are also not in evidence, although we have not attempted any formal
statistical tests to detect clustering.
We have examined plots of
residuals for Iteration 1 for the wtransformed and antilog fits (not
shown) and found no apparent clustering effects of. positive and negative
residuals.
Values of R12 for Iteration 1 for the antilog and log fits tend to be
larger than for the untransformed fits (except for stratum 6 for the log
fit).

Iterating tends to result

in smaller values of R12 for all three

fits.
Ideally, R12 should be zero.
The residuals and observed values
for stratum 4 are plotted in Figure 22 for the antilog fits, Iterations

1 and 3.

These illustrate the reduction in R,* for that strata achieved

by the iterating procedure.

We have also computed Ro?, which is the square of the linear correlation
coefficient between residuals and estimated values (Figure 23).
Values
of Ro? near 1 would indicate that large estimates (%.) tend to be less

than the corresponding observed datum (y.), and small estimates tend to

be larger than the observed datum.

Figure 23 indicates values of Ro? in

the range of from near zero up to about 0.20 except for stratum 6 for

the antilog scale, where R22 is about 0.5.
Rp* is reduced in most cases
by iterating, and there appears to be little evidence to suggest the
antilog or log fits are preferable to the fits in untransformed scale if

Ro? is used as a criterion.

CONCLUSIONS

On the basis of results from three iterations, it appears that iterating
on residuals can improve estimates of the true concentration surface for
the Area 13 (Project 57) data set.
If the results are interpreted in
the original scale, fitting in units of logs and then transforming the
estimated log-surface back to the original scale appears to be preferable
to fitting in the untransformed scale.
Alternately, the log fits could
be left in log scale if interpretation in log units is desired.
In
making this conclusion, it is assumed that the estimated concentration
surface of **!Am obtained using FIDLER is approximately the same as the
true concentration surface for 239?24%Pu,
Iterating on residuals tends to yield a better fitting surface to observed
concentrations at sample collection points using as a criterion the size
of the average absolute

(mean or median)

size of residuals,

the standard

deviation of residuals, or the proportion of the total variability in
the data explained by the fit.
This is true for all three scales (untransformed,

log-transformed,

and log).

However,

estimated concentrations at

grid nodes (not sample collection points) are not necessarily improved
This is particularly true for the untransby the iteration procedure.
formed scale, where negative grid estimates are present and become even

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