STAT 331/361/SYDE 334 Assignment 2
Due: Thursday, February 14, 2008
in class
Note:
Question 5 requires using R. Computing outputs need to be integrated into your answers at
appropriate places. Stacking your computing stuff all together and putting them at the back is
NOT acceptable!
1. If
y
and
, then the sample correlation coefficient between
and
)
,...,
(
1
n
y
y
=
)
,...,
(
1
n
x
x
x
=
y
x
is
defined as
)
/(
xx
yy
xy
s
s
)
,
(
x
y
r
s
=
. Let
)
,...,
(
1
n
e
e
e
=
be the residuals from fitting the simple
linear regression model
i
i
x
i
y
ε
β
β
+
+
=
1
0
using the least square method. Show that
0
)
,
(
=
x
e
r
.
2.
Suppose that the simple linear regression model with the assumptions given in Section 2.1.1 holds.
Show that
(
)
2
1
2
)
2
(
σ
−
=
∑
=
n
e
E
n
i
i
. (
Hint
: First show
xx
xy
yy
n
i
i
s
s
s
e
/
2
1
2
−
=
∑
=
xx
s
, then show
and
).
xx
s
n
2
1
2
)
1
β
σ
+
−
E
yy
s
E
(
)
(
=
xx
xy
s
s
2
2
2
1
2
)
(
σ
β
+
=
3.
Consider the simple linear regression model
,
,...,
1
,
1
0
n
i
x
y
i
i
i
=
+
+
=
ε
β
β
where
and
2
)
(
,
0
)
(
σ
ε
ε
=
=
i
i
V
E
n
ε
ε
ε
,
...
,
,
2
1
are independent.
This
preview
has intentionally blurred sections.
Sign up to view the full version.

This is the end of the preview.
Sign up
to
access the rest of the document.
- Winter '08
- YuliaGel
- Correlation Coefficient, Regression Analysis, linear regression model
-
Click to edit the document details