Suppose all of the regression assumptions in Key Concept 4.3 are satisfied except that the first assumption is replaced with E(u;|X) = 2. Which parts of Key Concept 4.40 continue to hold? Which change? Why? (Is B normally distributed in large samples with mean and variance given in Key Concept 4.40? What about Bo?) The Least Squares Assumptions Y-Bo+BX+ui=1,...,n, where 1. The error term u; has conditional mean zero given X; E(u,|X) = 0; 2. (X, Y),i=1,...,n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: X and Y have nonzero finite fourth moments. Large-Sample Distributions of Bo and B If the least squares assumptions in Key Concept 4.3 hold, then in large samples Bo and B, have a jointly normal sampling distribution. The large-sample normal dis- tribution of B is N(B,, ), where the variance of this distribution, o, is KEY CONCEPT 4.3 KEY CONCEPT 4.4 1 var| (X +x)u; = n [var(X)] The large-sample normal distribution of B is N(B), where (4.21) = 1 var(Hu) [E(H) . where H-1- (4.22) E(X).