regression.txt

Polynomial fit functions === === === === RegressionObject.cls contains a class that provides an

Polynomial fit functions
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RegressionObject.cls contains a class that provides an easy way to add polynomial regression functionality to any application. If you just want linear regression or a very high degree, no matter: this class has good performance and scales seamlessly with the complexity of your problem.

What is a regression anyway?
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Given a number of two dimensional data points - maybe as pairs (x,y) of coordinates, maybe as measured values of current and voltage, etc. - the problem arises how to fit a theoretical curve that matches these data as good as possible. Very common is the use of linear approximation or polynomial fits of the form:

    y(x) = c0*x^0 + c2*x^1 + c3*x^2 + c4*x^4 + ...

Two special cases of these polynoms everyone is familiar with are the first and second order curves (straight line and parabel):

    y(x) = m*x + n          (linear regression)
    y(x) = a*x^2 + b*x + c  (parabolic regression)

The good news is: That's all you need to know about mathematics. These functions exist and can give a smooth fit for your data.

Ok, how to use the class?
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Include RegressionObject.cls to your project workspace and create an instance of the class:

    Dim Reg As New RegressionObject
    
Decide for the highest power of x (the degree of the polynom) you want to consider. Carful with too high values! Use 1 for linear regression and 2 for parabolic. The class limits the degree to 25. Higher values lead to datatype overflow and even 10 is much higher than I can think of. If you have a shortage of memory: change the limit in RegressionObject.cls, "Private Const MaxO& = 25", to a smaller value.

    Reg.Degree = 2 '2 is also the default value
    
Then add your data points. No extra memory is consumed, because these data are not actually stored in the class. Add as many as you like!

    For i= 1 To MyDataCount
    	Reg.XYAdd MyData(i).Voltage, MyData(i).Current
    Next i
    
When done, maybe you want to draw the fit curve to a PictureBox?
    
    Pic1.CurrentX = xMin
    Pic1.CurrentY = Reg.RegVal(xMin)
    For X = xMin to xMax
    	Pic1.Line -(X, Reg.RegVal(X))
    Next X
    
That's it!

I know my Math, give me the coefficients!
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The work that the class object does for you is to calculate the coefficients ( c0, c1, c2, c3, ...) in the general equation of the polynom:

    y(x) = c1*x^0 + c2*x^1 + c3*x^2 + c4*x^4 + ...
    
If you want to use them outside of the class object, you can retrieve them with the property Coeff():

    a = Reg.Coeff(2)
    b = Reg.Coeff(1)
    c = Reg.Coeff(0) ' gives the coeffs for y = a*x^2 + b*x + c

or

    m = Reg.Coeff(1)
    n = Reg.Coeff(0) ' for y = m*x + n

Additional Notes
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It is not possible to retrieve the original data from the class object, because they are NOT stored there. However, if you forgot it, you can check which number of datapoints you already added to the regression. the property XYCount is for that purpose.

I used VB 6.0 (SP4) to build and test the code. It is supposed to work with previous VB editions without any changes.

This class is build on my knowledge of mathematics and on the implementation suggestion for the gauss algorithm from R. Sedgewicks "Algorithms ..." book.
Thanks to U.Hanneman for bringing up the idea of implementing a second order regression in the first place, which I extendend to this more general task.

Frank Schindler, Dresden, Germany, 16.9.2000