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	3.2
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.)

Use α = 0.05 to test the significance of β₁.

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

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

Sol:

Perform multiple regression in excel

Data >Data analysis>Regresssion

select Y as Gross revenue

Television Ad and newspaper ad as X

we get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.960859
R Square	0.92325
Adjusted R Square	0.89255
Standard Error	0.495581
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	14.772	7.385998	30.07316	0.001632
Residual	5	1.228005	0.245601
Total	7	16
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	85.72849	1.246164	68.79391	1.23E-08	82.52512	88.93185
Television Advertising	1.831811	0.237159	7.723992	0.000581	1.222175	2.441446
Newspaper	0.997997	0.260566	3.830115	0.012246	0.328191	1.667802

(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.)

F=30.07

p=0.002

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

Use α = 0.05 to test the significance of β1.

t=7.72

p=0.001

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

Use α = 0.05 to test the significance of β2.

t=3.83

p=0.012

p-value =