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 7.443 2.990 2.489 0.010 x1 0.214 0.044 4.864 0.000 x2 − 1.143 0.581 − 1.967 0.028 x3 − 0.159 0.057 − 2.789 0.114 x4 0.579 0.314 1.844 0.001 x5 − 0.024 0.021 − 1.143 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 1,975.76 395.2 9.68 0.000 Residual Error 55 2,244.25 40.80 Total 60 4,220.01 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 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.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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 | 7.443 | 2.990 | 2.489 | 0.010 | ||||||||
| x1 | 0.214 | 0.044 | 4.864 | 0.000 | ||||||||
| x2 | − | 1.143 | 0.581 | − | 1.967 | 0.028 | ||||||
| x3 | − | 0.159 | 0.057 | − | 2.789 | 0.114 | ||||||
| x4 | 0.579 | 0.314 | 1.844 | 0.001 | ||||||||
| x5 | − | 0.024 | 0.021 | − | 1.143 | 0.112 | ||||||
| Analysis of Variance | ||||||||||
| Source | DF | SS | MS | F | p-value | |||||
| Regression | 5 | 1,975.76 | 395.2 | 9.68 | 0.000 | |||||
| Residual Error | 55 | 2,244.25 | 40.80 | |||||||
| Total | 60 | 4,220.01 | ||||||||
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.)
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c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)
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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 answers 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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