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I need to find the line having minimal distance to all points. I found linear regression and linear interpolation algorithms. But their minimal distance is only in y-axis: $D = y - f(x)$.

But I need to find $a,b,c$ for line: $ax + by + c = 0$ where distance is computed this way: $D_i = \dfrac{|ax_i + by_i + c|}{\sqrt{a^2+b^2}}$

Is there any way or algorithm to solve this problem?

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    Yes. They are in 2D.2011-09-23

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What you want to do is called total least squares or orthogonal regression. Netlib has a bunch of routines for doing this, and a bit of searching turns up routines for other systems, e.g. MATLAB.

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    @Rahul: SVD is just too useful for data analysis, methinks. ;)2011-09-23