STAT 212: Quiz 11 - Formulas for Descriptive and Inferential Statistics, Study notes of Data Analysis & Statistical Methods

Download STAT 212: Quiz 11 - Formulas for Descriptive and Inferential Statistics and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! STAT 212: Quiz 11 Formulas • x̄ = 1 n n∑ i=1 xi • s2 = 1 n− 1 n∑ i=1 (xi − x̄)2 = 1 n− 1 { n∑ i=1 x2i − ( ∑n i=1 xi) 2 n } • s = √ s2 • r = 1 n− 1 n∑ i=1 ( xi − x̄ sx )( yi − ȳ sy ) • ŷ = b0 + b1x; b1 = r sy sx , b0 = ȳ − b1x̄ • µX = ∑ xipi • σ2X = ∑ (xi − µX)2pi • σ2a+bX = b2σ2X • σ2X+Y = σ2X + σ2Y + 2ρσXσY • σ2X−Y = σ2X + σ2Y − 2ρσXσY • µx̄ = µ; σx̄ = σ√ n • P (X = k) = n! k!(n− k)! pk(1− p)n−k; µ = np, σ = √ np(1− p) • P (X = k) = e −µµk k! • x̄± z∗ σ√ n • n = ( z∗σ m )2 • z = x̄− µ (σ/ √ n) • t = x̄− µ (s/ √ n) • x̄± t∗ s√ n • z = (x̄1 − x̄2)− (µ1 − µ2)√ σ21 n1 + σ 2 2 n2 • t = (x̄1 − x̄2)− (µ1 − µ2)√ s21 n1 + s 2 2 n2 • (x̄1 − x̄2)± t∗ √ s21 n1 + s22 n2 • p̂± z∗ √ p̂(1− p̂) n • n = ( z∗ m )2 p∗(1− p∗) • z = p̂− p0√ p0(1− p0)/n • (p̂1 − p̂2)± z∗ √ p̂1(1− p̂1) n1 + p̂2(1− p̂2) n2 • z = (p̂1 − p̂2)√ p̂(1− p̂) ( 1 n1 + 1n2 ) , p̂ = X1 +X2n1 + n2 • SST = Total SS, SSR = Regression SS, SSE = Residual SS • SST = SSE + SSR • SSE = n∑ i=1 (yi − ŷi)2 = (n− 1)s2y(1− r2) • SST = n∑ i=1 (yi − ȳ)2, SSR = n∑ i=1 (ŷi − ȳ)2 • s = √ SSE n− 2 • t = b1 − β1 SEb1 • SEb1 = s√ (n− 1)s2x • t = r √ n− 2√ 1− r2 • r2 = SSR SST = 1− SSE SST • ŷ ± t∗SEµ̂, SEµ̂ = s √ 1 n + (x∗ − x̄)2 (n− 1)s2x • ŷ ± t∗SEŷ, SEŷ = s √ 1 + 1 n + (x∗ − x̄)2 (n− 1)s2x