Substituut‐variabelen in correlatieberekingen

The recently repeated assertion that in correlation analysis it makes little difference whether one variable (x2) is used instead of another one (x3), provided the coefficient of correlation (r23) between x2 and x3 is high, is scrutinized. To that purpose the ranges of coefficients of correlation with respect to the substitute variable are expressed in formula 3. Moreover, by way of example, extreme values of coefficients of simple correlation (r13 and r34), of multiple correlation (R1.34 and R3.14) and of regression (α13 and α14, α31 and α34) relating to the substitute variable, are calculated on the basis of empirical values of coefficients of simple correlation relating to the substituted and the remaining variables. The outcome of those calculations are summarized in the tables 1 and 3, and in the graph. Table 1 presents ranges of r13 for given values of r12 and r23, table 3 shows extreme values of coefficients of single and multiple correlation and regression in case an additional variable x4 is introduced and r12, r14, r24 and r23 are given. The graph shows an ellipse as the boundary of the inner closed domain of compatible values of r13 and r34. Those results clearly indicate the need for caution in substituting one variable by another.