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From: Frédéric Bergeron on 25 Jun 2010 14:13
Hi all,

I posted a message earlier today, but I didn't get any response, so I'll simplify my problem to make it more accessible for everyone. You can find my previous thread at:
http://www.mathworks.com/matlabcentral/newsreader/view_thread/285440.

I search a way of adding a height difference constraint in a linear regression. I've already used regress() and lsqlin() and I think it might be possible using these function. I want to make a 2-dimensional linear regression (find the equation of the best-fit line) trought a set of data in a such way that the ratio between the total difference between the actual points over the line and the line, on the total difference between the points under the best-fit line and the line is equal to a previously defined ratio, R.

For example, if I write my regression like this:

%My regression
%xdata and ydata: my data for the linear regression
n=length(xdata);
[a,b]=lsqlin([xdata ones(n,1)], ydata);
%or [a,b]=regress(ydata, xdata ones(n,1)]);
%y=a*x+b, the equation of the best fit line

I want that after the regression, I found the coeffecient a and b that fit:

R=variable defined before the regression;
points_over=ydata>a*xdata+b;
points_under=ydata<=a*xdata+b;
sum(ydata(points_over))=R*sum(ydata(points_under));
%or the ratio R= sum(sum(ydata(points_over)))/sum(ydata(points_under));

Is there a way of defining this ratio R before the regression so that the regression take it as a constraint?

Thanks for your help,
From: Frédéric Bergeron on 25 Jun 2010 14:31
> I want that after the regression, I found the coeffecient a and b that fit:
>
> R=variable defined before the regression;
> points_over=ydata>a*xdata+b;
> points_under=ydata<=a*xdata+b;
> sum(ydata(points_over))=R*sum(ydata(points_under));
> %or the ratio R= sum(sum(ydata(points_over)))/sum(ydata(points_under));

Excuse me! The last part of my code is suppose to be the following to fit what I mean by the ratio R:

yfit=a*xdata+b;
sum( ydata(points_over) - yfit(points_over) )=...
R*sum( yfit(points_under) - ydata(points_under) );
%R=(sum of height difference over) / (sum of height difference under)
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