Question

By using the data $\overline{x}=25,\overline{y}=30,b_{yx}=1.6$ and $b_{xy}=0.4$, find:
(a) The regression equation $y$ on $x$.
(b) What is the most likely value of $y$ when $x=60$?
(c) What is the coefficient of correlation between $x$ and $y$?

Answer 1

Let $\overline{x}=25,\overline{y}=30$

$b_{yx}=1.6$

$b_{xy}=0.6$

Repression eqn $y$on $x$ will be

$y-\overline{y}=b_{yx}(x-\overline{x})$

$y-30=1.6(x-25)$

$y-30=1.6x-40$

$y=1.6x-10$

Value of $y$ when $x$ = 60

$y=1.6\times 60-10$

$y=86$

Coefficient of correlation between $x$ and $y$

The correlation coefficient $r$ is the geometric mean of the regression coefficient.

$r=\pm \sqrt{\left(b_{yx}{b}_{xy}\right)}$

$r=\pm \sqrt{(1.6\times 0.6)}$

$r=\pm \sqrt{96}$