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Stat 301 Exam 1 Formulas Inference for population parameters (general): −null • Test statistic: T = estimate Std Error • Prediction sd: q Std Error2 + s2 • Error df: N − # estimates One sample (one mean): model: EY = µ data: Y = µ + ε Estimate of µ: Y r Standard deviation s: Std Error of Y : Σ(Yi −Y )2 n−1 √s n Two sample (one mean): model: EY = µi data: Yij = µi + ij Estimate of the difference µ1 − µ2 : Y 1 − Y 1 r Pooled est. of sd, sp : Std Error of the difference Y 1 − Y 1 : s r r Std Error of diff., not pooled: (n1 −1) s21 +(n2 −1) s22 n1 +n2 −2 1 n1 s21 n1 + 1 n2 s22 n2 + Simple linear regression: model: EY = β0 + β1 X data: Y = β0 + β1 X + ε estimate of intercept, β̂0 : Y − β̂1 X estimate of slope, β̂1 : estimate of sd around line, s: Std error of estimated slope: Σ(Xi −X) Yi Σ(Xi −X)2 r (Yi −Ŷi )2 n−2 r s Σ(Xi −X)2 s 1 n SE of mean prediction at X = X0 : s + (X0 −X)2 Σ(Xi −X)2 s SD of predicted observation at X = X0 : s 1 + r 1 n + (X0 −X)2 Σ(Xi −X)2 = s2 + s2µ̂Y0 1