Re: leasqr question

[Dirk Eddelbuettel]

On Thu, Sep 05, 2002 at 09:49:07AM -0400, Tom Kornack wrote:
> I am unfamiliar with all the complicated output of leasqr and I was 
> hoping if someone could provide me with an algorithm to extract a 
> measure like chi^2 or R^2. Could someone suggest a reference that might 
> elucidate the output variables of leasqr?

No -- R2 only works for linear models, but leasqr.m is for nonlinear ones.

As you asked, R^2 should be defined in any semi-decent statistics intro --
it is the ratio of regression sum of squares [SSR := sumsq(fitted -
mean(fitted))] to total sum of squares [SST := sumsq (y - mean(y))]. Then
you get R2 as SSR/SST.  Alternatively, define sum of squared residuals [SSE
:= sumsq (y - fitted)] and use R2 := 1 - SSE/SST. There are variations which
account for the nb of variables (as adding new variables, even if
meaningless, will always increase R2, some people prefer adj. R2).  

But more importantly, R2 is only for linear models. Its geometry cannot be
applied to nonliear fits such as those computed by leasqr.m. The Draper and
Smith reference in leasqr.m is a good one, it will have details on
appropriate diagnostics for nonlinear models.

Dirk

-- 
Good judgement comes from experience; experience comes from bad judgement. 
                                                            -- Fred Brooks



-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------