11_TwoVariables0830_handout

15 cmu y kryukov degrees of freedom df 1 n u i2 i

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Unformatted text preview: Y. Kryukov Variance-covariance matrix Matrix of estimated variances ˆ and covariances of β ‘s () () ˆ ⎛ ⎡β 0 ⎤ ⎞ ⎡ V β ˆˆ 0 ˆ V⎜⎢ ⎥⎟ = ⎢ ⎜ ⎢ β ⎥ ⎟ cov β 0 , β1 ˆ ˆˆˆ ˆ ˆ ⎝⎣ 1 ⎦⎠ ⎣ () () ˆˆ cov β 0 , β1 ⎤ ⎥ ˆ ˆβ V1 ⎦ Can be reported after running a regression in statistical software It is used in various tests p. 15 © CMU / Y. Kryukov Degrees of freedom (d.f.) 1 N ˆ ˆ σ= U i2 ∑i =1 N −2 2 2 1 N ˆ σ= ∑i =1 (Yi − Y ) N −1 2 Y (N – 2), (N – 1) are called degrees of freedom: We can prove that they eliminate bias # of r.v.’s (N) minus # of estimates: ˆ2 σY Y is an estimate, hence (N – 1) in ˆ ˆ U i is a function of the two β ‘s Why are we subtracting # of estimates? N 2...
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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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