Question
In: Statistics and Probability
A statistical program is recommended. The owner of a movie theater company would like to predict...
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 =
Solutions
Expert Solution
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 =
orchestra answered 1 year agoRelated Solutions
A statistical program is recommended. The owner of a movie theater company would like to predict...
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
2.3
94
2.5
4.2
94
3
2.5
(a)
Use α = 0.01 to test the hypotheses
H0:
β1 =...
A statistical program is recommended. The owner of Showtime Movie Theaters, Inc., would like to predict...
A statistical program is recommended.
The owner of Showtime Movie Theaters, Inc., 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
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
a) Predict weekly gross revenue (in dollars) for a week when
$3,300...
The owner of a movie theater company would like to predict weekly gross revenue as a...
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...
The owner of a movie theater company would like to predict weekly gross revenue as a...
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
2.3
94
2.5
4.1
94
3
2.5
(a)
Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...
The owner of a movie theater company would like to predict weekly gross revenue as a...
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
2.3
94
2.5
4.1
94
3
2.5
1. Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks follow
has been collected in the Microsoft Excel Online file below. Open
the spreadsheet and perform the required analysis to answer the
questions below.
Weekly Gross Revenue ($1000s)
Television Advertising ($1000s)
Newspaper Advertising($1000s)
97
6
1.5
91
2
2
96
5
1.5
93
2.5
2.5
95
4
3.3
94
3.5
2.3
95...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., 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 ($1000s) Televison Advertising ($1000s)
Newspaper Advertising ($1000s) 97 5 1.5 90 2 3 96 4 2.5 92 2.5 2.5
95 3 3.3 95 3.5 2.3 95 2.5 4.2 95 3 3.5 Use = .01 to test the
hypotheses for the model y = 0 + 1 x 1...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., 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 ($1000s)
Televison Advertising ($1000s)
Newspaper Advertising ($1000s)
97
5
1.5
90
2
3
96
4
2.5
93
3.5
2.5
96
3
4.3
94
3.5
2.3
95
2.5
5.2
95
3
3.5
a. Use to test the hypotheses
and/or is not equal to zero
for the model , where
television advertising...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., 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
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
(a)
Develop an estimated regression equation with the amount of
television advertising as the independent variable. (Round...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., 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
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
(a)
Develop an estimated regression equation with the amount of
television advertising as the independent variable. (Round...
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