| T O P I C R E V I E W |
| tony_lincoln |
Posted - 10/05/2006 : 10:31:38 PM
Dear friends,
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 |
| 1 L A T E S T R E P L I E S (Newest First) |
| larry_lan |
Posted - 10/08/2006 : 01:45:41 AM
Hi 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.
Larry
OriginLab Technical Services
Edited by - larry_lan on 10/08/2006 03:20:44 AM |
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