How to find the points furthest from a linear regression line?

I have fit a linear regression to a set of data that oscillates back and forth over the regression line. I'd like to find the points furthest from the regression line. How should I go about this?

Answer 1

[Roger Stafford]

If by “furthest” you mean furthest in a direction orthogonal, (rather than vertical,) to your regression line, then do the following. Suppose your line of regression has the equation y = m*x+b and X and Y are x and y coordinate vectors of your data set.

   [d,ix] = max(abs(Y-m*X-b));
   d = d/sqrt(1+m^2);

Then (X(ix),Y(ix)) is the data point having the greatest distance and that distance is d.

Answer 2

[Walter Roberson]

polyval() the project the position of the line at the points. Then you can take the distance between the actual data and the projected data, and find the furthest points.

pointdist = abs(y - polyval(Coeffs, x));
[~, furthest_point_idx]] = max(pointdist);
far_points_idx = find(pointdist > some_cutoff);