STATS 100C Midterm Exam 1 Information (Spring 2009)
•Midterm exam 1: Monday, April 20, 2-2:50pm in MS 8125.
•This is a closed-book exam, but you can use a calculator and the formulas provided.
•The z, t and F tables will be provided if necessary.
•Material: Chapters 1-3, HW 1-3.
The following formulas will be provided.
Chapter 2: Simple Linear Regression
The pdf of N(µ, σ2) is f(x) = 1
√2πσ exp[−(x−µ)2
2σ2].
Model: yi=β0+β1xi+#i. LSE: ˆ
β1=sxy
sxx ,ˆ
β0= ¯y−ˆ
β1¯x, ˆµ0=ˆ
β0+ˆ
β1x0.
Variance: V(ˆ
β1) = σ2/sxx,V(ˆ
β0) = σ2(1
n+¯x2
sxx ), V(ˆµ0) = σ2(1
n+(x0−¯x)2
sxx ).
Notation: r=sxy/√sxx syy ,sxx =!(xi−¯x)2=!x2
i−1
n(!xi)2
sxy =!(xi−¯x)(yi−¯y) = !(xi−¯x)yi=!xiyi−1
n(!xi)(!yi)
SST =!(yi−¯y)2,SSR =!(ˆµi−¯y)2=ˆ
β2
1sxx and SSE =!(yi−ˆµi)2.
Chapter 3: Random Vectors Suppose E(y) = µand V(y) = Σ.
E(Ay +b) = Aµ +b, V (Ay +b) = AΣA#, V (y) = E[(y−µ)(y−µ)#], cov(a#y, b#y) = a#Σb.
The pdf of a n-variate normal distribution N(µ, Σ) is
f(x) = (2π)−n
2|Σ|−1
2exp[−1
2(x−µ)#Σ−1(x−µ)]
1