# difference between RAW regression coefficient of slope vs. Pearson's correlation (with two variables)? [duplicate]

I know that the equations for obtaining the RAW regression coefficient of the slope and Pearson's correlation (r) are different, but conceptually, how do those two differ when you only have two variables?

• What exactly do you mean by a "RAW" regression coefficient?
– whuber
Commented Jan 26, 2017 at 21:19
• I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. Commented Jan 26, 2017 at 22:02

In case of simple regression where we use $X$ to predict $Y$, the relation is as follows

$$\hat {\beta} = \frac{\rm{cov}(X, Y) }{ \rm{var}(X)} = {\rm cor}(Y, X) \cdot \frac{ {\rm SD}(Y) }{ {\rm SD}(X) }$$

while correlation is

$${\rm cor}(X, Y) = \frac{ {\rm cov}(Y, X) }{ {\rm SD}(Y) \,{\rm SD}(X) }$$

So in the case of just two variables, regression slope is re-scaled (not in $[-1,1]$) and non-symmetric (slope for $Y$ given $X$ is different then for $X$ given $Y$) correlation coefficient.

• Wow, you managed to post an answer 38 minutes after the question was closed. Commented Jan 26, 2017 at 23:21
• @amoeba yes that's strange... I started writing it, then was doing other things and came back to post it half an hour later.
– Tim
Commented Jan 27, 2017 at 5:59