Talk:Multiple regression

This task needs more clarification, like a link to a suitable wikipedia page. —Donal Fellows 17:04, 29 June 2009 (UTC)

This task requires merging with Polynomial Fitting already representing least squares approximation example in the basis {1, x, x²}. Linear regression is just same in the basis {1, x}. --Dmitry-kazakov 18:31, 29 June 2009 (UTC)

OK, there's now implementations in two languages. It's not clear to me how this is different from the polynomial fitting task either, but I'm a completionist (for Tcl) and not a statistician... —Donal Fellows 10:34, 9 July 2009 (UTC)

An explanation from the Lapack documentation may be helpful. [1] The idea is that you want to model a set of empirical data

$\{(x_{1},F(x_{1}))\dots (x_{m},F(x_{m}))\}$

by fitting it to a function of the form

$F(x)=\sum _{i=1}^{n}\beta _{i}f_{i}(x)$

where you've already chosen the $f_{i}$ functions and only the $\beta$'s need to be determined. The number of data points $m$ generally will exceed the number of functions in the model, $n$, and the functions $f_{i}$ can be anything, not just $x^{i}$.

I don't believe the Ruby and Tcl solutions on the page solve the general case of this problem because they assume a polynomial model. I propose that the task be clarified to stipulate that the inputs are two tables or matrices of numbers, one containing all values of $f_{j}(x_{i})$ and the other containing all values of $F(x_{i})$ with $i$ ranging from 1 to $m$ and $j$ ranging from 1 to $n$, and $m>n$. --Sluggo 12:52, 9 August 2009 (UTC)