Download Stat 301 Exam 1 Formulas

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