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Comparison of coefficients of the straight lines fitted in Figs.
4.12
and
4.13
shows that 1968 and 2008 data have approximately the same slope but 2008
intercepts are markedly greater than 1968 intercepts. In Fig.
4.12
the straight
lines are based on 18 and 27 data points for 1968 and 2008, respectively. All data
points were used for the lognormals of Fig.
4.13
. Because slope differences are
small, it can be assumed that 1968 slopes are unbiased estimates of 2008 slopes.
This is illustrated in Fig.
4.14
for 1968 copper and ore weight data where the best-
fitting lines were forced to have the 2008 slopes. The intercept of the Pareto
distribution for copper weight in Fig.
4.12a
is less than its intercept in Fig.
4.12c
.
Suppose this difference is written as
Δ
P
¼0.4585. Equations of the straight lines in
Figs.
4.12
,
4.13
, and
4.14
are of the form
y
bx
+
a
indicating that the dependent
variable (
Y
) was regressed on the explanatory variable (
x
). All uncertainty is
assumed to be associated with
Y
that is plotted in the vertical direction. These
equations can be rewritten as
x
¼
b
0
y
+
a
0
; for example,
x
¼
¼
0.9843
y
+ 3.3737 for
Fig. 5d and
x
0.9843
y
+ 3.1080 for Fig.
4.13b
. It is noted that the least squares
method used in this section results in slightly biased estimates of the coefficients.
If this type of bias cannot be neglected, a different method of fitting the Pareto
The intercept (
a
0
) of the lognormal distribution in Fig.
4.14b
is only
¼
Δ
L
¼
0.2627
less than the intercept in Fig.
4.13d
. Each intercept difference
corresponds to a
factor of 10
Δ
for increase in average weight per cell between 1968 and 2008. These
factors are 2.875 for copper and 1.831 for copper ore, respectively. Incorporating a
6.1 % correction related to the relatively slight increase in total number of cells with
known deposits due to new discoveries (
cf
. Fig.
4.10
), the factors of increase in total
weight become 3.049 for the copper-weight Pareto model, and 1.943 for the
ore-weight lognormal model. Observed factors of increase are 3.026 for total
copper weight and 3.030 for total ore weight, respectively. Consequently, the
copper-weight Pareto agrees better with observed increase in total copper weight
than the ore-weight lognormal, which significantly underestimates observed overall
change in total ore weight. As an additional test, it was determined from the straight
lines in Fig.
4.12b, d
, that
Δ
P
¼0.4885 for total ore weight, resulting in an increase
factor of 3.266, slightly overestimating the observed value of 3.030.
Δ
4.4.3 Final Remarks on Application of the General Linear
Model to Abitibi Copper
The large copper deposits in the Abitibi are almost all of the volcanogenic massive
sulphide type. These deposits are associated with geological and geophysical vari-
ables that can be mapped. Other types of deposits may not so clearly associated with
mappable variables. For example, in the Abitibi area there are many lode gold
deposits that occur in places that are not clearly different from other places in the
region with respect to the geological and geophysical variables used in the appli-
cation of the general linear model to Abitibi copper.
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