1
STAT 512
MidTerm I (2/15/2012)
Spring 2012
Section (circle):
12:30 pm
1:30 pm
Name: ___
KEY
______________________________________
INSTRUCTIONS
1. This exam is open book/open notes. All papers (but no electronic devices except for calculators) are
allowed.
2. There are 4 pages in addition to the cover sheet. If you need more room for a problem, use the back
of the sheets; clearly indicate where the location of the answer is.
3. Work is required to receive credit. Partial credit will be given for work that is partially correct. Points
will be deducted for incorrect work even if the final answer is correct.
4. If I cannot read your answer, it will be marked wrong.
5. Good Luck!
Question
Possible
Score
1
45
2
21
3
40
Total
107
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(45 pts.) 1. The TriCity Office Equipment Corporation sells and performs maintenance on imported
copiers via a franchise business. They want to know if there is a relationship between the number
copiers serviced (X = number) and the total number of minutes spend by the service person (Y = time).
The following data is based on 42 recent calls for routine preventive maintenance.
Parameter
Standard
Variable
DF
Estimate
Error
t Value
Pr > t
Intercept
1
0.58016
2.80394
?
0.8371
number
1
15.03525
0.48309
?
<.0001
a) Write down the simple linear regression model and the assumed distribution of the errors.
Y
i
=
0
+
1
X
i
+
i
with
i
???
~
N
(0,
2
) where Y
i
is the time in minutes, X
i
is the number of copiers
b) Write down the estimated regression line.
Ŷ
i
= 0.58016 + 15.03525 X
i
c) Explain the difference between parts a) and b).
a) refers to the model with the true parameters and b) refers to a calculation from the data. a) refers to
the actual points (the error term) and b) refers to only the best fit line
Note: you did not need to include all of these points to get full credit.
d) What is the fitted value of Y for X = 6? If the actual value of Y is 96, what is the residual?
Ŷ
6
= 0.58016 + 15.03525 (6) = 89.63134
e
6
= 96  89.63134 = 6.36866
e) Calculate the missing t values for the intercept and slope.
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 Fall '08
 Staff
 Linear Regression, Normal Distribution, Regression Analysis, administrator, Yi

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