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Math Help - correlation

  1. #1
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    Question 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
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  2. #2
    MHF Contributor matheagle's Avatar
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    I doubt you mean that x1=x2.
    What is your regression model?
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by ben.mahoney@tesco.net View Post
    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?
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  5. #5
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    the full model before backward elimination has 9 individual variables.
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  6. #6
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    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}
    Last edited by novice; January 5th 2010 at 11:00 AM.
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