Ex14-8. The following regression output was obtained from a study of architectural firms

| August 30, 2017

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 7.987 2.967 2.690 0.010
X1 0.122 0.031 3.920 0.000
X2 –1.120 0.053 –2.270 0.028
X3 –0.063 0.039 –1.610 0.114
X4 0.523 0.142 3.690 0.001
X5 –0.065 0.040 –1.620 0.112
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Analysis of Variance
Source DF SS MS F p-value
Regression 5 3710.00 742.00 12.89 0.000
Residual Error 46 2647.38 57.55
Total 51 6357.38
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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 answers should be indicated by a minus sign.)

? = + X1 + X2 + X3 + X4 + X5.

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

Sample n

Independent variables k

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c-1. State the decision rule for .05 significance level: H0: ?1 = ?2 = ?3 =?4 =?5 =0; H1: Not all ?’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.)

Computed value of F is

c-3. Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level.

H0. of the regression coefficients are zero.

For X1 For X2 For X3 For X4 For X5
H0: ?1 = 0 H0: ?2 = 0 H0: ?3 = 0 H0: ?4 = 0 H0: ?5 = 0
H1: ?1 ? 0 H1: ?2 ? 0 H1: ?3 ? 0 H1: ?4 ? 0 H1: ?5 ? 0
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d-1. State the decision rule for .05 significance level. (Round your answers to 3 decimal places.)

Reject H0 if t .

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

t ? value
X1

X2

X3

X4

X5

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d-3. Which variable would you consider eliminating?

Consider eliminating variables .

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