# If you regress random variable Y against random variable X, would the results be the same if you regressed X against Y?

##### 1 Answer

Nov 8, 2015

They would be the same only if the

#### Explanation:

The Pearson **correlation coefficient** will always be the *same* regardless what the variances are. However, the regression lines will have different slopes (hence, not the same) unless the variances are equal.

This may be more *technical* than what you are looking for, but here is the **slope** of the regression line for both cases:

As you can see, they will only have the same slope if the variances are equal.

hope that helped