Formulas for the 2009 final exam

Formulas for the 2009 final exam - I n ¯ Yij − Y • •...

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Unformatted text preview: I n ¯ Yij − Y • • 2 I n = i=1 j =1 ¯ ¯ Yi • − Y • • 2 I n + i=1 j =1 ¯ Yij − Yi • 2 i=1 j =1 total SS = (between-groups SS) + (within-groups SS) (N − 1) = (I − 1) + (N − I ) − F -statistic = (between-groups SS)(/(I−I1) (within-groups SS)/ N ) MSEF = (n−1)s2 +(n−1)s2 +···+(n−1)s2 1 2 I N −I F -statistic = ( SSER – SSEF ) / ( dfR – dfF ) SSEF / dfF ¯ ¯ (Y2 − Y1 ) ± tN −I (1 − α ) · MSE(1/n1 + 1/n2) 2 ¯ ¯ ¯ γ = c1 Y1 + c2 Y2 + . . . + cI YI ˆ ˆ ˆ ˆ Yi = µ(Y | Xi ) = β0 + β1 Xi ˆ ˆ ˆ (β1 − β1 )/SE(β1) ∼ tn−2 SE(ˆ) = MSE · γ σ2 = ˆ n i=1 c2 I i i=1 ni ˆ (Yi − Yi )2 /(n − 2) 1 n ˆ SE[ µ(Y | X0 ) ] = σ 2 · ˆ + ¯ (X0 −X )2 (n−1)s2 X SE ( pred Y | X0 ) = σ 2 + ( SE [ µ(Y | X0 ) ] ) 2 ˆ ˆ n i=1 ¯ ( Yi − Y ) 2 = rXY = n i=1 n i=1 ˆ ¯ ( Yi − Y ) 2 + n i=1 ˆ ( Yi − Yi ) 2 (n − 1) = 1 + (n − 2) n i=1 ¯ ¯ (Xi − X )(Yi − Y ) ¯ ¯ (Xi − X )2 n=1 (Yi − Y )2 i 1/2 log Y vs. X : median (Y | X + c) = median (Y |X ) · ecβ1 Total SS = Regression SS + Lack of ﬁt SS + Residual SS N − 1 = 1 + (I − 2) + (N − I ) R2 = (total SS)−(residual SS) total SS ...
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