Question: n i=1 - - let denote the sample correlation coefficient between Y and X (defined formally below), and let = 1 (yi ) and

n i=1 - - let denote the sample correlation coefficient between Y 

n i=1 - - let denote the sample correlation coefficient between Y and X (defined formally below), and let = 1 (yi ) and = - 1(xi). (These notations are also defined in slides 44-46 of Chapter 1 Part A notes.) Then, prove that from above also satisfies the following form: 1 = X Y where = n ox - (xi)(yi ) - n 1(xi ) 1 (Yi ) ng = vi and x = vi 1 and with as above. What does this result tell us about the nature of the relationship between B and p? And also between B and p (which is the same as R, the coefficient of determination)? (Note: For all proofs above, you must show in detail all your steps in arriving at the final conclusions.)

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