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		7.131			3.085			2.312			0.010
x1		0.203			0.170			1.194			0.000
x2	−	1.176			0.553		−	2.127			0.028
x3	−	0.089			0.311		−	0.286			0.114
x4		0.682			0.381			1.790			0.001
x5	−	0.030			0.025		−	1.200			0.112

Analysis of Variance
Source	DF		SS		MS		F		p-value
Regression	5		1,946.79		389.4		7.67		0.000
Residual Error	47		2,385.55		50.76
Total	52		4,332.34

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.

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

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

1. 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 0. (Round your answer to 2 decimal places.)

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

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

1. 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

1. 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.)

1. d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.

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