steinberg wrote:
>
> 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.
You are computing the squared deviations from the sample mean, which
is derived from the sample precisely by the mechanism you describe
in 1. That is, you impose a restriction on your data points which
translates into the loss of one degree of freedom.
> 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?
Here you are computing the squared deviations from a target value
that uses two data items, namely the intercept and slope of the
regression line. Both of those are computed from the sample and
impose restrictions on your data.
