Question: Let (x 1 , y 1 ), (x 2 , y 2 ), ..., (x n , y n ) be a set of measurements

Let (x1, y1), (x2, y2), ..., (xn, yn) be a set of measurements whose sample correlation coefficient is r. Show that

r = B n - i=1 nEy i=1 n i=1 Xi i=1

where βˆ1 is the maximum likelihood estimate for the slope.

r = B n - i=1 nEy i=1 n i=1 Xi i=1 2 2

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