# Math Help - correlation

1. ## correlation

Hi, can anyone tell me how to see if say X1 and X2 are correlated where

X1 = X2 = results from a regression model.

Thanks

2. I doubt you mean that x1=x2.

3. no sorry i meant that both x1 and x2 are the responses from a regression model, they are home and away scores for rugby matches.

my regression model is x1 = intercept + a1i*(form on last 5 games) + a2i*(league position) +.....
x2 has the same model.

4. Originally Posted by ben.mahoney@tesco.net
no sorry i meant that both x1 and x2 are the responses from a regression model, they are home and away scores for rugby matches.

my regression model is x1 = intercept + a1i*(form on last 5 games) + a2i*(league position) +.....
x2 has the same model.
For multi-correlation, you can only correlate two independent variables at a time by holding the other independent variables constant.

How many independent variables do you have?

5. the full model before backward elimination has 9 individual variables.

6. Since you are interested only in the relation between $X_1$and $X_2$, you will need the partial correlation.
This alone is very labor intensive.
The correlation between $X_1$ and $X_2$, keeping $X_3, X_4,...,X_9$ constant:

$
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 $r_{12.456789}$ for example. You must first reduce it into
$r_{12.56789},$,
then $r_{12.56789}$,
then $r_{12.6789}$,
then $r_{12.789}$,
then $r_{12.89}$,
then $r_{12.9}$
and finally $r_{12}$.

Where $r_{12}= \frac{x_1x_2}{\sqrt{(\Sigma x_1^2)(\Sigma x_2^2)}}$

where $x_1=X_1-\overline X$and $x_2=X_2-\overline X$.

Repeat the process for $r_{13.456789}$ and $r_{23.456789}$