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	P
Constant	7.987	2.967	2.69	-
X1	0.12242	0.03121	3.92	0.0000
X2	-0.12166	0.05353	-2.27	0.028
X3	-0.06281	0.03901	-1.61	0.114
X4	0.5235	0.1420	3.69	0.001
X5	-0.06472	0.03999	-1.62	0.112
Analysis of Variance
Source	DF	SS	MS	F	P
Regression	5	3710.00	742.00	12.89	0.000
Residual Error	46	2647.38	57.55
Total	51	6357.38

X1 - # of architects employed by the company

X2 - # of engineers employed by the company

X3 - # of years involved with health care projects

X4 - # of states in which the firm operates

X5 - % of the firms work that is health care-related

1. Write out the regression equation
2. How large is the sample? How many independent variables are there?
3. Conduct a global test of hypothesis to see if any of the set of regression coefficients could be different from 0. Use the .05 significance level. What is your conclusion?
4. Conduct a test of hypothesis for each independent variable. Use the .05 significance level. Which variable would you consider eliminating first?
5. Outline a strategy for deleting independent variables in this cas

Answer 1

1. The regression equation will be,

2. As the total DF is 51. So the sample size is 51. There are 5 independent variables which are given below,

     X1 - # of architects employed by the company

X2 - # of engineers employed by the company

X3 - # of years involved with health care projects

X4 - # of states in which the firm operates

X5 - % of the firms work that is health care-related

3. The coefficients of the independent variables are say,

Now take a hypotheses as

against   .

Now from the analysis of variance table we see the p-value of the F-statistics, which is 0.000. The p-value is less than 0.05. Then we are going to reject the null hypotheses. We can conclude that at least one of the coefficients is zero.

4. Now we are going to test of hypotheses for each variables. Here we see that the p-value of and is less than 0.05. So these variables are insignificant. Here we eliminate first. Then we will eliminate as the effect of on the model is greater than as coefficient of is less than and as they are both negative.
5. Here and are insignificant. So we should delete these two independent variables.