The owner of a movie theater company 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 1.5 91 2 2 95 4 1.5 92 2.5 2.5 95 3 3.2 94 3.5 2.2 94 2.5 4.2 94 3 2.5 (a) Use ? = 0.01 to test the hypotheses H0: B1 = B2 = 0 Ha: B1 and/or B2 is not equal to zero for the model y = B0 + B1x1 + B2x2 + E, where x1 = television advertising ($1,000s) x2 = newspaper advertising ($1,000s). Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. - Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. (b)Use a = 0.05 to test the significance of B1. State the null and alternative hypotheses. H0: B1 ≠ 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 ≠ 0 H0: B1 < 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 < 0 H0: B1 = 0 Ha: B1 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is insufficient evidence to conclude that B1 is significant. -Do not reject H0. There is sufficient evidence to conclude that B1 is significant. - Do not reject H0. There is insufficient evidence to conclude that B1 is significant. -Reject H0. There is sufficient evidence to conclude that B1 is significant. Should x1 be dropped from the model? Yes No (c) Use ? = 0.05 to test the significance of ?2. State the null and alternative hypotheses. H0: B2 = 0 Ha: B2 < 0 H0: B2 ≠ 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 ≠ 0 H0: B2 < 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ??

The owner of a movie theater company 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 1.5 91 2 2 95 4 1.5 92 2.5 2.5 95 3 3.2 94 3.5 2.2 94 2.5 4.2 94 3 2.5 (a) Use ? = 0.01 to test the hypotheses H0: B1 = B2 = 0 Ha: B1 and/or B2 is not equal to zero for the model y = B0 + B1x1 + B2x2 + E, where x1 = television advertising ($1,000s) x2 = newspaper advertising ($1,000s). Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. - Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. (b)Use a = 0.05 to test the significance of B1. State the null and alternative hypotheses. H0: B1 ≠ 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 ≠ 0 H0: B1 < 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 < 0 H0: B1 = 0 Ha: B1 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is insufficient evidence to conclude that B1 is significant. -Do not reject H0. There is sufficient evidence to conclude that B1 is significant. - Do not reject H0. There is insufficient evidence to conclude that B1 is significant. -Reject H0. There is sufficient evidence to conclude that B1 is significant. Should x1 be dropped from the model? Yes No (c) Use ? = 0.05 to test the significance of ?2. State the null and alternative hypotheses. H0: B2 = 0 Ha: B2 < 0 H0: B2 ≠ 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 ≠ 0 H0: B2 < 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ??

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 a movie theater company 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	1.5
91	2	2
95	4	1.5
92	2.5	2.5
95	3	3.2
94	3.5	2.2
94	2.5	4.2
94	3	2.5

(a)

Use ? = 0.01 to test the hypotheses

H₀:	_B1 = B₂ = 0
H_a:	_B1 and/or B₂ is not equal to zero

for the model

y = B₀ + B₁x₁ + B₂x₂ + E,

where

x₁	=	television advertising ($1,000s)
x₂	=	newspaper advertising ($1,000s).

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

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

p-value = ??

State your conclusion.

-Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

-Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

- Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

-Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

(b)Use a = 0.05 to test the significance of B₁.

State the null and alternative hypotheses.

H₀: B₁ ≠ 0

H_a: B₁ = 0

H₀: B₁ = 0

H_a: B₁ ≠ 0

H₀: B₁ < 0

H_a: B₁ = 0

H₀: B₁ = 0

H_a: B₁ < 0

H₀: B₁ = 0

H_a: B₁ > 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

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

p-value = ??

State your conclusion.

-Reject H₀. There is insufficient evidence to conclude that B₁ is significant.

-Do not reject H₀. There is sufficient evidence to conclude that B₁ is significant.

- Do not reject H₀. There is insufficient evidence to conclude that B₁ is significant.

-Reject H₀. There is sufficient evidence to conclude that B₁ is significant.

Should x₁ be dropped from the model?

Yes

(c)

Use ? = 0.05 to test the significance of ?₂.

State the null and alternative hypotheses.

H₀: B₂ = 0

H_a: B₂ < 0

H₀: B₂ ≠ 0

H_a: B₂ = 0

H₀: B₂ = 0

H_a: B₂ ≠ 0

H₀: B₂ < 0

H_a: B₂ = 0

H₀: B₂ = 0

H_a: B₂ > 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

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

p-value = ??

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