CHAPTER 14. CORRELATION AND SIMPLE LINEAR REGRESSION
Cannot be used with different transformations of
cannot be used to compare models
that are fit to different transformations of the
variable. For example, many people try fitting a
and choose the model with the highest
. This is not appropriate as
terms are no longer comparable between the two models.
Cannot be used for non-nested models.
cannot be used to compare models with different
variables unless one model is nested within another model (i.e. all of the
the smaller model also appear in the larger model). So using
to compare a model with
to a model with
is not appropriate as these two models are not nested. In
these cases, AIC should be used to select among models.
A no-intercept model: Fulton’s Condition Factor
It is possible to fit a regression line that has an intercept of 0, i.e., goes through the origin. Most computer
packages have an option to suppress the fitting of the intercept.
The biggest ‘problem’ lies in interpreting some of the output – some of the statistics produced are
misleading for these models. As this varies from package to package, please seek advice when fitting
The following is an example of where such a model may be sensible.
Not all fish within a lake are identical. How can a single summary measure be developed to represent
the condition of fish within a lake?
In general, the the relationship between fish weight and length follows a power law:
is the observed weight;
is the observed length, and
are coefficients relating length
to weight. The usual assumption is that heavier fish of a given length are in better condition than than
lighter fish. Condition indices are a popular summary measure of the condition of the population.