Question

A statistical program is recommended.

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	4.2
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.

State the null and alternative hypotheses.

H₀: β₁ = 0

H_a: β₁ < 0

H₀: β₁ = 0

H_a: β₁ > 0

    

H₀: β₁ ≠ 0

H_a: β₁ = 0

H₀: β₁ = 0

H_a: β₁ ≠ 0

H₀: β₁ < 0

H_a: 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 =

c.

Use α = 0.05 to test the significance of

β₂.

State the null and alternative hypotheses.

H₀: β₂ = 0

H_a: β₂ ≠ 0

H₀: β₂ = 0

H_a: β₂ < 0

    

H₀: β₂ < 0

H_a: β₂ = 0

H₀: β₂ = 0

H_a: β₂ > 0

H₀: β₂ ≠ 0

H_a: 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 =  

Answer 1

applying regression on above:

ANOVA
	df	SS	MS	F	Significance F
Regression	2	14.80	7.40	30.94	0.0015
Residual	5	1.20	0.24
Total	7	16.00
	Coefficients	Standard Error	t Stat	P-value
Intercept	85.86	1.20	71.70	0.0000
TV ads	1.82	0.23	7.84	0.0005
News ads	0.95	0.24	3.90	0.0114

a) value of the test statistic =30.94

p value =0.002

b)

H0: β1 = 0

Ha: β1 ≠ 0

value of the test statistic =7.84

p value =0.001

c)

H0: β2 = 0

Ha: β2 ≠ 0

value of the test statistic =3.90

p value =0.011