Formula Sheet - Population Parameters Estimators (Sample)...

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Population Parameters Estimators (Sample) Univariate Measures (distribution of a single variable – Y) [] 1 N i i Y i i Y E Y f Y N µ = == = i Y n = 2 () iY Y Y N σ = 2 (- ) -1 i Y Y Y s n = Sampling Distribution for Y Y Y n = Y Y s s n = Bivariate Measures (joint distribution of X and Y) 1 1 ( - ) ( - ) N ii XY i Cov X N µµ = = ( ) i i XY Y x y −− X Y Cov ρ σσ = XY XY s r s = Portfolio Expected Return and Risk ( ) ( 1 ) () EP wEX wEY =+ ; 22 (1 ) 2 ) P X Y ww w w + Regression Measures (X causes Y to change) 1 β 2 1 2 - ˆ - i i i n X Y y x x X YY n x x X X = ∑∑ 0 01 ˆˆ - X ββ = EYX X ˆ YX [ ] Var u E u 2 2 ˆ 2 i e n = Sampling Distributions for OLS Estimators 0 ˆ 0 2 ˆ i i X Var nx βσ 0 ˆ 2 ˆ i i X s = 1 2 ˆ 1 2 ˆ i Var x 1 2 ˆ 2 ˆ i s x = 0 2 2 0 ˆ 0 2 1 ˆ Y i XX Var Y ⎡⎤ + ⎢⎥ ⎣⎦ 0 2 2 0 ˆ 2 1 ˆ Y i s
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Confidence intervals for Y µ univariate distribution : When Y σ is known: (/ 2 ) Y Y z α ±⋅ When Y is not known: 2 ,- 1 ) n Y t
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This note was uploaded on 05/19/2008 for the course RES-ECON 312 taught by Professor Lass during the Fall '07 term at UMass (Amherst).

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Formula Sheet - Population Parameters Estimators (Sample)...

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