A least squares fit
can be done to the scattered data as follows.
The linear least squares fit
to the data shows that a sample of 0% crystallinity by density has a crystallinity of 3% by XRD.
The particle diameter was determined from a nonlinear least squares fit
of the predicted scattering based on Mie theory and the measured data.
Position and width can also be included as parameters in a either a non-linear least squares fit
by sequential simplex for example (23) or by including first and second derivative profiles in a linear fit (24).
Solid lines show the least squares fits
, whereas the two dashed lines show the range of one standard deviation.
The straight lines are weighted least squares fits
to a power law, -[DELTA][R.sub.H] = s[R.sub.x.sup.[delta]].
This should reduce the number of extraneous parameters when performing least squares fits
, thereby improving the significance of the remaining parameters.