Item9 eBook Item 9 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 9.601 3.153 3.045 0.010 x1 0.221 0.110 2.009 0.000 x2 − 1.168 0.577 − 2.024 0.028 x3 − 0.106 0.073 − 1.452 0.114 x4 0.631 0.361 1.748 0.001 x5 − 0.043 0.029 − 1.483 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 1,844.31 368.9 9.37 0.000 Residual Error 56 2,205.62 39.39 Total 61 4,049.93 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. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.) 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 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 values 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Item 9
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 | 9.601 | 3.153 | 3.045 | 0.010 | ||||||||
| x1 | 0.221 | 0.110 | 2.009 | 0.000 | ||||||||
| x2 | − | 1.168 | 0.577 | − | 2.024 | 0.028 | ||||||
| x3 | − | 0.106 | 0.073 | − | 1.452 | 0.114 | ||||||
| x4 | 0.631 | 0.361 | 1.748 | 0.001 | ||||||||
| x5 | − | 0.043 | 0.029 | − | 1.483 | 0.112 | ||||||
| Analysis of Variance | ||||||||||
| Source | DF | SS | MS | F | p-value | |||||
| Regression | 5 | 1,844.31 | 368.9 | 9.37 | 0.000 | |||||
| Residual Error | 56 | 2,205.62 | 39.39 | |||||||
| Total | 61 | 4,049.93 | ||||||||
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.
- Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)
- How large is the sample? How many independent variables are there?
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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?
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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 | ||||
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d-2. Compute the value of the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
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d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.
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