id: 06024970
dt: j
an: 2012c.00655
au: Fox, William P.
ti: Issues and importance of “good” starting points for nonlinear
regression for mathematical modeling with Maple: Basic model fitting to
make predictions with oscillating data.
so: J. Comput. Math. Sci. Teach. 31, No. 1, 1-16 (2012).
py: 2012
pu: Association for the Advancement of Computing in Education (AACE),
Waynesville, NC
la: EN
cc: K85
ut: regression; mathematical modelling; stochastic modelling; mathematical
applications; goodness of fit
ci:
li:
ab: Summary: The purpose of our modeling effort is to predict future outcomes.
We assume the data collected are both accurate and relatively precise.
For our oscillating data, we examined several mathematical modeling
forms for predictions. We also examined both ignoring the oscillations
as an important feature and including the oscillations as an important
element. Our goal was a class project to model casualties in
Afghanistan in an effort to support or refute Gen(Ret) McCaffrey’s
statement that casualties in Afghanistan would double in 2010. The
casualty data set is more complex so we began analyzing a simpler data
set we found concerning carbon dioxide levels as part of a lab
exercise. We used regression packages in Maple using the Fit command as
well as we wrote a program to calculate parameter estimates for
nonlinear regression using the Levenberg-Marquardt algorithm. The Fit
programs produced results that were not useful unless we included
“good” initial parameter estimates. Some computational effort was
required to obtain relatively good starting points that resulted in
much better models for predicting the future. We additionally give
suggestions as to how to obtain these better starting points. Finally,
we present some sensitivity issues of the parameters.
rv: