Nonlinear Data (Curve Fitting)
- In many cases, data from experimental tests are not linear, so we need to fit to them some function other than a first-degree polynomial.
- Popular forms are the exponential form
- The exponential forms are usually linearized by taking logarithms before determining the parameters, for the case
:
- We now fit the new variable
as a linear function of
or
as described earlier.
- Here we do not minimize the sum of squares of the deviations of
from the curve, but rather the deviations of
.
- In effect, this amounts to minimizing the squares of the percentage errors, which itself may be a desirable feature.