Tutorial 5
1. Suppose we have
n
= 10 observations (
X
i
, Y
i
) and fit the data with model
Y
i
=
β
0
+
β
1
X
i
+
ε
i
with
ε
i
, i
= 1
, ...,
10 are IID
N
(0
, σ
2
). We have the following calculations.
¯
X
= 0
.
5669
,
¯
Y
= 0
.
9624
,
n
i
=1
Y
2
i
= 10
.
2695
,
n
i
=1
X
2
i
= 4
.
0169
,
n
i
=1
X
i
Y
i
= 6
.
2841
.
(a) Write down the estimated model
(b) Test
H
0
:
β
1
= 1 with
α
= 0
.
05
(c) For a new
X
= 1, find the 95% CI for its expected response
(d) For a new
X
= 0
.
5, find the 95% prediction interval for its possible response
2. For the least square estimator
b
0
, b
1
of simple linear regression model, find
Cov
(
b
0
, b
1
)
3. Suppose
A
:
m
×
n
is a constant matrix and
Y
:
n
×
1
,
is a random vector. Then
Var
(
AY
) =
A
Var
(
Y
)
A
Please give your proof for
m
= 2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 XIAYingcun
 Linear Regression, Regression Analysis, Yi, 2 j, Xi Yi

Click to edit the document details