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
H_{0}: | β_{1} = β_{2} = 0 |
H_{a}: | β_{1} and/or β_{2} is not equal to zero |
for the model
y = β_{0} + β_{1}x_{1} + β_{2}x_{2} + ε,
where
x_{1} | = | television advertising ($1,000s) |
x_{2} | = | 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 β_{1}.
Find the value of the test statistic. (Round your answer to two decimal places.)
c) Use α = 0.05 to test the significance of β_{2}.
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 =
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
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