Question: Consider the following population model yi = Pixi + Ei where & has mean 0 and variance o. Note that we do not have the

Consider the following population model

Consider the following population model yi = Pixi + Ei where &has mean 0 and variance o. Note that we do not have

yi = Pixi + Ei where & has mean 0 and variance o. Note that we do not have the intercept here (it is not necessary and adding it in does not change anything). Define b, to be the least squares estimator of B1. Let b, be some other (hypothetical) estimator of B, that may not be the least squares estimator. We want to show that n n (1) i=1 i=1 so let us do it step-by-step. a) Show that-ER, ( Vi - bix:)2 - 2ER,( V. - bix()2 4 2ER, x?(b1 - b,)2. Hint 1: Notice that (yi - bix;) = (yi - bix; + bix; - bix;).b) Argue that (a) implies (1). Also, what does (1) mean

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