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 your numerical values to two decimal places. Let x1 represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) ŷ = (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x1 represent the amount of television advertising in $1,000s, x2 represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) ŷ = (c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? , it is ? in part (a) and ? in part (b). (d) Predict weekly gross revenue (in dollars) for a week when $3,700 is spent on television advertising and $1,100 is spent on newspaper advertising. (Round your answer to the nearest cent.) $

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 12PPS

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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 your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.)

ŷ =

(b)

Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.)

ŷ =

(c)

Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?

, it is ? in part (a) and ? in part (b).

(d)

Predict weekly gross revenue (in dollars) for a week when $3,700 is spent on television advertising and $1,100 is spent on newspaper advertising. (Round your answer to the nearest cent.)

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