On Fri, 17 Aug 2012 01:49:39 -0400, Rich Ulrich <firstname.lastname@example.org> wrote:
[snip, a bunch] > >I *think* what follows is a safe, conservative procedure -- >The minimum, proper fitted equation will show no less error >than the measurement error. For that, the pooled SD is
Keep in mind that the MS-residual is an estimate of the variance (which is the square of the standard deviation) of the residual.
When I was learning to use regression, it helped me when I realized that fact. Then I started making a point of noticing that variance, and taking the square root ... just to make sure that I was still analyzing the same set that I thought I was, and that nothing was going strange.
>about 42, or the "Mean-square-residual" is the square of >42, with 10 d.f. Take the Mean square for Regression from >the 5-point regression and divide it by *this* residual, >instead of the computed residual, to get the safe F-test.
Oops! slligh correction -- For the 5 point regression, each point is the average of three measures. The SD of the *3* taken separately is 42; the SD of the average is, naturally, the raw SD divided by the square root of N, or sqrt(3). Or - the MS is not 42-squared, but is 42-squared, divided by 3.
> >The ratio of the two so-called Residual terms can be used as >a test of whether the regression is "over fitted". > Still useful, but you do use the corrected value.