Although it seems heretical to many ecologists who like to play with
statistics, it sometimes happens that curvilinear relationships can have
functional causes that are fundamentally described by mathematical
relationships. For example, although you can describe a growth curve by a
parabola, an exponential curve not only gives a better fit but actually
describes what is happening.
There is virtually no biological process that is fundamentally described by
a polynomial. Exponentials, yes. Hyperbolic tangents, yes. But quadratics?
Statistical fittings, especially when using biologically meaningless
functions like polynomials, are merely descriptive and offer lttle insight
into biological processes. If one can develop even a simple biological model
of the processes involved, that may suggest functional forms that offer true
insight and understanding.
Bill Silvert
----- Original Message -----
From: "Nabin Baral" <[email protected]>
To: <[email protected]>
Sent: sexta-feira, 17 de Dezembro de 2010 14:27
Subject: [ECOLOG-L] Interpreting quadratic terms in regression
Hello Listserv: I am requesting your help in interpreting the results of
quadratic terms in multiple regression.
I've hypothesized a curvilinear relationship (inverted U) between a
dependent and an independent variable. To test this hypothesis, I centered
the independent variable, squared it and entered it along with the linear
term in the regression model. I got different results with independent
variables and I have tried to summarize them in the following questions:
1. Is it necessary to have a positive linear term and a negative quadratic
(squared term) to support the curvilinear relationship?
2. Is it necessary to have a significant linear term too? How you
interpret
the result when both the linear and quadratic terms are significant
compared
to when the quadratic term is significant while the linear term is not?
3. How do you interpret when both the linear and quadratic terms have
negative beta coefficients?
I would greatly appreciate your time and help.
Happy holidays.
Thanking you.
Nabin Baral
