Need 1 question in 4 hour-Statistics homework Assignment
Assignment iv
Suppose you expect the true relationship between a variable Y and X1 to be as follows:
Y = 5% + 2 X1 + u
However, you don’t observe X1. Instead you observe X2 = X1 + e. You run the following
regression:
Y = a + b X2 + v
You know the variance of e is 4, the variance of v is 16, the variance of the X1 is 2, and the
variance of X2 is 6. The expected value of e, u, and v are zero and they are uncorrelated with
each other and with X1. The expected value of X1 is 1%. What are the expected values of the
regression coefficients ‘a’ and ‘b’?
