Question

Suppose that discrete random variables X and Y have joint probability mass function given by: f(x,y) = { 1/2, (x,y) ? {(0,0), (2,1)} 0, otherwise (This means that there is equal probability that the points (0,0) and (2,1) are drawn; there is zero probability that any other point is drawn.) Let g(x) = ?0 + ?1 x be a predictor for y, and define the error, ? = Y ? g(X). 1. (3 points) If you impose the moment condition, E[?] = 0, what one point in the plane must the predictor pass through? (In some places, this point is referred to as the grand mean.) 2. (3 points) Assuming E[?] = 0, write an expression for cov[X, ?] = cov[X, Y ? g(X)] in terms of ?1. 3. (3 points) In your own words, explain how the sign of cov[X, ?] is related to the angle of the line. 4. (3 points) What predictor fulfills both E[?] = 0 and cov[X, ?] = 0?

          Suppose that discrete random variables X and Y have joint probability mass function given by:
f(x,y) = { 1/2, (x,y) ? {(0,0), (2,1)}
         0, otherwise
(This means that there is equal probability that the points (0,0) and (2,1) are drawn; there is zero probability that any other point is drawn.)
Let g(x) = ?0 + ?1 x be a predictor for y, and define the error, ? = Y ? g(X).

1. (3 points) If you impose the moment condition, E[?] = 0, what one point in the plane must the predictor pass through? (In some places, this point is referred to as the grand mean.)

2. (3 points) Assuming E[?] = 0, write an expression for cov[X, ?] = cov[X, Y ? g(X)] in terms of ?1.

3. (3 points) In your own words, explain how the sign of cov[X, ?] is related to the angle of the line.

4. (3 points) What predictor fulfills both E[?] = 0 and cov[X, ?] = 0?

Suppose that discrete random variables X and Y have joint probability mass function given by:
f(x,y) = 1/2, (x,y) ? (0,0), (2,1)
0, otherwise
(This means that there is equal probability that the points (0,0) and (2,1) are drawn; there is zero probability that any other point is drawn.)
Let g(x) = ?0 + ?1 x be a predictor for y, and define the error, ? = Y ? g(X).

1. (3 points) If you impose the moment condition, E[?] = 0, what one point in the plane must the predictor pass through? (In some places, this point is referred to as the grand mean.)

2. (3 points) Assuming E[?] = 0, write an expression for cov[X, ?] = cov[X, Y ? g(X)] in terms of ?1.

3. (3 points) In your own words, explain how the sign of cov[X, ?] is related to the angle of the line.

4. (3 points) What predictor fulfills both E[?] = 0 and cov[X, ?] = 0?

Added by Tom-S L.

Question

Please give Ace some feedback