in the textbook "Introductory to Econometrics" Wooldridge writes


where $\hat{\beta}_1$ is the OLS-Estimator, $\hat{p}_{xy}$ is the correlation between $x$ and $y$, and $\hat{\sigma}_x$ is the standard deviation of $x$. When I derive this formula I always come up with


Also according to wikipedia this formula is true. Did Wooldridge accidentally invert the fraction?

  • 2
    $\begingroup$ It looks like you got it right. Wooldridge made a mistake at least with that one case. $\endgroup$ Mar 29, 2017 at 22:56

1 Answer 1


Yes this is a typo. In simple regression,

$$y = a + bx + u$$

the OLS estimator for $b$ is $$\hat b = \frac {\hat Cov(x,y)}{\hat \sigma^2_x}$$

Since $\text{Cov}(x,y) = \hat \rho_{x,y}\cdot \hat \sigma_x \cdot \hat \sigma_y$ we get

$$\hat b = \hat \rho_{x,y}\frac {\hat \sigma_y}{\hat \sigma_x}$$


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