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

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Orthogonal Linear Regression by using PCA

Updated

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"
(http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/orthoregdemo.html),
which is Copyright 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
(ivo.petras@tuke.sk, igor.podlubny@tuke.sk)

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

Stuart McGarrity