and if you're not used to that notation...
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.
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 and .
(alpha and beta have hats on but I couldn't get the latex to work for that)
You can work out from the given information. But I'm not sure where to begin to compute the correlation.
using and the definitions of those in terms of x and i got...
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?