Question Consider the heterogeneous regression model Y; = Boi + Bi;X; + Uj, where By and Bi; are random variables that differ from one observation to the next. Suppose that E(u;|X;) = 0 and (Bozs Bu) are distributed independently of X. a. Let ßpLS denote the OLS estimator of B1 given in Equation (17.2). Show that BLS P, E(B), where E(B) is the average value of Bi; in the population. b. Suppose that var(u;|X;) = 0, + 0,X}, where 0, and 0 are known posi- tive constants. Let BLS denote the weighted least squares estimator. Does BWLS P, E(B1)? Explain. Equation (17.2). 2(X, - X)(Y; – Y) i=1 Σ-X

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A:

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.