11_TwoVariables0830_handout

3 cmu y kryukov approach want distribution of s s are

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Unformatted text preview: tatistical tests p. 3 © CMU / Y. Kryukov Approach ˆ Want distribution of β ’s ˆ β ’s are functions of Xi’s and Yi’s Yi’s are function of Xi’s and ui’s We observe Xi’s So we condition on them I.e. we hold Xi’s fixed Some books just have Xi as part of population ˆ What could β ’s be given Xi? ˆ Only independent random variable is ui β Which affects ’s via Yi’s ˆ How do β ’s depend on Yi’s and ui‘s? p. 4 © CMU / Y. Kryukov Estimator as a function of error Take estimator of β1 : Some algebra gives us : ˆ= N β1 ∑i =1 Xi...
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