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.

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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.

 

  1. Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)

 

 

 

 

  1. How large is the sample? How many independent variables are there?

 

 

 

 

  1. c-1. At the 0.05 significance level, state the decision rule to test: H0: β1 = β2 = β34 = β5 = 0; H1: At least one β is 0. (Round your answer to 2 decimal places.)

 

 

 

 

  1. c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)

 

 

 

 

  1. c-3. What is the decision regarding H0: β1 = β2 = β3 = β4 = β5 = 0?

 

 

 

 

 

  1. 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
 

 

 

 

 

  1. 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.)

 

 

 

 

  1. d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.

 

 

 

 

 
 
 
 
 
 
 
 
 
 
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