Question: Best linear prediction. Suppose X; Y 2 L2 and (without loss of generality) V.X/ D 1. What is the best approximation of Y by an

Best linear prediction. Suppose X; Y 2 L2 and (without loss of generality) V.X/ D 1.

What is the best approximation of Y by an affine function a C bX of X? Show that the quadratic deviation E



.Y abX/2

is minimised by b D Cov.X; Y / and a D E.Y bX/. What does this mean when X; Y are uncorrelated?

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