252
Nonlinear LS estimation. The equation is nonlinear when the values
of one or more of the constant coefficients of the equation can not be
directly calculated from the values of the independent and dependent
variables, i.e.,
Eq. A2
where a, b, a and g are the nonlinear coefficients which can not be
directly calculated from the values of the independent variable t and
dependent variable C. To fit data to equation A2, using non-linear least
square analysis computer programs (for example see Appendix I)
preliminary estimates of all parameters must be avaiable. If these
estimates are not close enough to the best values of the parameters,
computer calculated estimates of the parameters may not converge on the
best values. The term 'best' rather than 'actual' is used in the
previous statement as there may be more than one set of 'best' values of
the parameters that can adequately describe the data.^
The traditional method of least squares estimation assumesa)
the correct form of equation has been chosen; b) the data respresent the
population; c) each datum is statistically independent; d) independent
variable is measured without any error; e) all data have the same, even
though unknown, variance; f) uncontrolled error in the data is randomly
distributed.
Weighting of data. In a non-weighted least square analysis, the
following function is minimized.
N
Eq. A3
i=l