Summary Econometrics 1 UvA first two weeks

Over view lecture 1a


Basic model least to estimate P
regressies squares
'

b)
'


( g- ✗ b) (
'

zei ✗
13 Pz 13h
min
✗ i. 2 c- e. e
= = -

+
yi
= + + +
X k Ei =
1 n
-


,
.




, .
. . .
.




,
.




is

'
b
' ' '
'
✗ b- ✗
b b. ✗ ✗
'
+
g. y y
= -




row
of ✗ Xi column of ✗ Xj
'

: :
,


/ '



yty ✗b ✗ ✗b
'

b.
=
z +
-




✗ b
fitted values : =
.




'
✗ ✗ Jb
' ' '

s zei =
0 -
2 ✗
y + [ ✗ ✗ +

=
✗b →
e
y
.
- =


y
-




'

✗b
'
✗
y ✗
=
-
+ =
o

estimated model =
✗ b. te
y
'

:




{
'




{
( ✗ b- g)
' '

✗ ✗ ✗ b ✗
y
=




'
'

# ✗5
'
× D= ✗
Differentiatie
e
y

sáx
dG AÏ
→ = =




Projecten matrix
j ' ' '
(✗ )
-




we have ✗ b and D= × ✗
y
=
,

→ SAI =
a
'
'



✗ (✗ × )
H
' -




then ✗ His
2X =
y
=
.




project ion

[A
'
] columns of X

Jxjxtx
→ = -1A × matrix on .




Then
y
=
Û te =

H + (l -



1-1)
y
=


H +
M




ijijijijijij
ij ij S. Veeling