On 24-Apr-2004, "Konrad Den Ende" <[EMAIL PROTECTED]> wrote:
> Suppose you know that a process follows a function
> y(t) = a + b e^-x, t >= 0.
> ALso, suppose you have following data.
> t: { 0, 1, 2, 3 }
> y: { 2.2, 1.4, 0.87, 0.44 }
>
> How does one estimate the values of a and b?
This isn't a "simple linear regression" problem. It is a nonlinear
regression problem. There are a number of nonlinear regression programs
that can solve your problem for a and b. Here is such a program that I ran
through my NLREG program (http://www.nlreg.com)
Variables t, y;
Parameters a, b;
Function y = a + b*exp(-t);
Plot;
Data;
0 2.2
1 1.4
2 0.87
3 0.44
The computed optimal values are:
a = 0.561880246
b = 1.7144082
Using these parameters, the proportion of variance explained (R^2) = 0.9434
(94.34%)
--
Phil Sherrod
(phil.sherrod 'at' sandh.com)
http://www.dtreg.com (decision tree modeling)
http://www.nlreg.com (nonlinear regression)
.
.
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