Southerly Showtime Movie Theaters, Inc. owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. (Let x1 represent Television Advertising ($100s), x2 represent Newspaper Advertising ($100s), and y represent Weekly Gross Revenue ($100s).) Market Weekly Gross Revenue ($100s) Television Advertising ($100s) Newspaper Advertising ($100s) Market 1 101.3 4.9 1.4 Market 2 51.9 2.9 3.1 Market 3 74.8 3.9 1.4 Market 4 126.2 4.4 4.2 Market 5 137.8 3.7 3.9 Market 6 101.4 3.4 2.4 Market 7 237.8 5.1 8.5 Market 8 219.6 7.0 5.7 (a) Develop an estimated linear regression equation with the amount of television advertising as the independent variable. (Round your numerical values to four decimal places.) ŷ = Test for a significant relationship between the amount spent on television advertising and weekly gross revenue at the 0.05 level of significance. (Use the t test.) Find the p-value. (Round your answer to four decimal places.) p-value = How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (a) explain? (Round your answer to two decimal places.) % (c) Develop an estimated linear regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to four decimal places.) ŷ = Test whether the parameter ?0 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = Test whether the parameter ?1 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = Test whether the parameter ?2 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (c) explain? (Round your answer to two decimal places.)

Southerly Showtime Movie Theaters, Inc. owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. (Let x1 represent Television Advertising ($100s), x2 represent Newspaper Advertising ($100s), and y represent Weekly Gross Revenue ($100s).) Market Weekly Gross Revenue ($100s) Television Advertising ($100s) Newspaper Advertising ($100s) Market 1 101.3 4.9 1.4 Market 2 51.9 2.9 3.1 Market 3 74.8 3.9 1.4 Market 4 126.2 4.4 4.2 Market 5 137.8 3.7 3.9 Market 6 101.4 3.4 2.4 Market 7 237.8 5.1 8.5 Market 8 219.6 7.0 5.7 (a) Develop an estimated linear regression equation with the amount of television advertising as the independent variable. (Round your numerical values to four decimal places.) ŷ = Test for a significant relationship between the amount spent on television advertising and weekly gross revenue at the 0.05 level of significance. (Use the t test.) Find the p-value. (Round your answer to four decimal places.) p-value = How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (a) explain? (Round your answer to two decimal places.) % (c) Develop an estimated linear regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to four decimal places.) ŷ = Test whether the parameter ?0 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = Test whether the parameter ?1 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = Test whether the parameter ?2 is equal to zero at a 0.05 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (c) explain? (Round your answer to two decimal places.)

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 115RE: Sales Barnes & Noble had annual sales of $6.8 billion in 2013 and $6.1 billion in 2015. Use the...

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Question

Market	Weekly Gross Revenue ($100s)	Television Advertising ($100s)	Newspaper Advertising ($100s)
Market 1	101.3	4.9	1.4
Market 2	51.9	2.9	3.1
Market 3	74.8	3.9	1.4
Market 4	126.2	4.4	4.2
Market 5	137.8	3.7	3.9
Market 6	101.4	3.4	2.4
Market 7	237.8	5.1	8.5
Market 8	219.6	7.0	5.7

(a)

Develop an estimated linear regression equation with the amount of television advertising as the independent variable. (Round your numerical values to four decimal places.)

ŷ =

Test for a significant relationship between the amount spent on television advertising and weekly gross revenue at the 0.05 level of significance. (Use the t test.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (a) explain? (Round your answer to two decimal places.)

(c)

Develop an estimated linear regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to four decimal places.)

ŷ =

Test whether the parameter ?₀ is equal to zero at a 0.05 level of significance.

Find the p-value. (Round your answer to four decimal places.)

p-value =

Test whether the parameter ?₁ is equal to zero at a 0.05 level of significance.

Find the p-value. (Round your answer to four decimal places.)

p-value =

Test whether the parameter ?₂ is equal to zero at a 0.05 level of significance.

Find the p-value. (Round your answer to four decimal places.)

p-value =

How much of the variation in the sample values of weekly gross revenue (in %) does the model in part (c) explain? (Round your answer to two decimal places.)

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