It looks like the %. calculates the alpha and beta, and
then the +/ . * creates a set of values that are combinations
of y that are close to the given x.
I made some notes to myself on this topic that I would
like to put into the record here:
We will use the abbreviation mp for matrix product. In J, mp =: +/ . *
For a square matrix y, %. y is the matrix inverse of y.
If y is not square, it must have more rows than columns, and
%. y is (%. (|:y) mp y) mp (|: y)
in math notation, %. y is (YtY)'Yt where '=inverse, t=transpose
x %. y is matrix division, which is defined as (%. y) mp x .
If x is a vector of observations and y is a matrix of explanatory variables,
x %. y gives the regression coefficients.
y mp x %. y gives the projection of x onto the column space of y .
%. fails when the columns are dependent. Regression using %. gives
poor results when the columns are almost dependent - use SVD,
part of the LAPACK addon, in that case.
Henry Rich
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On Behalf Of June Kim
> Sent: Saturday, August 19, 2006 9:51 AM
> To: Programming forum
> Subject: [Jprogramming] Linear Least Squares
>
> On 10E. Approximation section of J Dictionary, there is a definition
> for "linear least squares fit of x and y".
>
> It's given as d1=: ] (] +/ .* %.) 1: ,. [
>
> What is the expected way of using it, and what does the result mean? I
> first thought it returned the least squares estimators(beta and
> alpha), but it didn't.
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