# Generalised least squares: from regression coefficients to correlation coefficients?

#### sqrtsqrt

##### New Member
Hi All, I asked this on Stack Exchange, but it seems no-one there knows the answer. I wonder if anyone on talkstats can shed some light on it.

For least squares with one predictor:

$$y = \beta x + \epsilon$$

If $$x$$ and $$y$$ are standardised prior to fitting (i.e. $$\sim N(0,1)$$), then:

- $$\beta$$ is the same as the Pearson correlation coefficient, $$r$$.
- $$\beta$$ is the same in the reflected regression: $$x = \beta y + \epsilon$$

For generalised least squares (GLS), does the same apply? I.e. if I standardise my data, can I obtained correlation coefficients directly from the regression coefficients?

From experimenting with data, the reflected GLS leads to different $$\beta$$ coefficients and also I'm not sure that I'm believing that the regression coefficients fit with my expected values for correlation. I know people quote GLS correlation coefficients, so I am wondering how they arrive at them and hence what they really mean.

Thanks for considering this