Choosing Initial Parameter Values for Nonlinear Regression

dataset

1

2

3

4

5

6

7

8

method

Automatic

accuracy

4

fit and plot

reset to default parameters

set initial to fitted parameters

precision

4

initial parameter values

y

0

150.

treat

y

0

as a

constant

fitted parameter

t

c1

42.

m

1

2.4

t

c2

44.

m

2

3.35

Automatic methodfitted parameters:

y

0

=

t

1

=

m

1

=

t

2

=

m

2

=

Fitting scattered experimental data with a multi-parameter model by nonlinear regression is frequently hampered by the difficulty in making sufficiently good guesses of the parameters' initial values. This Demonstration lets you plot the points from one of eight datasets and then use the model to generate a curve that approximately matches the data by manually adjusting the parameters’ values with sliders. The values that produce the visually matched curve are then used as the initial guesses to the regression procedure. The method is demonstrated with different scattered peaked datasets to be fitted with a double-stretched exponential model having four or five adjustable parameters. Hints: Start by matching

y

0

first. Try the Gradient method if Automatic frequently fails.