Is the significance of slope for linear regression the same thing as the significance of the correlation?


1 Answer 1


Yes, because the slope can be expressed as:

$$ \beta = \frac{cov(X, Y)}{var(X)} $$

While the correlation coefficient is:

$$ \rho= \frac{cov(X, Y)}{\sqrt{var(X)*var(Y)}} $$

Whatever significance test you do can be justified with an exact permutation test that shuffles the dependence of X on Y, which leaves $var(X)$ and $var(Y)$ as constants, so significance tests on both the slope and the correlation coefficient can be imagined as a significance test on the covariance of your two variables.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.