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 Television Gross Revenue ($1,000s) 96 90 95 92 95 94 94 94 Newspaper Advertising Advertising ($1,000s) ($1,000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x₂), in thousands of dollars, and newspaper advertising (x₂), in thousands of dollars. The estimated regression equation was ŷ= 83.2 +2.29x₂ + 1.30x₂. (a) What is the gross revenue (in dollars) expected for a week when $3,000 is spent on television advertising (x₁=3) and $2,500 is spent on newspaper advertising (x₂2.5)? (Round your answer to the nearest dollar.) $ 103 x (b) Provide a 95% confidence interval (in dollars) for the mean revenue of all weeks with the expenditures listed in part (a). (Round your answers to the nearest dollar.) $93 x to $ 94 x (c) Provide a 95% prediction interval (in dollars) for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a). (Round your answers to the nearest dollar.) $ 92 1x to $95 x
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 Television Gross Revenue ($1,000s) 96 90 95 92 95 94 94 94 Newspaper Advertising Advertising ($1,000s) ($1,000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x₂), in thousands of dollars, and newspaper advertising (x₂), in thousands of dollars. The estimated regression equation was ŷ= 83.2 +2.29x₂ + 1.30x₂. (a) What is the gross revenue (in dollars) expected for a week when $3,000 is spent on television advertising (x₁=3) and $2,500 is spent on newspaper advertising (x₂2.5)? (Round your answer to the nearest dollar.) $ 103 x (b) Provide a 95% confidence interval (in dollars) for the mean revenue of all weeks with the expenditures listed in part (a). (Round your answers to the nearest dollar.) $93 x to $ 94 x (c) Provide a 95% prediction interval (in dollars) for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a). (Round your answers to the nearest dollar.) $ 92 1x to $95 x
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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 Television
Newspaper
Gross Advertising Advertising
($1,000s) ($1,000s)
Revenue
($1,000s)
96
90
95
92
95
94
94
94
5.0
2.0
4.0
2.5
3.0
3.5
2.5
3.0
1.5
2.0
1.5
2.5
3.3
2.3
4.2
2.5
The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x₁), in thousands of dollars, and newspaper advertising (x₂), in thousands of dollars. The estimated regression equation was
ŷ = 83.2 + 2.29x₁ + 1.30x₂.
(a) What is the gross revenue (in dollars) expected for a week when $3,000 is spent on television advertising (x₁ = 3) and $2,500 is spent on newspaper advertising (x₂ = 2.5)? (Round your answer to the nearest dollar.)
$ 103
x
(b) Provide a 95% confidence interval (in dollars) for the mean revenue of all weeks with the expenditures listed in part (a). (Round your answers to the nearest dollar.)
$93
x to $ 94
x
(c) Provide a 95% prediction interval (in dollars) for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a). (Round your answers to the nearest dollar.)
$ 92
X to $ 95
X
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