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?


1 Answer 1


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 $$ s.d(\hat{\beta}_1) = 0.2355/7.53. $$


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