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

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## Fitted (predicted) values for y

### Xβˆ

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## Distribution of βhat

### βˆ ∼ N(β, σ2(XT X)−1)

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## 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

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## 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]

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