Our least squares estimator is just one of an infinite number of possible estima

Question

Our least squares estimator is just one of an infinite number of possible estimators. For example, your roommate, Pat, proposes randomly selecting two observations noting that two observations are sufficient to determine a line. The slope of that line is thus Pat's estimate of B_2.b_p = y_2-y_1/x_2-x_1. (Pat calls this the "Patstimator.") Show that b_p is a linear estimator Show that b_p is an unbiased estimator. Find the variance of b_p. Convince your roommate that the Patstimator is not as good as the least squares estimator.

Explanation / Answer

d.

If the response have true linear relationship with the predictors, the least square provides 'minimum variance' (best) unbiased estimator. But patestimator is biased as his least sqaure line chooses two observations sufficient to determine a line.

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