Regression model, Mathematics

Consider the regression model  Yi = a + bXi + ui,  where the  Xi  are non-stochastic and the  ui  are independently and identically distributed with  E[ui] = 0  and  var[ui] = s2.  

(a)  What estimator of  b  would you use if you did not know  a?   What is the variance of this estimator?

(b)  What estimator of  β  would you use if you knew  (i)  a = 0,  (ii)  a = 1?  What is the variance of each of these estimators of  b?

(c)  How do the magnitudes of the variances of the estimators of  β  in  (a)  and  (b) compare?  In particular, what happens if  Σi=1,n Xi2 = 10,  Σi=1,n Xi = 9, and  n = 9?

Posted Date: 3/14/2013 3:36:26 AM | Location : United States

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