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 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 $2,000 is spent on television advertising (x1 = 2) and $2,000 is spent on newspaper advertising (x2 = 2)? (Round your answer to the nearest dollar.) $ __________. (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.) $ to $_. 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.) $ to $ ________.

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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Question

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

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 $2,000 is spent on television advertising

(x₁ = 2) and $2,000 is spent on newspaper advertising (x₂ = 2)? (Round your answer to the nearest dollar.)

$ __________________.

(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.)

$__________ to $_______________.

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.)

$____________ to $ ________________.

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