Suppose (Xi, i, i) are IID as triplets across subjects i = 1,..., n, where n is

Suppose (Xi, δi, i) are IID as triplets across subjects i = 1,..., n, where n is large; and Xi , δi , i are mutually independent. Furthermore, E(Xi) = E(δi) = E(i) = 0 while E(Xi 2) = E(δi 2) = 1 and E(i 2) =

σ2 > 0. The response variable Yi is in truth this:

Yi = a Xi + i .

We can recover

a, up to random error, by running a regression of Yi on Xi . No intercept is needed. Why not?