Question

If for a bivariate data $\overline{x}=10,\overline{y}=12,Var\left(X\right)=9,{\sigma }_Y=4$ and $r=0.6$, estimate $y$ when $x=5$.

Answer 1

Mean of $x=10$

Mean of $y=12$

$Var\left(X\right)=9$

$Var\left(Y\right)=4^2=16$

$r=0.6$

$byx=r.\frac{{\sigma }_y}{{\sigma }_x}$

$0.6\times \frac{3}{4}=0.45$

$bxy=r.\frac{{\sigma }_x}{{\sigma }_y}=0.6\times \frac{4}{3}=0.8$

$\therefore (x-10)=0.8(y-12)$

$x-10=0.8y-9.6$

$x=0.8y+0.4\to 1$

$(y-12)=0.45(x-10)$

$y-12=0.45x-4.5$

$y=0.45x+7.5\to 2$

$x=0.8y+0.4$

$y=0.45x+0.75$

$y=0.45\times 5+0.75$

$y=3$