Hi, can anyone tell me how to see if say X1 and X2 are correlated where
X1 = X2 = results from a regression model.
Thanks
Since you are interested only in the relation between $\displaystyle X_1 $and $\displaystyle X_2$, you will need the partial correlation.
This alone is very labor intensive.
The correlation between $\displaystyle X_1$ and $\displaystyle X_2$, keeping $\displaystyle X_3, X_4,...,X_9$ constant:
$\displaystyle
r_{12.3456789}=\frac{r_{12.456789}-r_{13.456789}r_{23.456789}}{\sqrt{(1-r^2_{13.456789})(1-r^2_{23.456789})}}
$
The subscripts after the dot indicate the variables held constant in each case.
There is a tremendous amount of work you must do for an equation of 9 independent variables.
Take $\displaystyle r_{12.456789}$ for example. You must first reduce it into
$\displaystyle r_{12.56789},$,
then $\displaystyle r_{12.56789}$,
then $\displaystyle r_{12.6789}$,
then $\displaystyle r_{12.789}$,
then $\displaystyle r_{12.89}$,
then $\displaystyle r_{12.9}$
and finally $\displaystyle r_{12}$.
Where $\displaystyle r_{12}= \frac{x_1x_2}{\sqrt{(\Sigma x_1^2)(\Sigma x_2^2)}}$
where $\displaystyle x_1=X_1-\overline X $and $\displaystyle x_2=X_2-\overline X$.
Repeat the process for $\displaystyle r_{13.456789}$ and $\displaystyle r_{23.456789}$