A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores.For the analysis of regression testing the significance of the equation,what are the df values for the F-ratio?
A)1, 11
B)1, 12
C)2, 10
D)2, 11

Question

Quizplus · Accepted Answer

The degrees of freedom for the F-ratio in a linear regression analysis are calculated as df1 = k - 1 for the numerator, where k is the number of predictors (in simple linear regression, k = 1, so df1 = 1 - 1 = 0, but for testing the significance of the regression equation, we consider k as 1, so df1 = 1), and df2 = n - k for the denominator, where n is the sample size and k is the number of predictors (in this case, n = 13 and k = 1, so df2 = 13 - 1 = 12). However, since the question asks for the F-ratio's degrees of freedom in the context of testing the significance of the regression equation, there seems to be a slight misunderstanding in my initial calculation. Correctly, for a simple linear regression, df1 (numerator) is indeed 1 (representing the regression itself), and df2 (denominator) should be n - k - 1, which equals 13 - 1 - 1 = 11. Therefore, the correct df values for the F-ratio are 1 for the regression and 11 for the error, making the correct choice A) 1, 11.

A Linear Regression Equation Is Computed for a Sample of N