Linear Regression

The form of the general least squares linear regression model is:

where f_j(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 f_j(X) may be nonlinear.

The parameters A_j are estimated by the method of least squares.
Standard error of the estimate:
where Xi, Yi are the data points,
n - Number of data points.

Basis functions

In FindGraph, linear regression model is linear combination of basis functions f_jk(X).

Polynomial	f_1k(X) = ((X-X₁)/W₁)^k

Rational	f_2k(X) = (W_2/(X-X₂))^k
	f_3k(X) = sqrt((X-X₃)/W₃)

Logarithmic	f_4k(X) = (log ((X-X₄)/W₄))^k

Exponential	f_5k(X) = exp((X-X₅)/W₅*k)

Fourier	f_6k(X) = sin((X-X₆)/W₆*k)
	f_7k(X) = cos((X-X₆)/W₆*k)

Parameters X_j and W_jare 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>.

See examples.
See Fitting, Interpolation.