# [R] Multivariate linear regression

Nagu thogiti at gmail.com
Thu Apr 6 02:09:06 CEST 2006

```Hi Bert,

But randomness is just a matter of "scale" of the object (Ramsey
Theory) . The X matrix does not explain the complete variation in Y
due to a large noise in X or simply the mapping f: X->Y is many valued
(or due to other finite number of reasons). Theoretically inverse does
not exist for many valued functions. In regression type problems, we
are evaluating the pseudoinverse of data space.

To estimate the inverses of many valued functions, theoretically, we
may have to use branch cuts method or something called Riemann
surfaces, they are partition of the domain of connected sheets.

As I am not a qualified statistician or have a good experience in
building statistical models for highly noisy data, I am wondering how
did you deal with such situations, if any exist, in your working
experience?

I will try your idea of feeding some random variables as predictors in X.

Thank you again,
Nagu

P.S. Why is that pattern recognition is all about finding patterns
that can not be seen easily, huh?

On 4/5/06, Berton Gunter <gunter.berton at gene.com> wrote:
> Ummm...
>
> If y is unrelated to x, then why would one expect any reasonable method to
> show a greater or lesser relationship than any other? It's all random. Of
> course, put enough random regressors into/"tune" the parameters enough of
> any regression methodology and you'll be able to precisely predict the data
> at hand -- but **only** the data at hand. I should note that such work
> apparently frequently appears in various sorts of "informatics"/"data
> mining"/"omics"/etc. journals these days, as various papers demonstrating
> the irreproducibility of numerous purported discoveries have infamously
> demonstrated. Let us not forget Occam!
>
> Just being cranky ...
>
> -- Bert Gunter
>
>
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nagu
> > Sent: Wednesday, April 05, 2006 3:52 PM
> > To: r-help at stat.math.ethz.ch
> > Subject: [R] Multivariate linear regression
> >
> > Hi,
> >
> > I am working on a multivariate linear regression of the form y = Ax.
> >
> > I am seeing a great dispersion of y w.r.t x. For example, the
> > correlations between y and x are very small, even after using some
> > typical transformations like log, power.
> >
> > I tried with simple linear regression, robust regression and ace and
> > avas package in R (or splus). I didn't see an improvement in the fit
> > and predictions over simple linear regression. (I also tried this with
> > transformed variables)
> >
> > I am sure that some of you came across such data. How did you
> > deal with it?
> >
> > Linear regressions are good for the data like y = x +
> > 0.01Normal(mu,sigma2) i.e. a small noise (data observed in a lab). But
> > linear regressions are bad for large noise, like typical market (or
> > survey) data.
> >
> > Thank you,
> > Nagu
> >
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