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	Coef	SE Coef			T
	Constant	10.237		3.447		2.97
	X1	0.392		-0.209		-1.88
	X2	-0.392		-0.099		3.96
	X3	0.207		-0.110		-1.88
	X4	0.794		0.201		3.95
	X5	-0.335		-0.126		2.66

  

Analysis of Variance
Source	DF		SS		MS		F
Regression	5		3710.00		742.00		15.14
Residual Error	48		2647.38		57.55
Total	53		6357.38

  

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 your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

  

Ŷ =  +  X1 +  X2 +  X3 +  X4 +  X5.

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

  

Sample n
Independent variables k

  

c-1.	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.)

  

Reject H0 if F >___________

  

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

  

The computed value of F is__________

  

c3.	Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level.

(RejectDo or not Reject)______ H0. (Not all or All)______of the regression coefficients are zero.

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-1.	State the decision rule for .05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if t <  or t > .________

d-2.	Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

	t − value
X1
X2
X3
X4
X5

  

e.	Which variable would you consider eliminating?

  

Consider eliminating variables_______(X1 and X3), (X2 and X3) , (X3 and X5) , or ( X2 and X5)

Answer 1

(a)

The regression model is

(b)

The sample size is:

n= 53+1 = 54

The number of independent variables is: k = 5

(c)

The degree of freedom of numerator: df1=5

The degree of freedom of denominator: df2 =48

The critical value of F using excel function "=FINV(0.05,5,48)" is 2.41.

Reject H0, if F > 2.41

c-2)

The test statistics is

F = 15.14

c-3)

Since F lies in the rejection region so we reject the null hypothesis and we can conclude that at least one coefficient is different from zero.

d-1)

The critical values of t for df = 48 are +/- 2.011.

Rejection region:

If t < -2.011 or t > 2.011, reject H0

Excel function used for critical value "=TINV(0.05,48)"

d-2)

	T
X1	-1.88
X2	3.96
X3	-1.88
X4	3.95
X5	2.66

e)

Since t for X1 and X3 does not lie in the rejection region so these are not significant to the model and we can eliminate them.