12.8 Predicting the Average Value of Y given X
Suppose we are interested in predicting the average value of Y given X = Xi, 
With 
and 
unbiased estimators of 
and 
, respectively, it follows that 
, that is, an unbiased estimator for the population regression line is the sample regression line. So with 
an estimator for 
, it can be shown that the estimated standard deviation of 
may be computed as
Under the assumption that ε is normally distributed and and are BLUE, it follows that
and ...
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