# When will regression coefficient equal correlation in multiple regression? [closed]

For the following

$$Y = B_0 + B_1X_1 + B_2X_2,$$

when will $B_1$ be equal to the correlation between $Y$ and $X_1$?
When will $B_2$ be equal to the correlation between $Y$ and $X_2$?
Why?

## closed as off-topic by mdewey, kjetil b halvorsen, whuber♦Dec 4 '16 at 19:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Self-study questions (including textbook exercises, old exam papers, and homework) that seek to understand the concepts are welcome, but those that demand a solution need to indicate clearly at what step help or advice are needed. For help writing a good self-study question, please visit the meta pages." – whuber
If this question can be reworded to fit the rules in the help center, please edit the question.

• If this is "homework" you should read stats.stackexchange.com/tags/self-study/info. – Carl Dec 4 '16 at 4:20
• – Paul Dec 4 '16 at 5:07
• @Paul Thank you for finding that thread. There may be a subtle difference, though: it concerns estimated coefficients whereas in the present case the question might be about the model coefficients. – whuber Dec 4 '16 at 19:13

## 1 Answer

The answer to both questions is that a slope coefficient will equal the correlation value when you have the equation in standardized form (i.e. when the Y and X variables are z-scores) and when the predictors are independent of each other.

Not a full proof of what I said - but you can see the two-predictor case here and you'll observe that the standardized coefficient will equal the correlation between Y and Xi when the correlation between X1 and X2 is r = 0