STAT 420
Fall 2008
Version B
Name ANSWERS
.
Exam 1
Page
Possible
Earned
1
5
2
11
3
10
4
9
5
10
6
7
7
12
8
6
9
10
Total
80
Be sure to show all your work; your
partial credit might depend on it.
No credit will be given
without supporting work.
The exam is closed book and closed notes.
You are allowed to use a calculator and
one 8½" x 11" sheet with notes on it.
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We wish to examine the relationship between the age of a vehicle in years (
x
) and the
selling price (
y
) (in thousands of $) for a particular brand of SUV at
Honest Harry’s
Used Car Dealership
. The data are as follows:
x
y
2
19
3
16
4
11
4
17
5
14
6
7
Σ
x
= 24,
Σ
y
= 84,
Σ
x
2
= 106,
Σ
y
2
= 1272,
Σ
x
y
= 310,
Σ
(
x
–
x
)
2
= 10,
Σ
(
y
–
y
)
2
= 96,
Σ
(
x
–
x
) (
y
–
y
) =
Σ
(
x
–
x
)
y
= – 26.
Consider the model
Y
i
=
α
+
β
x
i
+
ε
i
, where
ε
i
’s are i.i.d.
N
(
0,
σ
2
).
a) (5) Find the equation of the leastsquares regression line.
( )
( )
( )
10
26
2
ˆ




=
=
x
x
y
y
x
x
=
–
2.6
.
OR
( )( )
( )
60
156
24
106
6
84
24
310
6
2
2
2
ˆ





=
=
=
⋅
⋅
⋅
x
x
n
y
x
y
x
n
=
–
2.6
.
6
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 Spring '10
 Stepanov
 Normal Distribution, Regression Analysis, critical value, leastsquares regression line

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