Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Replies: 3   Last Post: Nov 18, 2012 10:02 AM

 Messages: [ Previous | Next ]
 Richard Ulrich Posts: 2,928 Registered: 12/13/04
Posted: Aug 17, 2012 9:39 PM

On Fri, 17 Aug 2012 01:49:39 -0400, Rich Ulrich
<rich.ulrich@comcast.net> 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.

--
Rich Ulrich

Date Subject Author
8/17/12 Richard Ulrich
11/18/12 Jinsong Zhao