197Regression
can be treated by linear regression after substituting X
2
for X and using it in Equation 6.79. This is a
special case of polynomial regression explained later in this chapter.
However, often we need to use a nonlinear equation relating Y to X of the general form
YfXp
= (,) (6.82)
where
f () is a function
p are parameters
For example, an exponential model with parameters k and Y
0
of the form is a good explanatory
model for light attenuation
YY kX
0
exp( ) (6.83)
known as Beer–Lambert law. Here, k is extinction coefcient and Y
0
is the light just below the sur-
face which is the measure reported at X = 0.
6.3.1 loG transforM
In cases like the one in Equation 6.83, we can transform the nonlinear model into a linear model by
use of l