STAT 420
Spring 2008
Homework #3
(due Friday, February 8, by 4:00 p.m.)
1.
An employee claims that drinking beer has no effect on the amount of time it takes for
him to perform a particular task. The following data show how many seconds he took
to perform the task after consuming various quantities of beer, measured in ounces:
Beer
Consumption,
x
Time,
y
0
62
12
50
24
59
36
74
48
59
60
83
72
68
Beer
Consumption,
x
Time,
y
( )
2
x
x

( )
( )
y
y
x
x


⋅
( )
2
y
y

0
62
1296
108
9
12
50
576
360
225
24
59
144
72
36
36
74
0
0
81
48
59
144
–72
36
60
83
576
432
324
72
68
1296
108
9
Sum:
252
455
4032
1008
720
SXX
SXY
SYY
7
252
=
=
n
x
x
=
36.
7
455
=
=
n
y
y
=
65.
Consider the model
Y
i
=
β
0
+
β
1
x
i
+
ε
i
., where
ε
i
’s are i.i.d.
N
(
0,
σ
2
).
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View Full Documenta)
Find the equation of the leastsquares regression line.
4032
1008
SXX
SXY
1
ˆ
=
=
=
0.25
.
x
y
⋅

=
1
0
ˆ
ˆ
= 65 – 0.25
⋅
36 =
56
.
Leastsquares regression line:
y
ˆ
= 56 + 0.25
x
.
x
y
y
ˆ
e
e
2
0
62
56
6
36
12
50
59
–
9
81
24
59
62
–
3
9
36
74
65
9
81
48
59
68
–
9
81
60
83
71
12
144
72
68
74
–
6
36
Sum:
0
468
RSS
b)
Give an estimate for
σ
, the standard deviation of the observations about the true
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 Spring '08
 STEPANOV
 Statistics, Harshad number, Statistical hypothesis testing, α, rejection region

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