In: Statistics and Probability
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 | 7.131 | 3.085 | 2.312 | 0.010 | ||||||||
x1 | 0.203 | 0.170 | 1.194 | 0.000 | ||||||||
x2 | − | 1.176 | 0.553 | − | 2.127 | 0.028 | ||||||
x3 | − | 0.089 | 0.311 | − | 0.286 | 0.114 | ||||||
x4 | 0.682 | 0.381 | 1.790 | 0.001 | ||||||||
x5 | − | 0.030 | 0.025 | − | 1.200 | 0.112 | ||||||
Analysis of Variance | ||||||||||
Source | DF | SS | MS | F | p-value | |||||
Regression | 5 | 1,946.79 | 389.4 | 7.67 | 0.000 | |||||
Residual Error | 47 | 2,385.55 | 50.76 | |||||||
Total | 52 | 4,332.34 | ||||||||
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.
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 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.