The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (2). Values of y, ₁, and 2 are expressed in thousands of dollars. The estimated regression equation was Weekly Gross Television Advertising ($1000s) ($1000s) 96 5.0 90 2.0 2.0 95 4.0 1.5 TIT 92 2.5 2.5 95 3.0 3.3 94 3.5 2.5 3.0 Revenue 94 94 Newspaper Advertising ($1000s) 1.5 2.3 4.2 2.5 ŷ= 83.23 +2.291 + 1.302 a. What is the gross revenue expected for a week where $3,500 is spent on television (₁= 3.5) and $1,800 is spent on newspaper advertising (x2= 1.8) (to 3 decimals)? thousand $ b. Provide a 95% prediction interval for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a) (to 2 decimals). ( $_ thousand, $ thousand)
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (2). Values of y, ₁, and 2 are expressed in thousands of dollars. The estimated regression equation was Weekly Gross Television Advertising ($1000s) ($1000s) 96 5.0 90 2.0 2.0 95 4.0 1.5 TIT 92 2.5 2.5 95 3.0 3.3 94 3.5 2.5 3.0 Revenue 94 94 Newspaper Advertising ($1000s) 1.5 2.3 4.2 2.5 ŷ= 83.23 +2.291 + 1.302 a. What is the gross revenue expected for a week where $3,500 is spent on television (₁= 3.5) and $1,800 is spent on newspaper advertising (x2= 1.8) (to 3 decimals)? thousand $ b. Provide a 95% prediction interval for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a) (to 2 decimals). ( $_ thousand, $ thousand)
Chapter4: Linear Functions
Section: Chapter Questions
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Transcribed Image Text:The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (2). Values of y, ₁, and 2 are expressed in thousands
of dollars.
The estimated regression equation was
Weekly Gross
Revenue
($1000s)
96
90
95
92
95
94
94
94
Television
Advertising
($1000s)
5.0
2.0
4.0
2.5
3.0
3.5
2.5
3.0
Newspaper
Advertising
($1000s)
1.5
2.0
1.5
2.5
3.3
2.3
4.2
2.5
Check My Work
ŷ = 83.23 +2.29x1 + 1.30x2
a. What is the gross revenue expected for a week where $3,500 is spent on television (1= 3.5) and $1,800 is spent on newspaper advertising (x2 = 1.8) (to 3 decimals)?
thousand
$
b. Provide a 95% prediction interval for next week's revenue, assuming that the advertising expenditures will be allocated as in part (a) (to 2 decimals).
($
thousand, $
thousand)
Check My Work
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