STAT 420
Spring 2008
Homework #4
(due Friday, February 15, by 4:00 p.m.)
1.
Recall Problems #5 and #6 from Homework 1:
It has been proposed that the brightness measured in some unit of color or a
commercial product is proportional to the time it is in a certain chemical reaction
during the production process, or
Y
i
=
β
x
i
+
ε
i
,
i
= 1, 2, … ,
n
, where
ε
i
’s are i.i.d.
N
(
0,
σ
2
),
where
Y
i
measures brightness,
x
i
measures time, and
β
is a parameter. The
following data on
x
and
Y are available:
x
1.0
1.2
1.4
1.6
1.8
2.0
Y
3.4
7.0
6.0
9.0
8.0
11.0
x
y
y
ˆ = 5
x
e
=
y
–
y
ˆ
1.0
3.4
5
–
1.6
1.2
7.0
6
1.0
1.4
6.0
7
–
1.0
1.6
9.0
8
1.0
1.8
8.0
9
–
1.0
Then
ˆ
=
=
=
n
i
i
n
i
i
i
x
y
x
1
2
1
=
5.
2.0
11.0
10
1.0
Without
β
0
in the model, SSTotal =
Y
T
Y
=
Σ
y
2
.
Without
β
0
in the model, dfTotal =
n
.
RSS =
Σ
e
2
.
Without
β
0
in the model, SS
Reg
=
Y
Y
ˆ
ˆ T
=
2
y
ˆ
=
Σ
2
ˆ
x
2
.
Set up the ANOVA table. Does
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 Spring '08
 STEPANOV
 Statistics, Null hypothesis, Previous question, Statistical hypothesis testing, Yi, certain chemical reaction

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