A statistical program is recommended.
The owner of a movie theater company would like to predictweekly 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 | 2.3 |
| 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 equalto 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 twodecimal places.)
Find the p-value. (Round your answer to three decimalplaces.)
p-value =
State your conclusion.
Reject H0. There is sufficient evidence toconclude that there is a significant relationship among thevariables.Do not reject H0. There isinsufficient evidence to conclude that there is a significantrelationship among thevariables.     RejectH0. There is insufficient evidence to concludethat there is a significant relationship among the variables. Donot reject H0. There is sufficient evidence toconclude that there is a significant relationship among thevariables.
(b)
Use α = 0.05 to test the significance of
β1.
State the null and alternative hypotheses.
    Â
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find the p-value. (Round your answer to three decimalplaces.)
p-value =
State your conclusion.
Reject H0. There is insufficient evidence toconclude that β1 is significant.Do not rejectH0. There is insufficient evidence to concludethat β1 issignificant.     RejectH0. There is sufficient evidence to concludethat β1 is significant.Do not rejectH0. There is sufficient evidence to concludethat β1 is significant.
Should
x1
be dropped from the model?
YesNo  Â
(c)
Use α = 0.05 to test the significance of
β2.
State the null and alternative hypotheses.
    Â
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find the p-value. (Round your answer to three decimalplaces.)
p-value =
State your conclusion.
Reject H0. There is sufficient evidence toconclude that β2 is significant.RejectH0. There is insufficient evidence to concludethat β2 issignificant.     Do not rejectH0. There is sufficient evidence to concludethat β2 is significant.Do not rejectH0. There is insufficient evidence to concludethat β2 is significant.
Should
x2
be dropped from the model?
YesNo  Â
