ISMT 111 Business Statistics
Simplified Solution for Problem Sheet 6
1.
(a)
1
ˆ
b
=
1.7483
0
ˆ
b
=
 8.0068
∴
y
ˆ
=  8.0068 + 1.7483
x
When there is a 1% increase in the market return, the average return on Dalton Company
’
s stock tends to
increase by 1.7483 %.
(b)
H
0
:
b
1
= 1
H
a
:
b
1
> 1
Test statistic
t
= 2.5963; and
t
α
,
n
–
2
=
t
0.05, 8
= 1.86
Since t > t
0.05, 8
, reject
H
0
at 0.05 level of significance.
We have sufficient evidence that Dalton
’
s Company
’
s Stock is sensitive to the market.
(c) A 90% P. I. for
y
given
x
= 10.5 is (6.6151, 14.0856)
(d)
r
= 0.9063
⇒
R
2
= 0.8214 or 82.14%
(e) A 98% C. I. for E(
y

x
= 14) is (13.2046, 19.7342)
2.
(a)
1
ˆ
b
=  364.6
On average, the Calorie content decreases by 364.6 when there is an unit increase in the Price per ounce.
(b)
H
0
:
b
1
= 0
H
a
:
b
1
≠
0
Test statistic
t
=  3.603; and
t
0.025, 7
= 2.365
Since 
t
 >
t
0.025, 7
, reject
H
0
at 0.05 level of significance.
The price is a good predictor of the calorie content.
(c)
R
2
= 0.6498 = 64.98%
That means 64.98% of the variability of the calorie content can be explained by the price.
3.
(a)
1
ˆ
b
= 0.564347826
0
ˆ
b
=
7.086956522
(b) 35.30434783
(c) A 95% P. I. is (2.039713895, 45.99506871)
4.
(a)
y
ˆ
= 0.22072 + 0.47114
x
(b) No.
It is not meaningful to interpret
(reasons should be given)
.
(c) For a unit increase in the test score (
x
), the grade point average (
y
) is expected to increase by 0.47114 points.
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 Spring '09
 AnthonyChan
 Statistics, Regression Analysis, C. I., P. I.

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