Formula sheet for final
Classical Linear Regression (CLR) model
The
n
observations
iK
i
i
X
X
Y
,
,
,
1
K
,
n
i
,
,
1
K
=
, on a dependent variable
Y
and
K
independent
variables
K
X
X
,
,
1
K
satisfy
(1)
i
iK
K
i
i
i
u
X
X
X
Y
+
+
+
+
=
b
b
b
L
2
2
1
1
for
n
i
,
,
1
K
=
.
Assumption 1:
n
i
u
i
,
,
1
,
K
=
are random variables with
0
)
(
=
i
u
E
Assumption 2:
K
k
n
i
X
ik
,
,
1
,
,
,
1
,
K
K
=
=
are deterministic, i.e. non-random, constants.
Assumption 3: (Homoskedasticity)
All
s
u
i
'
have the same variance, i.e. for
n
i
,
,
1
K
=
(2)
2
2
)
(
)
(
s
=
=
i
i
u
E
u
Var
Assumption 4 (No serial correlation)
The random errors
i
u
and
j
u
are not correlated for all
n
j
i
,
,
1
K
=
≠
(3)
0
)
(
)
,
(
=
=
j
i
j
i
u
u
E
u
u
Cov
For the CLR model with normal errors we make the additional assumption:
Assumption 5. The random error terms
n
i
u
i
,
,
1
,
K
=
are random variables with a normal
distribution.