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Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all _; and Y, being i.i.d., all ,
Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all _\; and Y, being i.i.d., all , and p having finite fourth moments, no perfect multicollinearity), the OLS estimators for the slopes and intercept: () have a normal distribution in small samples as long as the errors are homoskedastic. have an exact normal distribution for n > 25. are BLUE. are unbiased and consistent
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