Linear Regression
The form of the general least squares linear regression model is:
where fj(X) are any arbitrary functions of X that are called the basis functions. In regression modeling, the term 'linear' means that the models dependence on its parameters Aj is linear. The functions fj(X) may be nonlinear.
The parameters Aj are estimated by the method of least squares.
The fit ftandard error:
where Xi, Yi are the data points,
the residual degrees of freedom is defined as the number of data points n minus the number of fitted coefficients m.
Basis functions
In FindGraph, linear regression model is linear combination of basis functions fjk(X).
Polynomial f1k(X) = ((X-X1)/W1)^k
Rational f2k(X) = (W2/(X-X2))^k
f3k(X) = sqrt((X-X3)/W3)
Logarithmic f4k(X) = (log ((X-X4)/W4))^k
Exponential f5k(X) = exp((X-X5)/W5*k)
Fourier f6k(X) = sin((X-X6)/W6*k)
f7k(X) = cos((X-X6)/W6*k)
Parameters Xj and Wj are fixed. The parameter k varies from 1 up to 8.
Fitting Log Window
FindGraph copies information about data fitting to the Log Fitting Window. To view it select menu item <View><Fitting Log>.
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