Correlation, Method of Least Squares, Linear Regression and the General Linear Model - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 123

45 50 55 59

1 5 10 15 20 25 30 35 40

1

5

10

LARGE SULPHIDE DEPOSITS
Zn ONLY

Cu ONLY

Cu AND Zn

15 CONTROL CELL

Fig. 4.6 Abitibi area; all cells were compared with a single control cell (C) containing giant
(Cu, Zn, Pb, Ag) sulphide deposit (Kidd Creek Mine); 12 black cells have geological setting
similar to that of C; 123 other cells with black frame have similarity index greater than average.
Systematic comparisons of this type are useful to problem-solving in exploratory strategy (Source:
Agterberg 1974 , Fig. 116)

4.3.2 Forward Selection and Stepwise Regression
Applied to Abitibi Copper

Standard methods of multiple regression were used for numerical analysis.
The main computational step consists of inversion of the XX 0 matrix. Because the
55 explanatory variables contain several linear and near-linear relationships,
the full matrix cannot be inverted. At a maximum, 51 explanatory variables could
be used. Results of forward selection are partially shown as seven contour maps in
Fig. 4.7 . As illustrated in Fig. 4.8 , the contours represent sums of estimated values
for overlapping (40 km 40 km) squares. Each larger unit square contains 16 values

estimated for the smaller (10 km 10 km) cells it contains. Estimated values for

the smaller cells are less than 1 and can be interpreted as probabilities of occur-
rence of one or more copper deposits. Any of the sums of 16 probabilities for
(40 km

40 km) unit areas represents the expected value of number of

(10 km 10 km) cells with one or more copper deposits (also called “control

cells”). Each contour map was scaled with respect to a relatively well explored
“control area” that contains the mining districts of Timmins, Kirkland Lake,
Noranda and Val d'Or. The sum of estimated probabilities in this control area
was set equal to the number of cells with copper deposits in this area. It is shown
that selection of eight variables (Fig. 4.7d ) already nearly produces the final pattern
based on 51 variables (Fig. 4.7g ).
In another experiment along the same lines, stepwise regression was used to
relate the copper cell values to all explanatory variables with individual stepwise
selection and final regression coefficients shown in Table 4.4 .The Q -value in this
table represents level of significance for the F -distribution for every forward or
backward step. Note that there occurred only a single backward step in this
application. It is customary to terminate the regression run when Q , at a forward