Logarithmic Example
Using a version of the logorithm it is possible to study a type of
nonlinear relationship within the context of a linear model (Jaccard,
Turrisi, and Wan, 1990). For instance, the additive change in the
response variable may be associated with constant proportional changes
in an independent variable. This requires regressing the response
variable on the log of the independent variable.
An Example:
When examining the relationship between population size of a state and
federal aid to state, one might consider the difference in federal aid
between states with a population size of 20 million and 40 million to be
of no greater importance than the difference between 1 and 2 million. The
absolute difference is 20 million between the larger states and only a
million between the smaller states; however, the ratios between both are
2:1. If one uses a logarithmic transformation the difference between these
sets of numbers will be equal. This basically allows for a decreasing
marginal effect. The following figure represents a plot of a regression
of federal aid to states on the log of state population.
(For a more detailed discussion see Darlinton (1990) and Cohen and Cohen
(1983).)
Back To:
Polynomials
Last updated: August 16, 1999