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.)

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.)

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 =

Answer 1

using excel: data-data analysis: regression :below is the output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9501
R Square	0.9026
Adjusted R Square	0.8637
Standard Error	0.6674
Observations	8.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	2.0000	20.6480	10.3240	23.1796	0.0030
Residual	5.0000	2.2270	0.4454
Total	7.0000	22.8750
	Coefficients	Standard Error	t Stat	P-value
Intercept	83.8448	1.6612	50.4721	0.0000
x1	2.1644	0.3180	6.8069	0.0010
x2	1.2780	0.3442	3.7130	0.0138

a)

value of the test statistic F =23.18

p value =0.003

b)

value of the test statistic =6.81

p value =0.001

c)

value of the test statistic =3.71

p value =0.014