13_InferenceA_handout

13_InferenceA_handout - Inference Single coefficient 73-261...

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Inference – Single coefficient 73-261 Econometrics Wooldridge 4.1-4.2 September 13
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p. 2 © CMU / Y. Kryukov 73-261 1.3 Inference – β j Overview Up to now: Estimation Population, Data, Estimates: Mean , variance s.e.( ), ANOVA, R 2 Starting: topic 1.3 Inference Is j different from zero? Is it greater than 1 ? Is j greater than m ? Is this regression better than the other one? Not just yes/no, but “how likely” Predicting y : Not just a number, but a confidence interval 1 2 ) ' ( ˆ V = X X σ ˆ β= ˆ E Y X X X ' ) ' ( ˆ 1 = Today
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p. 3 © CMU / Y. Kryukov 73-261 1.3 Inference – β j Hypothesis testing on j How likely it is that j = 0 ? We cannot write: Prob[ j = 0 ] j is a not a random variable, it’s . . . . . . . . We know , realization of a random var. What do we need to compute Distribution . . . . , derived from distribution of u j ˆ ( ) ? 0 ˆ Prob j
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p. 4 © CMU / Y. Kryukov 73-261 1.3 Inference – β j Distribution of u What did we assume about u ? Mean E[ u | x ] = ? Variance V[ u | x ] = ? Can we compute Prob[ u 1.5 | x ] ? What do we need to do it? The Ultimate Assumption: u ~ Normal[0, σ 2 ] Very strong – picking . . . . . . . . Central Limit Theorem says it’s OK if N is large (we will talk about it in topic 1.4)
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p. 5 © CMU / Y. Kryukov 73-261 1.3 Inference – β j Distribution of
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This note was uploaded on 01/21/2011 for the course ECON 73-261 taught by Professor Kyrkv during the Fall '09 term at Carnegie Mellon.

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13_InferenceA_handout - Inference Single coefficient 73-261...

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