a. State the null and alternative hypotheses.

(a) H0: β2 < 0

Ha: β2 = 0

(b)H0: β2 ≠ 0

Ha: β2 = 0

    

(c)H0: β2 = 0

Ha: β2 ≠ 0

(d)H0: β2 = 0

Ha: β2 > 0

(e)H0: β2 = 0

Ha: β2 < 0

3b. Find the value of the test statistic. (Round your answer to two decimal places.)

3c. Find the p-value. (Round your answer to three decimal places.)

p-value =

3d. State your conclusion.

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

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

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

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

3e. Should x₂ be dropped from the model?

Yes

No

Answer 1

Applying regression on above data:

Regression Statistics
Multiple R	0.948392
R Square	0.899448
Adjusted R Square	0.859227
Standard Error	0.678253
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	20.57487	10.28743	22.36268	0.003206
Residual	5	2.300134	0.460027
Total	7	22.875
	Coefficients	Standard Error	t Stat	P-value
Intercept	83.87376	1.688853	49.66316	6.26E-08
x1	2.155039	0.32232	6.686029	0.001131
x2	1.271898	0.350232	3.631583	0.015036

a)

value of the test statistic =27.36

p-value =0.003

since p value <0.05

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

2)

a) option B

b) value of the test statistic =6.69

c) p value =0.001

d) (c) Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

No

3a) option C

b) value of the test statistic =3.63

c) p value =0.015

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

No