that the change of variable X = p Y does not change the total variance of the data.

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Chapter 7.5, Problem 12E

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To show: that the change of variable X=pY does not change the total variance of the data.

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Suppose the x-coordinates of the data (x1, V1), .., (x,, Vn) are in mean deviation form, so that E x; = 0. Show that if X is the design matrix for the least-squares line in this case, then XTX is a diagonal matrix.

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