- a **4. Suppose we have a sample of n pairs of iid observations (X1,Y), (X2,Y2),...,(Xn, Yn). Our model is Y; = a + BX,

[answerhappygod]

A 4 Suppose We Have A Sample Of N Pairs Of Iid Observations X1 Y X2 Y2 Xn Yn Our Model Is Y A Bx 1 (50.45 KiB) Viewed 15 times

- a **4. Suppose we have a sample of n pairs of iid observations (X1,Y), (X2,Y2),...,(Xn, Yn). Our model is Y; = a + BX, + where E(ui) = 0, and X; and Ui are independent for all i. Recall that the ordinary least squares estimators â and B are the values of a and B that minimize the sum of squared errors L=(Y; - a - BX:)? (a) Show that â and ß are consistent. (b) Suppose that we know B = 0 for some reason. Let à be the value of a that minimizes the restricted sum of squared errors Li-(Y; -a)?. Give a formula for a in terms of the sample observations. Show consistency. (c) Suppose that we know a = 0 for some reason. Let ß be the value of B that minimizes the restricted sum of squared errors 21-(Y; - BX;)?. Give a formula for B in terms of the sample observations. Show consistency