With exponential equation y= A0 + A1*(1-exp(tau1*x)), I got the Tau1 and its error Tau3. How does the Origin calculate the error? And R-Square? What is the reference? Thanks. Tony
Getting the parameters error of non-linear fitting is somewhat complicated, which includes some matrix calculation. For example, given the nonlinear model: where is a vector of parameters and is a vector of predictors and
Firstly, get the sum of squared residuals RSS by: And we can get the model estimated error variance: And then we calculate the coefficient variances. Let and , Then we can get the parameters error from the estimated asymptotic covariance matrix of the regression coefficients:
The calculation of R^2 is similar to the linear model: where
Above is only a brief algorithm, you can read the following referances for more detail about the calculation of nonlinear fitting:
1. David A.Ratkowsky. HandBook of Nonlinear Regression Models. 1990. Marcel Dekker, INC.
2. Douglas M.Bates and Donald G. Watts. Nonlinear Regression Analysis and Its Application. 1988. John Wiley & Sons.
3. G.A.F.Seber and C.J.Wild. Nonlinear Regression. 2003. Wiley Interscience.
How does the Origin calculate the error?
Posted - 10/05/2006 : 10:31:38 PM
is a vector of parameters and 
is a vector of predictors and 
, Then we can get the parameters error from the estimated asymptotic covariance matrix of the regression coefficients:
