Summary STA2005: Studentised Residuals Proof

, Proof of studentised Residuals

✗ ci )
design matrix ,

with ith row removed


Yii) similar to xci)

Bci ) y

Xi ith row of ✗ matrix

Yi ith element of y
Ii ith estimated residual
,

when all observations used to calculate §

Expression for studentised residuals
externally
n

ti point )
}
= Yi -
Xi .
Bci) Memorise our start
Sii ) ( I -1 x :( ✗F) ✗ ;)
- '
a kit

>
Similar to M matrix
'
ie ) M In ✗ ( ✗ Tx) XT
-

= -




v

show that expression can
be simplified to


ti = eli
still hii -