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Math Help - Linear Regression

  1. #1
    Member
    Joined
    Mar 2006
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    Linear Regression

    Hello guys,

    I have a small question please:

    An experiment was made to find correlation between X and Y.
    2 Regression lines has been build:

    1. Y=a+bx

    2. X=n+mY

    It is known that: m=-0.4 and b=-0.625

    Find the correlation r.

    Is the answer -0.5 ?

    cheers !
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  2. #2
    MHF Contributor
    Joined
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    using the standard formula for a OLS slope coefficient:

    -0.4 = \frac{Cov(X,Y)}{Var(Y)}
    -0.625 = \frac{Cov(X,Y)}{Var(X)}

    multiply together

    -0.4 * -0.625 = \frac{Cov(X,Y)^2}{Var(Y) Var(X)}
    -0.4 * -0.625 = r^2
    r=0.5 or -0.5



    interesting problem. I agree with you that you should choose the negative solution since both coefficients are negative.
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