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From: Steve &lt;srjm72499@frontiernet.net&gt;
Newsgroups: comp.soft-sys.matlab
Subject: Help with orthogonal least squares line fit with slope constraint...
Date: Thu, 13 Dec 2007 12:21:13 -0800 (PST)
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If I have a group of points, I know I can do a least-squares line fit
in the orthogonal sense by doing an eigenvector-type approach.  The
code I've been using for this is:

    Xm = mean(X);
    A = cov(X);
    [V,D] = eig(A);
    [ignore,imx] = max(diag(D)); % Choose eigenvector with max.
eigenvalue
    t=4;
    x = Xm + V(:,imx)'*t;
    t=-t;
    x2 = Xm + V(:,imx)'*t;
    slope=(x2(2)-x(2))/(x2(1)-x(1));
    b=((x2(2)+x(2))-(slope.*(x(1)+x2(1))))./2;

Now, I am looking to do a best fit line through the data, again in an
(orthogonal) least-squares sense, but this time where the slope of the
fitting line is a pre-determined (fixed) value.  Is there a simple
solution to this problem?  I am currently getting an approximate
solution by rotating the first line about Xm until it's slope is as
desired, but of course this doesn't always work well.  I have
considered doing a coordinate transform to make the predetermined
slope the x-axis, then doing a standard (non-orthogonal) regression
where the only uncertainty is in the vertical direction, but I'm
guessing there's probably a better way...

Any thoughts?  Thanks.
-SL

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