Consider the following regression:

Yi = 𝛽o + 𝛽1xi + ui

where u; = xe, E(e) = 0, and x and e are independent.

a) Show that E(ulx) = 0.

b) Show that var (u|x) = x² var(e).

c) Since the variance of the error term varies with x, which of the SLR assumptions is violated? Explain.

d) Because this SLR assumption is violated, is the estimation of ₁ necessarily biased? Explain.