Required Formulas Flashcards Preview

MAS223 > Required Formulas > Flashcards

Flashcards in Required Formulas Deck (17):
1

General form for a linear model

y = Xβ + ε, εi ∼ N(0, σ2)

2

Best fit for β

βˆ = [(XTX)^(-1)]XTy

3

Fitted (predicted) values for y

Xβˆ

4

Distribution of βhat

βˆ ∼ N(β, σ2(XT X)−1)

5

Vector of residuals

= y − yhat

6

Residual sum of squares

eTe

7

Unbiased estimator of σ squared

RSS/n-p

8

F-statistic

[(RSSr − RSSf )/(pf − pr)]/RSSf /(n − pf )∼ Fpf −pr,n−pf

9

p-value for F-test

p = P(Fpf −pr,n−pf > F)

10

R squared statistic

Gonna have to look in the notes son, it's too big (that's what she said)

11

Prediction of a future Y* value

= xTβ + ε∗

12

100(1 − α)% prediction interval for Y*

xTβ^ ± Gonna have to look in the notes for the rest son, it's too big (that's what she said)

13

distribution of residuals

e ∼ N(0, σ2(I − P)),
P = X(XT X)^(−1)X

14

Estimated standardised residuals

Gonna have to look in the notes, the notation is too weird son.

15

t-distribution for βˆ

Gonna have to look in the notes son, it's too big (that's what she said)

16

RSSr

RSSf + sum of i = 1 to g [ni(¯yi• −y¯••)^2]

17

100(1 − α)% confidence interval for µhat in ANOVA model

µˆi ± tn−g,1−α/2 sqrt(σˆ2/ni)