Least Squares Method for best line fitting

I have a set of X and Y coordinates data taken from Laser scanning

X=[x1 x2 x3 x4 .....] Y=[y1 y2 y3 y4 .....]

Elements of both the X and Y include some errors.

I tried to find the best fitting line using polyfit and polyval command in matlab, but it can use only to calculate the Yhat w.r.t. X data.

At the end it will give X and Yhat only.

If I want to know calculate both the Xhat and Yhat, how can I use polyfit and polyval ?

Answer 1

[Torsten]

I think you are talking about "orthogonal linear regression".

Try

http://www.mathworks.com/matlabcentral/fileexchange/16800-orthogonal-linear-regression

Polyfit is not suited for this kind of Fitting ; it assumes there are no errors in the independent variable.

Best wishes

Torsten.

[Tharindu Weerakoon]

Yes Torsten. Thanks a lot.

Still the problem is how to compute the Xhat and Yhat from x and y dataset with errors.

Initially I have a data set from LRF (laser scanner): [theta, d] from this data det I compute the x and y.

[theta, d] ---> [d*cos(theta) d*sin(theta)]=[x, y]

It is difficult to use [theta, d], which d is having error only. Because no constrain to use.

So [x y] only be used for segment the data and Orthogonal linear regression to find the best fitted line.