STATS 3A03: Fall 2025
Some Useful Formulae
1. Preliminaries
P
P 2
• Sxx =
(xi − x)2 =
xi − nx2
P
P
• Sxy =
(xi − x)(yi − y) =
xi yi − nx y
• Cov(X, Y ) = E [(X − µX )(Y − µY )] = E(XY ) − µX µY
√
Sxy
r n−2
Cov(X, Y )
√
r = p
∼ tn−2
• ρ = p
Sxx Syy
1 − r2
Var(X)Var(Y )
2. For the simple linear regression model:
Sxy
• β̂0 = y − β̂1 x
β̂1 =
Sxx
P
SSE
(yi − ŷi )2
• σ̂ 2 =
=
n−2
n−2
2
• Var(µ̂0 ) = n1 + (x0S−x̄)
σ2
xx
s
s.e. β̂0
= σ̂
1
x2
+
n Sxx
σ̂
s.e. β̂1 = p
Sxx
2
Var(ŷ0 ) = 1 + n1 + (x0S−x̄)
σ2
xx
1