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 Revenue ($1,000s) ($1,000s) ($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 x, represent the amount of television advertising in $1,000s and y represent the weekly gros revenue in $1,000s.) 988.64 +1.60x1 X (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 x, 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= 83.23 +2.29x + 1.30x2 (e) Is the estimated regression equation coefficient for television advertising expenditures the same in nart (a) and in part (h)?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 11CT
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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
Gross
Newspaper
Advertising Advertising
($1,000s) ($1,000s)
Revenue
($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
1
(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.)
y = 88.64 + 1.60x1
X
(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 = 83.23 +2.29x₁ + 1.30x₂
(c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?
No
it is 1.60
in part (a) and 2.29
in part (b).
I
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 Gross Newspaper Advertising Advertising ($1,000s) ($1,000s) Revenue ($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 1 (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.) y = 88.64 + 1.60x1 X (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 = 83.23 +2.29x₁ + 1.30x₂ (c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? No it is 1.60 in part (a) and 2.29 in part (b). I
(c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?
No
, it is 1.60
✓in part (a) and 2.29
✔
in part (b).
Interpret the coefficient in each case.
O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant.
O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant.
O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with
television advertising held constant.
O In part (a) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising expenditure.
O In part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising expenditure with television advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with
newspaper advertising held constant.
(d) Predict weekly gross revenue (in dollars) for a week when $3,300 is spent on television advertising and $1,500 is spent on newspaper advertising. (Round your answer to the nearest cent.)
$ 94
x
Transcribed Image Text:(c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? No , it is 1.60 ✓in part (a) and 2.29 ✔ in part (b). Interpret the coefficient in each case. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. O In part (a) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising expenditure. O In part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising expenditure with television advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. (d) Predict weekly gross revenue (in dollars) for a week when $3,300 is spent on television advertising and $1,500 is spent on newspaper advertising. (Round your answer to the nearest cent.) $ 94 x
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