formula sheet - Use Useful Formulas Variance of a random...

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Use Useful Formulas Variance of a random variable [] [] () [] 22 2 VX E X EX EX ⎡⎤ =− = ⎣⎦ Variance of several random variables [ ] [ ] [ ] [ ] [ ] [ ] [ ] 222 V aX bY cZ a V X b V Y c V Z 2abcov X,Y 2accov X,Z 2bccov Y,Z ++ = + + + + + Sample Variance 2 1 ˆ 1 T t t x x VX N = = Covariance [ ] [ ] ( ) [ ] ( ) , COV X Y E X E X Y E Y Sample covariance 1 ˆ , 1 T tt t x xy y COV X Y N = −− = Some useful expressions 2 111 0, TTT t t ttt x xx x x x x === −= = ∑∑∑ Simple linear regression model 12 t yx e β =+ + OLS residuals ˆ t ey b b x =−− OLS estimator 1 2 2 1 T t T t t by b x x b = = =
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Variance of the OLS estimator [] () 2 t 2 1 2 t 2 2 2 t x Vb Tx x xx σ =
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formula sheet - Use Useful Formulas Variance of a random...

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