Correlation, Method of Least Squares, Linear Regression and the General Linear Model - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 136

Fig. 4.16 Expected total amounts of copper for ore-rich cells predicted by Fig. 12.2 a. Contour
values are logarithms (base 10) for (30 km 30 km) unit cells (Source: Agterberg 1973 , Fig. 5A)

mappable geological variables with variable regional mean was developed by
Agterberg and Cabilio ( 1969 ).
In most mineral potential research studies it is assumed that the size and grade
distribution of the deposits is independent of location within areas considered
favorable for their occurrence (see, e.g., Singer and Menzie 2010 ). However, a
hypothesis worthy of investigation is that frequency of occurrence in more favor-
able environments is positively correlated with amounts of metal contained in the
deposits. Examples of positive correlations of this type will be given later for gold
deposits in Meguma Terrane, Nova Scotia (Sect. 5.2.1 ) and worldwide occurrence
of porphyry copper deposits (Sect. 10.2.3 ). The following example taken from
Agterberg ( 1973 , 1977 ) applies to volcanogenic massive sulphide deposits in the
Abitibi area (Fig. 4.16 ). This example will be discussed in more detail in an
application of the jackknife method for bias elimination (Sect. 12.1.2 ) . The Abitibi
study area contained 35 (10 km 10 km) cells with one or more large copper

deposits. Two types of multiple regressions were carried out with the same
explanatory variables. First the dependent variable was set equal to 1 in the
35 control cells, and then it was set equal to a logarithmic measure (base 10) of
short tons of copper per control cell. Suppose that estimated values for the first
regression are written as P i and those for the second regression as Y i . Both sets of
values were added for overlapping square blocks of cells to obtain estimates of
expected values (30 km

Y i / P i is
shown as a pattern that is superimposed on the pattern for the P i values only in
Fig. 12.22 (see later). The values of Y i * cannot be estimated when Y i and P i are
both close to zero. Little is known about the precision of Y i * for P i

30 km) unit cells. In Fig. 4.16 the ratio Y i * ¼

0.5. These
values ( Y i *) should be transformed into estimated amounts of copper per cell here
written as X i . Because of the extreme positive skewness of the size-frequency
distribution for amounts of copper per cell ( X i ), antilogs (base 10) of the values
of Y i * as observed in the 55 control cells were multiplied by the constant c

X

¼

X 10 Y i in order to reduce bias under the assumption of approximate lognor-
mality ( cf . Box 3.1 ). The pattern of Fig. 4.16 is useful as a suggested outline of
subareas where the largest volcanogenic massive sulphide deposits are more likely
to occur.

X i =