Hey kingsolomonsgrave.

I take it that this is a population mean regression model for the data. Even so, your distributions of the parameters you are estimating should be consistent and this means that variance shrinks when you have more data.

Intuitively this looks completely wrong, but I guess you should first start by defining the distributions of u_i|x first for this particular population model. Asymptotically, they should take a normal distribution with the estimator being consistent (i.e. have 1/N property of the variance as opposed to N*sigma^2).