Orthogonal Linear Regression in 3D-space by using PCA

Orthogonal Linear Regression by using PCA

Orthogonal Linear Regression in 3D-space by using Principal Components Analysis

This is a wrapper function to some pieces of the code from the Statistics Toolbox demo titled "Fitting an Orthogonal Regression Using Principal Components Analysis"
(https://www.mathworks.com/examples/statistics/mw/stats_featured-ex25288136-fitting-an-orthogonal-regression-using-principal-components-analysis), which is Copyrighted by the MathWorks, Inc.

Input parameters:
- XData: input data block -- x: axis
- YData: input data block -- y: axis
- ZData: input data block -- z: axis
- geometry: type of approximation ('line','plane')
- visualization: figure ('on','off') -- default is 'on'
- sod: show orthogonal distances ('on','off') -- default is 'on'

Return parameters:
- Err: error of approximation - sum of orthogonal distances
- N: normal vector for plane, direction vector for line
- P: point on plane or line in 3D space

Example:

>> XD = [4.8 6.7 6.2 6.2 4.1 1.9 2.0]';
>> YD = [13.4 9.9 5.8 6.1 6.7 10.6 11.5]';
>> ZD = [13.7 13.1 11.3 11.8 12.5 16.2 18.5]';
>> fit_3D_data(XD,YD,ZD,'line','on','on');
>> fit_3D_data(XD,YD,ZD,'plane','on','off');

Note: Written for Matlab 7.0 (R14) with Statistics Toolbox

We sincerely thank Peter Perkins, the author of the demo, and John D'Errico for their comments.

Ivo Petras, Igor Podlubny, May 2006
([e-mail], [e-mail])

An example of application can be found at:
http://uk.arxiv.org/abs/math/0609789

For additional codes for the Orthogonal Linear Regression also known as Total Least Squares Method see link:
http://www.mathworks.com/matlabcentral/fileexchange/31109