# Is Square Root of the Variance of a Regression Coefficient the Standard Error?

Quick question, in the textbook "Introductory Econometrics", the variance of a Regression Coefficient is given as:

$var(\hat\beta_j) = \frac{\sigma^2}{SST_j(1-R_j^2)}$

where, $SST_j$= $\sum_{i=1}^n (x_{ij}-\bar x)^2$

$\sigma^2$ is the variance of errors of y against its predicted values

$R_j^2$ is the strength of fit when regressing the jth predictor against the other predictors.

So am I right in assuming that the Standard Error of the Regression Coefficient is the square root of this $var(\hat\beta)$ value?

• You're correct. "Standard error" is used in two senses, one to refer to $\sqrt{var(\hat{\beta}_j)}$ and another to refer to the estimate that results from replacing $\sigma^2$ with an estimate in $\sqrt{var(\hat{\beta}_j)}$ – user179309 Jan 8 '18 at 4:34

## 1 Answer

Yes that is correct. You may be confused because, while we give separate terminology to standard deviation and standard error, the square is called a "variance" in both cases.

• It might be worth adding that (of course) the standard error is a standard deviation, the standard deviation of the sampling distribution of the statistic. Which may be another reason why this is so confusing. – mdewey Jan 8 '18 at 13:30