FORMULASHEET - Decision Tree Parameter µ Distribution XX...

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Unformatted text preview: Decision Tree Parameter µ Distribution XX XXX XXX X Test Statistic z z= x¯ pµ s/ n x¯ ± za/2 psn t t= x¯ pµ s/ n x¯ ± ta/2 psn s2 c2 c2 = (n 1)s2 s2 p z z= p pˆ p p(1 p)/n µ1 µ2 P QPP Q PP Q PP Q PP Q Q Q Q Q z t p1 z= t= t= p2 z PP PP P PP P P z z= z= (x¯1 (x¯r 1 x¯2 ) (µ1 µ2 ) ⇣ ⌘ s2p n1 + n1 (x¯1 2 (x¯1 r x¯2 ) (µ1 µ2 ) (x¯1 s2 s2 1 2 n1 + n2 r x¯D pµD sD / n D 1 F s21 /s22 µ1 , µ2 , · · · F MST MSE ( pˆ1 2 r ( pˆ1 pˆ2 ) D pˆ1 (1 pˆ1 ) pˆ2 (1 + n n s21 /s22 (n 1)s2 c21 a/2 UCL = q p(1 ˆ p) ˆ n x¯2 ) ± za/2 q s21 n1 q s21 n1 s2 + n22 r ⇣ ⌘ x¯2 ) ± ta/2 s2p n11 + n12 x¯2 ) ± ta/2 s2 + n22 x¯D ± ta/2 psnDD pˆ1 pˆ2 ⇣ ⌘ p(1 ˆ p) ˆ n1 + n1 1 (n 1)s2 c2a/2 pˆ ± za/2 2 s2 1 s2 n1 + n2 t= t LCL = (x¯1 r x¯2 ) (µ1 µ2 ) 1 t µD Confidence Interval 2 pˆ2 ) ( pˆ1 pˆ2 ) ± za/2 pˆ2 ) ± za/2 LCL = s21 /s22 q q Fa/2,n1 ,n2 pˆ1 (1 pˆ1 ) n1 + pˆ2 (1n2 pˆ2 ) pˆ1 (1 pˆ1 ) n1 + pˆ2 (1n2 pˆ2 ) UCL = F1 s21 /s22 a/2,n1 ,n2 Formula Sheet µ= ÂNi=1 xi N x¯ = Âni=1 xi n s2 = E[x] ¯ = µx sx p n s2 = sx¯ = COV(X,Y ) = r= z= p n= t= r= z= pˆ p p(1 p)/n pˆ ± za/2 z2a/2 s2 w2 n= (x¯r 1 x¯2 ) (µ1 µ2 ) ⇣ ⌘ s2p n1 + n1 x¯ ± za/2 psn p)/n ˆ c2n p ◆2 p(1 ˆ p) ˆ w d f = n1 + n2 2 (x¯1 1= (n 1)s2 s2 n= cov(x, y) = tn 1 2 n2 1 s= p s2 s= p s2 q s µ cv = = LCL = z2a/2 (.5)2 w2 x¯ pµ s/ n (n 1)s2 c2a/2,n 1 z= (x¯1 p(1 p) n Âni=1 xi yi nx¯y¯ n 1 s x¯ x¯ ± ta/2 psn UCL = (n 1)s2 c21 a/2,n 1 (x¯1 r x¯2 ) (µ1 µ2 ) r ⇣ ⌘ 1 1 2 x¯2 ) ± ta/2 s p n1 + n2 s2p = (s2 /n1 +s2 /n2 ) d f = 21 2 2 2 2 (s1 /n1 ) + (s2 /n2 ) n1 1 s pˆ = ¯ i y) ¯ Âni=1 (xi x)(y n 1 CV = p(1 ˆ za/2 Âni=1 xi2 nx¯2 n 1 E[ p] ˆ =p cov(x,y) sx sy x¯ pµ s/ n p x n cov(x, y) = 2 (x¯1 r x¯2 ) (µ1 µ2 ) s21 s2 2 n1 + n2 ✓ s2 = pˆ = ÂNi=1 (xi µx )(yi µy ) N x µ s 1 t= ¯2 Âni=1 (xi x) n 1 COV(X,Y ) sx sy z= ÂNi=1 (xi µ)2 N 2 s2 1 + s2 n1 n2 (n1 1)s21 +(n2 1)s22 n1 +n2 2 x¯2 ) ± ta/2 q s21 n1 s2 + n22 t= x¯D pµD sD / nD UCL = F1 d f = nD s21 /s22 a/2,n1 ,n2 z= nj xi j x¯ = 1n Âkj=1 Âi=1 R2 cov(x,y) s2x SSE SST =1 Fk,n k 1 t =r q d= = = q ( pˆ1 pˆ2 ) D pˆ1 (1 pˆ1 ) pˆ2 (1 + n n 1 ¯ i y) ¯ Âni=1 (xi x)(y ¯2 Âni=1 (xi x) = SSR SST MSR MSE = [cov(x,y)]2 s2x s2y Adj.R2 = yˆ ± ta/2 se St = wyt + (1 R p = w1 R1 + w2 R2 pˆ2 ) ± za/2 =1 (x 1 q tn k 1 1)s21 + · · · + (nk Fk x) ¯2 1)s2x SSFE = Âni=1 (yi 1,n k = b0 = y¯ se = = x1 +x2 n1 +n2 pˆ1 (1 pˆ1 ) pˆ (1 pˆ ) + 2 n2 2 n1 SSE n k SSE/(n k 1) SST/(n 1) Fa/2,n1 ,n2 2 se (n 1)s2x 1 + 1n + (ng w)St 1 s21 /s22 pˆ = sb1 = p (SSR f SSRr )/kd MSE f r LCL = pˆ1 pˆ2 ⇣ ⌘ p(1 ˆ p) ˆ n1 + n1 MSE = Âni=1 xi yi nx¯y¯ Âni=1 xi2 nx¯2 k 1) f r s21 s22 x¯ j )2 SSE = (n1 SST k 1 = Fkd ,(n n 2 1 r2 Âni=2 (ei ei 1 )2 Âni=1 e2i ( pˆ1 pˆ2 ) 2 MST = F= z= j ¯ 2 SSE = Âkj=1 Âni=1 x) (xi j SST = Âkj=1 n j (x¯ j b1 = p2 = 0 H0 : p1 p2 = D 6= 0 H0 : p1 x¯D ± ta/2 psnDD 1 q bi bi sbi yˆ ± ta/2 se 1)s2k MST MSE b1 x¯ SSE n k 1 bi ± ta/2 sbi r (xg x) ¯2 1 + n (n 1)s2x Fi )2 MAD = Âni=1 |yi Fi | n q q 2 2 2 2 s(R p ) = w1 s1 + w2 s2 s(R p ) = w21 s21 + w22 s22 + 2rw1 w2 s1 s2 To Find Critical Values To Find P Values ...
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