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
9.387
3.069
3.059
0.010
x1
0.232
0.204
1.137
0.000
x2
−
1.214
0.584
−
2.079
0.028
x3
−
0.273
0.424
−
0.644
0.114
x4
0.642
0.362
1.773
0.001
x5
−
0.060
0.028
−
2.143
0.112
Analysis of Variance
Source
DF
SS
MS
F
p-value
Regression
5
2,364.50
472.9
10.29
0.000
Residual Error
53
2,436.07
45.96
Total
58
4,800.57
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. (Negative answers should be indicated by a
minus sign. Round your answers to 3 decimal places.)
b. How large is the sample? How many
independent variables are there?
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 not
0. (Round your answer to 2 decimal
places.)
c-2. Compute the value of
the F statistic. (Round your answer
to 2 decimal places.)
c-3. What is the decision
regarding H0: β1 =
β2 = β3 = β4 =
β5 = 0?
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
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.)
d-3. For each variable, make a decision about
the hypothesis that the coefficient is equal to zero.