I am seeking better understanding of the concept of degrees of
freedom. Here's what I think I know:
1) Whenever a sum of squares is estimated, the result is
constrained by the fact that the deviations about the mean must
sum to zero. The number of scores free to vary is therefor n-1.
2) When estimating the population SD from a sample, SS/n is a
biased estimate because the sample tends to be less variable than
the population from which it comes. SS/(n-1) is an unbiased
estimate.
Here are the problems I am having:
a) I have difficulty seeing the relation between 1 and 2 above.
That is, given that 1 is true, it does not seem to imply that n-1
is better than n when estimating sigma. This is implied from 2.
b) I am looking at the ANOVA table for a regression with two
preditors and n=395. The total df is 394. I can explain that from
either 1 or 2 above. However the df for regression is 2. Doesn't
the fact that a sum of squares was computed for regression have
an impact here as in 1 above? Isn't SSR also an estimate as in 2
above?
Milton Steinberg
