Suppose We Omit X₃ (A Variable That Does Not Affect $\beta$

Multiple Choice

Suppose we omit X₃ (a variable that does not affect Y) from the following in a bivariate model
Y_i = $\beta$ ₀ + $\beta$ ₁X_1i + $\beta$ ₂X_2i + $\varepsilon$ _i
And suppose each of the independent variables are correlated with the other independent variables. What is the consequence of omitting X₃ on $\beta$ ₁hat?

A) No effect; $\beta$ ₁hat will be unbiased.
B) The bias will depend only on the correlation of X₁ and X_3.
C) The bias will depend on the correlations of all the independent variables_.
D) The bias will depend only on the correlation of X₁ and X_2.