RE: regress vs polyfit

[Mike Miller]

On Mon, 20 Jun 2011, address@hidden wrote:

> From Thomas Grzybowski:
>
> > I am new to octave and want to fit a single regression line to some 
> > data.  I have been using polyfit, and was looking at regress, but I 
> > find regress confusing.  From the regress "Help":
> >
> >   * `X' is a matrix of regressors, with the first column filled with 
> > the constant value 1
> >
> > I do not understand the help instructions.  My data is simply x,y pairs 
> > - what is this help about - "the constant value 1" ?
>
> The program appears to fit an equation like y = a0*x0+a1*x1+a2*x2... 
> where a0 is the constant term and the x0's are all 1, so that if you 
> didn't want a constant term you would just omit that first column.


I'm sure that's right.  This is the standard way of doing things.  In this 
equation...

y = X*b + e

...y and e are vectors of length N, X is an N x p matrix and b is a vector 
of length p.  If you have X and y and you want the least-squares solution 
for b, do this:

b = X\y ;

That's the easiest way.

To have an intercept term in the model, there has to be a column of ones 
in the X matrix.  The b element that corresponds to that column of ones 
(normally the first column) is the intercept.

Mike