Re: polyfit with a fixed slope ??

[Carlo de Falco]

On 25 May 2010, at 15:24, Carlo de Falco wrote:

> On 25 May 2010, at 14:20, Oisín Ó Cuanacháin wrote:
>
> > Hi,
> >
> > Does anyone know if there is a function to fit a line with a  
> > specified slope to some data. I have a load of data 'x' and
> > polyfit(1:length(x),x,1) gives me the best-fit line, with arbitrary  
> > slope.
> > What I want however is the best fit line with a particular slope.  
> > This is essentially just a minimization problem and I know I could  
> > code something up myself, but x has 100's of millions of elements  
> > I'm guessing my coding efforts will take forever to run, so does  
> > such a nice function already exist? It is essentially polyfit with  
> > an added constraint that the slope is fixed.
> >
> > Thanks,
> >
> > Oisín.
>
> If I understand correctly, given two data vectors x and y and a  
> slope a you want to find the value b that minimizes
>
> R(b) = sum ((a*x + b - y).^2);
>
> isn't that just
>
> b = sum (a*x-y)/2

sorry, I think it's
b = - sum (a*x-y)/2

> ?
> c.