Question

In the linear model, Cov( X, u ) has the same value as:

A) X*u

B) E( X*u )

C) u

D) None of the Above.

Answer 1

Answer:

Given the value of X for a linear, model we know that:
E(XU | X) = 0

Therefore, we have here the covariance computed as:
Cov(X, U) = E(XU) - E(X)E(U)

For linear model, the mean error is 0, therefore E(U) = 0

Therefore, we have here:
Cov(X, U) = E(XU)

Therefore B) E(XU) is the correct answer here.

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