# Math Help - Linear Regression

1. ## Linear Regression

Hello guys,

I have a small question please:

An experiment was made to find correlation between X and Y.
2 Regression lines has been build:

1. Y=a+bx

2. X=n+mY

It is known that: m=-0.4 and b=-0.625

Find the correlation r.

cheers !

2. using the standard formula for a OLS slope coefficient:

$-0.4 = \frac{Cov(X,Y)}{Var(Y)}$
$-0.625 = \frac{Cov(X,Y)}{Var(X)}$

multiply together

$-0.4 * -0.625 = \frac{Cov(X,Y)^2}{Var(Y) Var(X)}$
$-0.4 * -0.625 = r^2$
r=0.5 or -0.5

interesting problem. I agree with you that you should choose the negative solution since both coefficients are negative.