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Two lines of regression Y on X and X on Y are Y = (l/m)X + c and X = (p/q)Y + b respectively (where m,…

The regression coefficients are \(b_{yx} = l/m\) and \(b_{xy} = p/q\). Since the product of the two regression coefficients satisfies \(b_{yx} b_{xy} = r^2 \le 1\), we have…

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Two lines of regression Y on X and X on Y are Y = (l/m)X + c and X = (p/q)Y + b respectively (where m, q > 0), then -

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The regression coefficients are byx=l/mb_{yx} = l/m and bxy=p/qb_{xy} = p/q. Since the product of the two regression coefficients satisfies byxbxy=r2≤1b_{yx} b_{xy} = r^2 \le 1, we have lpmq≤1\frac{lp}{mq} \le 1, and since m,q>0m, q > 0, multiplying by mqmq gives lp≤qmlp \le qm.

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