correlation

**ben.mahoney@tesco.net** · January 3rd 2010, 10:51 AM

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

X1 = X2 = results from a regression model.

Thanks

**matheagle** · January 3rd 2010, 11:45 AM

I doubt you mean that x1=x2.
What is your regression model?

**ben.mahoney@tesco.net** · January 4th 2010, 08:24 AM

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.

**novice** · January 4th 2010, 02:12 PM

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?

**ben.mahoney@tesco.net** · January 5th 2010, 02:40 AM

the full model before backward elimination has 9 individual variables.

**novice** · January 5th 2010, 09:52 AM

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:

$<br /> r_{12.3456789}=\frac{r_{12.456789}-r_{13.456789}r_{23.456789}}{\sqrt{(1-r^2_{13.456789})(1-r^2_{23.456789})}}<br />$

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 $r_{23.456789}$

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