11_TwoVariables0830_handout

1 two vriable ols a 0 0 1 1 i 1wi ui n 1 p 5

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Unformatted text preview: − X ( N X2−X2 ) Yi = ∑i =1Wi Yi N 1 Expand Yi and simplify ˆ β1 = 73 2 Au- 3 61 g1 1.1 Two vriable OLS -a = 0 * β 0 + 1* β1 + ∑i =1Wi ui N 1 p. 5 © CMU / Y. Kryukov ˆ Mean of β1 Mean, conditional on X = (X1,…,XN): [ ˆ E β1 | X = Key assumption: E [u | x ] = 0 satisfied if u is independent of x. Assumption gives us an . . . . . . . . estimator: [ ˆ E β1 | X = Assumption failure is called . . . . . . . . . . . . : a third variable correlated with both x and y 73 2 Au- 3 61 g1 1.1 Two vriable OLS -a p. 6 © CMU / Y. Kryukov ˆ...
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