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Fig. A.1.


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Two correlated random variables X1 and X2 spanning plane ℋ in L2(Ω). The projection of Y onto plane ℋ has strictly larger R2 than the that of the projection of Y onto either X1 or X2 alone. However, when expressed in (X1, X2) coordinates, the expression of Proj(Y) is misleading, since the coordinates of this projection are large due to the fact variables X1 and X2 are almost collinear (in fact they are larger than those of the projection of Y onto X1 or X2 individually).

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