How to Reshape Linear Regression Model using Correlation Coefficient instead of slope?

Asked Apr 25 '17 at 19:50

Active Apr 25 '17 at 19:50

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I try to reproduce Results from Harding and Pagan (2004), p.12, where they try to estimate the correlation coefficient $\rho_{S} = cor(S_{y,i},S_{x,i})$ using regression on

$$ \frac{S_{y,t}}{\hat{\sigma_{S_x}}\hat{\sigma_{S_y}}} = \alpha_1 + \frac{\rho_S}{\hat{\sigma_{S_x}}\hat{\sigma_{S_y}}} S_{x,t} + \varepsilon_{1,t} $$.

But whatever I try to transform the equations for linear relation between $S_{x,t}$, $S_{x,t}$

$$ S_{y,t} = \alpha_0+\beta S_{x,t}+\varepsilon_{0,t} $$

and the definition of the correlation coefficient $\hat{\beta} = \rho_S\frac{\hat{\sigma_{S_y}}}{\hat{\sigma_{S_x}}}$, I never manage to get the result in the first equation. Any ideas?

Thank's a lot!!

asked Apr 25 '17 at 19:50

EliteTUM

This is correct if both the $\beta$ and $\rho$ are estimates. – Michael R. Chernick Apr 25 '17 at 20:04
By "this" you mean the first equation? Can you point to any Source I can take further reading in? – EliteTUM Apr 25 '17 at 20:24
I was talking about your claim regarding your final equation. I think you can find this in any regression book (e.g. Draper and Smith). – Michael R. Chernick Apr 25 '17 at 20:28

How to Reshape Linear Regression Model using Correlation Coefficient instead of slope?

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