Let x-3y+4=0 and 2x-7y+8=0 be two lines of regression computed from some bivariate data. If b_{yx} and b_{xy} are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of b_{xy}+7b_{yx}?

Explanation

Let the line of y on x be 2x-7y+8=0 \implies y = \frac{2}{7}x + \frac{8}{7}, which gives b_{yx} = \frac{2}{7}. Let the line of x on y be x-3y+4=0 \implies x = 3y - 4, which gives b_{xy} = 3. The product b_{yx}b_{xy} = \frac{6}{7} \lt 1, which confirms our assumption is valid. Then b_{xy} + 7b_{yx} = 3 + 7(\frac{2}{7}) = 3 + 2 = 5.

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