I want to use polyfit in a NxM matrix rather than a for loop

How can I do this in one line of code? For Loops Take too long.

    for i=1:2^(9)
        polydata_Run1 = polyfit((1:2^(11))',SEG_RUN1(:,i),1);
        Best_Fit_(:,i) = polyval(polydata_Run1,(1:2^(11)));
    end

Answer 1

[Matt J]

A=[linspace(0,1,2^11);ones(1,2^11)].';

 [Q,R]=qr(A,0);

Best_Fit_ = A*(R\(Q'*SEG_RUN1));

[Richard Liggiero]

That is it! Would have never figured that one out, you are a math legend

[Matt J]

Come to think of it, you can probably simplify to

 A=[linspace(0,1,2^11);ones(1,2^11)].';
 Best_Fit_ = A*(A\SEG_RUN1);

I've set A up to be pretty well-conditioned, so QR-deomposition shouldn't be necessary.