Unformatted text preview: tatistical tests p. 3
© CMU / Y. Kryukov Approach
Want distribution of β ’s
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?
Only independent random variable is ui
Which affects ’s via Yi’s ˆ
How do β ’s depend on Yi’s and ui‘s?
© 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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