Math Help - [SOLVED] Regression of many variables

1. [SOLVED] Regression of many variables

I have a pretty good understanding of regressions from high school statistics, with one independent variable and one dependent variable.

I would like to create a regression with a vector of N independent variables and a vector of M dependent variables. At this point I don't know what shape my data will be, so I figure a high-order polynomial regression will work. Maybe something of this form:
$y_i = \sum_{j=1}^N\sum_{k=0}^{order}{a_{ijk}*{x_j}^k}$

Is this something that is done very often or am I on the wrong track? I would be happy to just get some links.

Thanks,
Neal

2. By letting $w_{jk}=x_j^k$ this is linear in the coefficient, a's.

So you can apply multivariate regression here.
The question is, whether or not your errors are normal or not.

See 'General linear data model' at http://en.wikipedia.org/wiki/Regression_analysis

3. Cool, thanks for that. I did a lot of reading and it turns out I was looking for supervised learning.