Minimizing distance (not square of distance) of linear fit to data points

Questions
1

Hi all,

I have a set of data {x1, y1}, {x2, y2}…
Is it possible to fit a regression line to this data that minimizes the total distance from the line to my data points? This would be better than Least-Squares in this instance.

Thank you

2

I think I solved the problem myself by using:

FindFit[{dataset}, a + b x, {a, b}, x, NormFunction → (Norm[#, Infinity] &)]

Thanks for looking.

3

Gustace, I don’t think it will take into account the ‘horizontal’ difference, only the vertical distance. Calculating the closest distance to a line is a little tricky, but can be done of course.

4

From the wording it appears that you are looking for a “total least squares” result. That can be done using the singular values decomposition.