## Regression

Hi, I posted this question in the advance forum for sometime but nobody could do it. I think this forum is more appropraite for this question. Thank you for any help

Consider the model

y i = α + β.x i + ui

where u i is a disturbance identically and independently normally distributed with mean 0 and variance σ^2 , and x i is a stochastic regressor, identically and independently normally distributed with mean 0 and variance λ^2 .

a) Suppose a researcher mistakenly regresses x on y, that is, runs the regression

x i = α + δ.y i + u i

and uses 1/δ as an estimator for β prove that 1/δ is not a consistent estimator for β.

b) What is the asymptotic distribution of the least squares estimator when the correct regression of y on x is run?