Question: Consider the simple regression model with classical measurement error, y 5 b0 1 b1xp 1 u, where we have m measures on xp . Write

Consider the simple regression model with classical measurement error, y 5 b0 1 b1xp 1 u, where we have m measures on xp

. Write these as zh 5 xp 1 eh, h 5 1, p , m. Assume that xp is uncorrelated with u, e1, p , em, that the measurement errors are pairwise uncorrelated, and have the same variance, s2

e. Let w 5 1z1 1 p 1 zm 2/m be the average of the measures on xp

, so that, for each observation i, wi 5 1zi1 1 p 1 zim 2/m is the average of the m measures. Let b1 be the OLS estimator from the simple regression yi on 1, wi

, i 5 1, p , n, using a random sample of data.

(i) Show that

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