Beau,

Thanks for the response.

Both methods are supposed to be minimising the sum of squared error
(SSE) sum(observed_i - predicted_i)^2. Therefore comparing the
parameter values/confidence interval is not the measure of difference
in the methods, it should be the SSE.

For the backslash division:
SSE = 0.759546

For the full wiki method implemented in O-Matrix:
SSE = 0.96827

Even within computation tolerances the SSE for both methods are far
from the same (> 25% variation) and it appears that O-Matrix is not
minimising the objective function to an appropriate tolerance. I am
just trying to reconcile the differences in the methods.

Yours,

Kurt


--- In omatrix@yahoogroups.com, "Harmonic Software" <beau@...> wrote:
>
> Kurt,
>
> Your solutions bhat, i.e. beta hat in the wiki article I believe
are within
> the stated confidence intervals? I believe that the stated bhat
values in
> the wiki article are the confidence intervals, of which the O-Matrix
> solution gives the estimate. Will look into that further for you.
>
>
>
> Beau
>
>
>
>
>
>
>
>
>
> From: omatrix@yahoogroups.com [mailto:omatrix@yahoogroups.com] On
Behalf Of
> kurtforrester
> Sent: Thursday, April 24, 2008 11:42 AM
> To: omatrix@yahoogroups.com
> Subject: [omatrix] Linear Algebra
>
>
>
> Trying to replicate the example from wikipedia for linear regression
> using the following O-Matrix script
> ##### Code Start ###################################
> height = {1.47, 1.5, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.7,
> 1.73, 1.75, 1.78, 1.8, 1.83}
> weight = {52.21, 53.12, 54.48, 55.84, 57.2, 58.57, 59.93, 61.29,
> 63.11, 64.47, 66.28, 68.1, 69.92, 72.19, 74.46}
>
> X = [ones(rowdim(height),1), height, height^2]
>
> s = inv(X'*X)
> bhat = X\weight # Backslash division
> bhat2 = s*X'*weight # As shown
> http://en.wikipedia.org/wiki/Linear_regression
>
> print bhat
> print bhat2
> ##### Code end #####################################
> # O-Matrix responds
> ##### Command window output begin ##################
> {
> 128.807
> -143.155
> 61.9582
> }
>
> {
> 132.617
> -147.417
> 63.0986
> }
> ##### Command window output end ##################
>
> Why if they are both implementations of linear regression (although
> different methods) are the results so different?
>
> Cheers,
>
> Kurt
>