Question

The following results were obtained as part of a multiple regression analysis involving 3 independent variables:...

The following results were obtained as part of a multiple regression analysis involving 3 independent variables:

SSR = 11440   SSYY = 16781       and n = 28

  1. What is the value of the calculated F statistic?
  2. What is the critical value for the model test if alpha = 0.05?
  3. What is the value of the coefficient of determination?
  4. What is the value of the standard error of the estimate?
  5. What is the value of adjusted R2?
  6. What are the total number of degrees of freedom?
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Homework Answers

Answer #1

SSYY = SSR + SSE

16781 = 11440 + SSE

SSE = 5341

SST = SSYY = 16781

df of the numerator = 3

df of the total = 28 - 1 = 27

df of the denominator = 27 - 3 = 24

The table is:

Source SS df MS F p-value F-critical
Regression 11440 3 3813.333 17.13537 0.0000 3.008787
Residual 5341 24 222.5417
Total 16781 27
  1. What is the value of the calculated F statistic?

17.13537

  1. What is the critical value for the model test if alpha = 0.05?

3.008787

  1. What is the value of the coefficient of determination?

r2 = SSR/SST = 11440/16781 = 0.682

  1. What is the value of the standard error of the estimate?

Standard error =

  1. What is the value of adjusted R2?

Adjusted r2 =

  1. What are the total number of degrees of freedom?

df of the total = 28 - 1 = 27

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