Re: Best formula

Virgil wrote:

The usual methods involve minimizing some measure of the total error of prediction. The most common measures involve taking all the differences between predicted values and actual values and either squaring them or taking their absolute values (to eliminate positive errors and negative errors from cancelling out when you add them) and then adding them up.
The result is called the "sum of squared errors" or the "sum of absolute errors" as appropriate, and is to be minimized.

There are standard and fairly simple techniques for minimizing the sum of squared errors for lots of situations. These processes are often collectively called the method of "least squares", and can be searched for under "least squares".

E,G.
http://mathworld.wolfram.com/LeastSquaresFitting.html
http://en.wikipedia.org/wiki/Least_squares
http://www.efunda.com/math/leastsquares/leastsquares.cfm

The methods of least absolute errors, while often more difficult to implement, is considerably less sensitive to the effects of outlier values in your data set.

There are many variations on both of the above methods as well as lots of others, if your results for the above prove unsatisfactory.

Since your prediction formula, v_n = a_n*x_n + b_n*y_n + c_n*z_n, is homogeneous and linear, least squares is a good place to start.

Great. Thanks a lot.

Best regards,

Jose Carlos Santos
.

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