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Math Help - Regression analysis

  1. #1
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    Regression analysis

    In a regression analysis using the usual model for Normal data, ten y values are observed, one at each of x=1,2,3,...10. Compute the estimated correlation between \alpha and \beta.

    (alpha and beta have hats on but I couldn't get the latex to work for that)

    You can work out S_{xx} from the given information. But I'm not sure where to begin to compute the correlation.
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  2. #2
    MHF Contributor matheagle's Avatar
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    r^2={ SS_{xy}\over  SS_{xx} SS_{yy}}

    and if you're not used to that notation...

    { \sum_j\sum_i(x_i-\bar x)(y_j-\bar y) \over \sum_i(x_i-\bar x)^2\sum_j(y_j-\bar y)^2}

    which is the sample covariance squared over the sample variances (using n instead of n-1, the MLEs)
    where we cancel the n's via algebra.
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  3. #3
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    using r^2= \frac{Cov(\alpha,\beta)^2}{Var(\alpha)Var(\beta)} and the definitions of those in terms of x and S_{xx} i got...

    r^2=\frac{n\bar{x}^2}{S_{xx}}+1 EDIT: whoops that logic is wrong, figured it out properly now.

    would this be correct? Then I can just use the values calculated of xbar and Sxx?
    Last edited by featherbox; March 7th 2010 at 11:15 AM.
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  4. #4
    Super Member Random Variable's Avatar
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    In the case of simple linear regression,  r = \sqrt{R^{2}} = \sqrt{\frac{SSR}{SSTO}} = \sqrt{1-\frac{SSE}{SSTO}}
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