The equations of two regression lines are \(16y+x=64\) and \(x+4y=5\). Find regression coefficients and correlation coefficient.Solution:Suppose that equation of regression line of \(Y\) on \(X\) be \(16y+x=64\) and equation of regression line of \(X…

Q.6 (C) (ii) The equations of two regression lines are \(16y+x=64\) and \(x+4y=5\). Find regression coefficients and correlation coefficient.

Solution:
Suppose that equation of regression line of \(Y\) on \(X\) be \(16y+x=64\) and equation of regression line of \(X\) on \(Y\) be \(x+4y=5\)
Now \(16y+x=64\) and \(x+4y=5\)
\(\therefore y=\frac{-1}{16}x+4\) and \(x=-4y+5\)
\(\therefore b_{yx}=\)[ ] and \(b_{xy}=\)[ ]
\(b_{yx}\times b_{xy}=\frac{1}{4}\)
\(\therefore b_{yx}\times b_{xy}\lt 1\)
\(\therefore\) Our assumption is correct.
\(\therefore r^2=\)[ ]
\(\therefore r=\)[ ]