
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 $\displaystyle \alpha$ and $\displaystyle \beta$.
(alpha and beta have hats on but I couldn't get the latex to work for that)
You can work out $\displaystyle S_{xx}$ from the given information. But I'm not sure where to begin to compute the correlation.

$\displaystyle r^2={ SS_{xy}\over SS_{xx} SS_{yy}}$
and if you're not used to that notation...
$\displaystyle { \sum_j\sum_i(x_i\bar x)(y_j\bar y) \over \sum_i(x_i\bar x)^2\sum_j(y_j\bar y)^2}$
which is the sample covariance squared over the sample variances (using n instead of n1, the MLEs)
where we cancel the n's via algebra.

using $\displaystyle r^2= \frac{Cov(\alpha,\beta)^2}{Var(\alpha)Var(\beta)}$ and the definitions of those in terms of x and $\displaystyle S_{xx}$ i got...
$\displaystyle r^2=\frac{n\bar{x}^2}{S_{xx}}+1$ 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?

In the case of simple linear regression, $\displaystyle r = \sqrt{R^{2}} = \sqrt{\frac{SSR}{SSTO}} = \sqrt{1\frac{SSE}{SSTO}}$