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	Coeff		SE Coeff		t		p-value
Constant	8.366		3.002		2.787		0.010
X1	0.225		0.301		0.748		0.000
X2	–1.216		0.538		–2..260		0.028
X3	-0.070		0.377		–0.186		0.114
X4	0.552		0.322		1.714		0.001
X5	-0.049		0.028		–1.750		0.112

Analysis of Variance
Source	DF		SS		MS		F		p-value
Regression	5		2197.68		439.5		9.68		0.000
Residual Error	59		2679.56		45.42
Total	64		4877.24

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. round 3 decimal places.

B.) State the decision rule for .05 significance level: H₀: β₁ = β₂ = β₃ =β₄ =β₅ =0; H₁: Not all β's are 0. (Round your answer to 2 decimal places.)

C.) Compute the value of the F statistic. Round to 2 decimal places

D.) State the decision rule for each independent variable. Use the 0.05 significance level. Round 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

Reject H0 if t<_______or t >_________.

Answer 1

A)      
Y^ =8.366+0.225*X1-1.216*X2-0.070*X3+0.552*X4-0.049*X5      
      
B)      
F(0.05,5,59)=   2.37  
reject Ho if F>2.37      
      
C)      
F=9.68      
      
D)      
t critical value, t(α/2,df) =    2.001  
reject Ho if t < -2.001 or t >2.001