E(Y ) = Pn i=1 yi P r(Y = yi ) σY2 = E(Y 2 ) − [E(Y )]2 p σY = σY2 =y) P r(Y = y|X = x) = P r(X=x,Y P r(X=x) P P r(Y |X = x) = ni=1 P r(Y = yi |X = x) P P cov(X, Y ) = ni=1 m j=1 (xi −µX )(yj −µY )P r(X = xi , Y = yj ) ρXY = corr(X, Y ) = √ cov(X,Y ) var(X)var(Y ) = σXY σX σY Pn Ȳ = 1 n s2y = 1 n−1 i=1 Yi Pn i=1 (Yi − Ȳ )2 q √ SE(Ȳ ) = s2y /n = sy / n tact = Ȳ Actual −µY SE(Ȳ ) tact = (Ȳm −Ȳw )−d) SE(Ȳm −Ȳw ) or tact = p − value = 2Φ(−|tact |) q 2 SE(Ȳm − Ȳw ) = nsww + βˆ1 −β1,0 SE(βˆ1 ) s2m nm 95%C.I. = [βˆ1 − 1.96SE(βˆ1 ), βˆ1 + 1.96SE(βˆ1 )] \Y ) = sxy = 1 Pn (Xi − X̄)(Yi − Ȳ ) cov(X, i=1 n−1 \Y ) = rxy = corr(X, βˆ1 = sxy sx sy Pn (X −X̄)(Yi −Ȳ ) i=1 Pn i 2 i=1 (Xi −X̄) = sxy s2x s = rxy sxy βˆ0 = Ȳ − βˆ1 X̄ 1 ESS T SS R2 = =1− SSR T SS R2 = (rxy )2 ESS = Pn − Ȳ )2 T SS = Pn − Ȳ )2 with T SS = ESS + SSR SSR = Pn − Ŷi )2 = i=1 (Ŷi i=1 (Yi i=1 (Yi R̄2 = 1 − n−1 SSR n−k−1 T SS SER = sû = s2û = 1 n−k−1 σβ21 = q Pn =1− 2 i=1 (ûi ) n−1 n−k−1 (1 SSR n−k−1 ˆ2 i=1 ui Pn = SSR n−k−1 1 var[(Xi −µx )ui ] n [var(Xi )]2 F = 2 2 (RU nrestricted −RRestricted )/q 2 (1−RU nrestricted )/(n−kU nrestricted −1) F = (SSRRestricted −SSRU nrestricted )/q (SSRU nrestricted )/(n−kU nrestricted −1) F = 1q { t21 +t22 −2ρ̂t1 ,t2 t1 t2 } 1−ρ̂2t1 ,t2 ∼ Fq=2,n−k−1 2 − R2 ) = 1 − s2u s2Y