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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.
___________________________________________________________________________
Academic Integrity
The University statement on your obligation to maintain academic integrity is:
If you engage in an act of academic dishonesty, you become liable to severe disciplinary action. Such acts include cheating;
falsification or invention of information or citation in an academic endeavor; helping or attempting to help others commit
academic infractions; plagiarism; offering bribes, favors, or threats; academic interference; computer related infractions; and
failure to comply with research regulations.
Rule 33 of the Code of Policies and Regulations Applying to All Students gives complete details of rules governing
academic integrity for all students. You are responsible for knowing and abiding by these rules.
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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

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