STA 6207 – Exam 2 – Fall 2009
PRINT Name ____________________________
All Questions are based on the following 2 regression models, where SIMPLE REGRESSION refers to
the case where
p
=1, and X is of full column rank (no linear dependencies among predictor variables).
(
29
(
29
I
0
ε
β
X
ε
Xβ
Y
2
2
1
1
0
,
~
1
'
'
:
2
Model
,
0
~
,...,
1
:
1
Model
σ
ε
β
N
p
p
n
NID
n
i
X
X
Y
i
i
ip
p
i
i
×
≡
×
≡
+
=
=
+
+
+
+
=
•
Show that for simple regression, when we have
n
i
observations at the i
th
distinct level of X, the Pure
error sum of squares can be written as
( 29
i
in
i
i
c
i
i
i
Y
Y
S
S
n
SSPE
,...,
of
variance
sample
the
is
where
1
1
2
1
2
∑
=

=
•
An experiment was conducted to study the relationship of between yield from a chemical reaction (y)
and the reaction temperature (x). The following data were obtained from n=12 runs. The fitted equation
based on n=12 runs was Yhat = 92.680.15x. Complete the table by filling in values for X=100.
Level(i) 1 2 3 4 5 6
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 Fall '08
 Park
 Regression Analysis, Elev, SBC

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