For a particular dataset, a simple linear regression of $y$ on $x$ was fitted and it yielded the following quantities:

$n = 25$

$R^2= 0.7114$

$ \hat{\beta}_1 = 0.2355$

$F$-statistic $= 56.68$

From my understanding, to obtain the standard error of the slope, the formula that needs to be applied is the follow:


But I cannot seem to be able to manipulate the given terms to come to a solution. Any help is appreciated


The T value is equal to $b1 / SE(b_1)$. Since $b_1$ is given and I calculated the $T$ value to be $7.565$, I believe the answer is $0.0311$. Could this be correct?


Recall that in simple linear model you have the identity $$ t^2 = F, $$ where $$ t^2 = \left( \frac{\hat{\beta}_1}{s.d(\hat{\beta}_1)} \right)^2, $$ hence $ t = \sqrt{56.68} = 7.53$, thus $$ s.d(\hat{\beta}_1) = 0.2355/7.53. $$


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.