# [R] model constant relations

Kyriakos Kachrimanis kgk at pharm.auth.gr
Mon Nov 10 11:57:40 CET 2003

```Dear list members,

this is not an R question and forgive me for using the list for irrelevant
questions, but this is the only place I know where I can find some good
statisticians and I need an expert opinion.
There is this power law kinetic model of the form:
M=kt^n
where t is the time, M is the fraction of drug released, k is the rate
constant and n is an exponent related to the mechanism of release.
I fit this equation to 100 different datasets (by linear regression, after
logarithmic transformation) and then I plot n vs k. What I get is a decay
pattern of n as k increases.
QUESTION 1: Is some theoretical reason for this kind of relation. Is it
expected? Is it "normal" that model parameters (intercept and slope in the
linearised form) should be correlated?
QUESTION 2: Is it theoretically sound to compare the magnitude of constants,
k, that correspond to different exponents, n? (k has dimensions of [time]^-n
so we are comparing quantities with different physical interpretation).
Practically speaking, does k=0.2 with an exponent n=0.5 mean that we have
the same release rate as in the case of k=0.2 but with n=1.0?

Thank you very much in advance.

Kyriakos.

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