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 7.166 3.075 2.330 0.010
x1 0.228 0.302 0.755 0.000
x2 -1.184 0.586 -2.020 0.028
x3 -0.193 0.110 -1.755 0.114
x4 0.572 0.293 1.952 0.001
x5 -0.056 0.022 -2.545 0.112
Analysis of Variance
Source DF SS MS F p-value
Regression 5 1,847.24 369.4 5.60 0.000
Residual Error 41 2,704.20 65.96
Total 46 4,551.44
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.)
y = 7.166 + 0.228x1 - 1.184x2 - 0.193x3 + 0.572x4 - 0.056x5
b. How large is the sample? How many independent variables are there?
Sample N = 46
Independent variables k = 5
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.)
Reject H0 if the calculated F statistic is greater than the critical F value.
c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)
F statistic = 5.60
c-3. What is the decision regarding H0: β1 = β2 = β3 = β4 = β5 = 0?
Reject H0, at least one regression coefficient is not equal to 0.