ANSWER:
SSR
=
SST
–
SSE
=1278.33-460.2 = 818.13
7.
What is the correlation coefficient for the stock returns of the two years? What sign does it have?
Why?
ANSWER:
r
=
2
0.64
R
= 0.80. It has a positive sign since
1
b
= 1.04 is positive.

Simple Regression
2
8.
What are the appropriate null and alternative hypotheses?
ANSWER:
0
1
:
0 and
:
0
H
H
9.
Test the hypothesis in the eightieth question at
= 0.05.
ANSWER:
The test statistic
2
2
2 / 1
0.80 13/ 0.36
4.807
1
/
2
r
t
r
n
r
r
n
Since
2,
13, 0.05
1.771
n
t
t
, we reject
0
H
at
=0.05. We conclude that the stock returns in
2004 and 2005 are positively correlated.
10.
Test
0
1
1
1
:
0 vs.
:
0 at
0.025
H
H
.
ANSWER:
The test statistic
1
1
1
/
1.04/0.2163
4.808
b
t
b
s
.Since,
2,
13, 0.025
2.16
n
t
t
, we
reject
0
H
at
=0.025 and conclude that there is a positive linear relationship between the stock
returns in 2004 and 2005.
11.
Prepare the analysis of variance table for regression.
ANSWER:
Source of variation
SS
df
MS
F
Regression
818.13
1
818.13
23.11
Error
460.2
13
35.4
Total
1278.33
14
12.
Use the
F
-statistic in the eleventh question to test the hypothesis in the tenth question at
= 0.05.

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- Fall '19