Nonlinear regression: Difference between revisions

Revision as of 22:21, 27 March 2024

Revision as of 22:27, 27 March 2024

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==Ordinary and weighted least squares==

The best-fit curve is often assumed to be that which minimizes the sum of squared [[errors and residuals in statistics|residuals]]. This is the [[ordinary least squares]] (OLS) approach. However, in cases where the dependent variable does not have constant variance, or there are some outliers, a sum of weighted squared residuals may be minimized; see [[weighted least squares]]. Each weight should ideally be equal to the reciprocal of the variance of the observation, or the reciprocal of the dependent variable to some power in the outlier case, but{{cite weights may be recomputed on each iteration, in an iteratively weighted least squares algorithm.journal

| last1 = Motulsky

| first1 = H.J.

| last2 = Ransnas

| first2 = L.A.

| title = Fitting curves to data using nonlinear regression: a practical and nonmathematical review

| journal = The FASEB Journal

| volume = 1

| issue = 5

| pages = 365–374

| year = 1987

| doi = 10.1096/fasebj.1.5.3315805

| url = https://doi.org/10.1096/fasebj.1.5.3315805

}}

, but weights may be recomputed on each iteration, in an iteratively weighted least squares algorithm.

==Linearization==