Content deleted Content added
m added AI methods for solving nonlinear regression problems |
|||
Line 32:
where <math>J_{ij} = \frac{\partial f(x_i,\boldsymbol\beta)}{\partial \beta_j}</math>. It follows from this that the least squares estimators are given by
:<math>\hat{\boldsymbol{\beta}} \approx \mathbf { (J^TJ)^{-1}J^Ty}
compare [[generalized least squares]] with covariance matrix proportional to the unit matrix.
The nonlinear regression statistics are computed and used as in linear regression statistics, but using '''J''' in place of '''X''' in the formulas. The linear approximation introduces [[bias (statistics)|bias]] into the statistics. Therefore, more caution than usual is required in interpreting statistics derived from a nonlinear model.
| |||