The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 8.302 3.083 2.693 0.010 x1 0.207 0.155 1.335 0.000 x2 − 1.001 0.556 − 1.800 0.028 x3 − 0.168 0.405 − 0.415 0.114 x4 0.536 0.260 2.062 0.001 x5 − 0.029 0.023 − 1.261 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 2,064.77 413.0 10.15 0.000 Residual Error 57 2,318.84 40.68 Total 62 4,383.61 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care−related. a. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) b. How large is the sample? How many independent variables are there? c-1. At the 0.05 significance level, state the decision rule to test: H0: β1 = β2 = β3 =β4 = β5 = 0; H1: At least one β is not 0. (Round your answer to 2 decimal places.) c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) c-3. What is the decision regarding H0: β1 = β2 = β3 = β4 = β5 = 0? d-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places.) For x1 For x2 For x3 For x4 For x5 H0: β1 = 0 H0: β2 = 0 H0: β3 = 0 H0: β4 = 0 H0: β5 = 0 H1: β1 ≠ 0 H1: β2 ≠ 0 H1: β3 ≠ 0 H1: β4 ≠ 0 H1: β5 ≠ 0 d-2. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.

The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 8.302 3.083 2.693 0.010 x1 0.207 0.155 1.335 0.000 x2 − 1.001 0.556 − 1.800 0.028 x3 − 0.168 0.405 − 0.415 0.114 x4 0.536 0.260 2.062 0.001 x5 − 0.029 0.023 − 1.261 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 2,064.77 413.0 10.15 0.000 Residual Error 57 2,318.84 40.68 Total 62 4,383.61 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care−related. a. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) b. How large is the sample? How many independent variables are there? c-1. At the 0.05 significance level, state the decision rule to test: H0: β1 = β2 = β3 =β4 = β5 = 0; H1: At least one β is not 0. (Round your answer to 2 decimal places.) c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) c-3. What is the decision regarding H0: β1 = β2 = β3 = β4 = β5 = 0? d-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places.) For x1 For x2 For x3 For x4 For x5 H0: β1 = 0 H0: β2 = 0 H0: β3 = 0 H0: β4 = 0 H0: β5 = 0 H1: β1 ≠ 0 H1: β2 ≠ 0 H1: β3 ≠ 0 H1: β4 ≠ 0 H1: β5 ≠ 0 d-2. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.

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 following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.

Predictor	Coefficient	SE Coefficient	t	p-value
Constant		8.302			3.083		2.693	0.010
x₁		0.207			0.155		1.335	0.000
x₂	−	1.001			0.556	−	1.800	0.028
x₃	−	0.168			0.405	−	0.415	0.114
x₄		0.536			0.260		2.062	0.001
x₅	−	0.029			0.023	−	1.261	0.112

Analysis of Variance
Source	DF	SS	MS	F	p-value
Regression	5		2,064.77		413.0	10.15	0.000
Residual Error	57		2,318.84		40.68
Total	62		4,383.61

x₁ is the number of architects employed by the company.
x₂ is the number of engineers employed by the company.
x₃ is the number of years involved with health care projects.
x₄ is the number of states in which the firm operates.
x₅ is the percent of the firm’s work that is health care−related.

a. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)

b. How large is the sample? How many independent variables are there?

c-1. At the 0.05 significance level, state the decision rule to test: H₀: β₁ = β₂ = β₃ =β₄ = β₅ = 0; H₁: At least one β is not 0. (Round your answer to 2 decimal places.)

c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)

c-3. What is the decision regarding H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0?

d-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places.)

For x₁	For x₂	For x₃	For x₄	For x₅
H₀: β₁ = 0	H₀: β₂ = 0	H₀: β₃ = 0	H₀: β₄ = 0	H₀: β₅ = 0
H₁: β₁ ≠ 0	H₁: β₂ ≠ 0	H₁: β₃ ≠ 0	H₁: β₄ ≠ 0	H₁: β₅ ≠ 0