STAT 3022,
April 4, 2009
TA: Jinghan Meng
Homework 6 Solutions
EX 11.13
(a)
We see from the table of coefficients that there were
p
= 5 explanatory variables.
The F statistic has df 5 and 524, so
n

p

1 = 524, meaning
n
= 530.
(b)
We were given
R
= 0
.
44, so the regression explains
R
2
= 19
.
36% of the variation
in percent fat mass.
(c)
Based on the positive coefficients, predicted fat mass is higher for females, those
who take in higher percents of energy at dinner, and children of parents with
higher BMIs.
The one negative coefficient tells us that predicted fat mass is
higher for those with underreported intake (low values of EI/predicted BMR)
and lower for those who overreported intake.
(d)
With
df
= 524, the appropriate critical value for a 95% confidence interval is
t
*
= 1
.
965, so a 95% CI for
β
2
is
ˆ
β
2
±
t
*
β
2
= 0
.
08
±
1
.
965(0
.
02) = [0
.
04
,
0
.
12]
Therefore, when that explanatory variable changes by 5%, percent fat mass
changes by 5
×
[0
.
04
,
0
.
12] = [0
.
2
,
0
.
6].
EX 11.15
(a)
Hypotheses
t
P
Conclusion
H
0
:
β
1
= 0 vs
H
a
:
β
1
6
= 0
4.55
p <
0
.
001
Reject
H
0
; GPA is significant.
H
0
:
β
2
= 0 vs
H
a
:
β
2
6
= 0
2.69
p <
0
.
01
Reject
H
0
; popularity is significant.
H
0
:
β
3
= 0 vs
H
a
:
β
3
6
= 0
2.69
p <
0
.
01
Reject
H
0
; depression is significant.
(b)
b
1
<
0, so marijuana use decreases with increasing GPA;
b
2
and
b
3
are positive,
so marijuana use increases with popularity and depression.
(c)
The numbers 3 and 85 are the degrees of freedom of the F statistic (
p
= 3
explanatory variables and
n

p

1 = 85 degrees of freedom left over after
estimating the four regression coefficients).
(d)
H
0
:
β
1
=
β
2
=
β
3
= 0 vs
H
a
: at least one
β
i
6
= 0.
EX 11.20
(a)
The regression equation is
ˆ
Score
= 3
.
96 + 0
.
86
Unfav
+ 0
.
66
Fav
(b)
Because
p <
0
.
01, we reject
H
0
:
β
1
=
β
2
= 0 in favor of
H
a
: at least one
β
1
, β
2
is nonzero.
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 Spring '08
 Staff
 Linear Regression, Regression Analysis, TA, Errors and residuals in statistics, Residual standard error, Jinghan Meng

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