Consider the following 2-variable linear regression where the error $e_i$ 's are independently and identically distributed with mean 0 and variance 1;

$y_i = α + β(x_i − \bar x) + e_i , i = 1,2,...,n.$

Let $ \hatα$ and $ \hat β$ be ordinary least squares estimates of α and β respectively. What is the correlation coefficient between $ \hatα$ and $ \hat β$?

There are options: $1, 0, -1, 1/2$


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