Consider the regression model Yi Xi ui, where ui and Xi satisfy the assumptions in Key Concept 4 3 Let denote an estimator of that is constructed as , where and are the sample means of Yi and Xi, respectively (a) Show that is a linear function of Yi Y2, , Yn (b) Show that is conditionally unbiased

Question: Consider the regression model Yi = Xi + ui, where ui and Xi{ satisfy the assumptions in Key Concept 4.3. Let denote an estimator of

Consider the regression model
Yi = βXi + ui,
where ui and Xi{ satisfy the assumptions in Key Concept 4.3. Let denote an estimator of β that is constructed as = /, where and are the sample means of Yi and Xi, respectively.
(a) Show that is a linear function of Yi Y2,..., Yn.
(b) Show that is conditionally unbiased.

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