standard error of the estimate from polyval?

[Mike]

Hi

In the following:

x=[1 2 3];y=[2 3.9 6];
[p,S]=polyfit(x,y,1);
[yp,delta] = polyval(p,x,S)

yp =

1.9667 3.9667 5.9667

delta =

0.1106 0.0943 0.1106

>> y-yp

ans =

0.0333 -0.0667 0.0333

I'd like to estimate standard error of the estimate between y and
predicted y by linear regression, but find that delta is not y-yp.
In manual, it says "[y,delta] = polyval(p,x,S) and [y,delta] = polyval
(p,x,S,mu) use the optional output structure S generated by polyfit to
generate error estimates, y±delta. If the errors in the data input to
polyfit are independent normal with constant variance, y±delta
contains at least 50% of the predictions." I don't understand this.

Mike

[Peter Perkins]

Mike wrote:

> In manual, it says "[y,delta] = polyval(p,x,S) and [y,delta] = polyval
> (p,x,S,mu) use the optional output structure S generated by polyfit to
> generate error estimates, y�delta. If the errors in the data input to
> polyfit are independent normal with constant variance, y�delta
> contains at least 50% of the predictions." I don't understand this.

Mike, I don't know what version you're using. The command line help for polyval in the current version says this:

DELTA is an estimate of the standard deviation of the error in
predicting a future observation at X by P(X).

If the coefficients in P are least squares estimates computed by
POLYFIT, and the errors in the data input to POLYFIT are independent,
normal, with constant variance, then Y +/- DELTA will contain at least
50% of future observations at X.

for some reason, the HTML reference page does not have that first part of the description. I've made a note to have that fixed.

By the way, the 50% comes from a worst-case scenario of 1 error degrees of freedom for a t-based confidence interval. In most cases, +/- delta will be closer to a 68% prediction interval.

Hope this helps.

[Mike]

On Apr 8, 11:01 am, Peter Perkins

Oh... I though help from HTML and command will be the same.
I don't find "DELTA is an estimate of the standard deviation of the
error in
> predicting a future observation at X by P(X)." in HTML.
My version is R2009a, the latest one.

thank you.

Mike