Statistics 512: Problem Set No. 3
Due Monday, October 4, 2010 (PTR & EPE)
Tuesday, October 5, 2010 (Divisions 2 & 3)
1. Consider the following data set that describes the relationship between the rate of an enzy
matic reaction (
V
) and the substrate concentration (
C
). A common model used to describe
the relationship between rate and concentration is the MichaelisMenten model
V
=
θ
1
C
θ
2
+
C
,
where
θ
1
is the maximum rate of the reaction and
θ
2
describes how quickly the reaction will
reach its maximum rate. With this mode,
1
V
can be written as a linear model with explanatory
variable
1
C
:
1
V
=
1
θ
1
+
θ
2
θ
1
1
C
Concentration
Rate
0.02
76
0.02
47
0.06
97
0.06
107
0.11
123
0.11
139
Concentration
Rate
0.22
159
0.22
152
0.56
191
0.56
201
1.10
207
1.10
200
(a) Generate a scatterplot of
V
vs
C
. Comment on the shape.
(b) Define new variables for
1
V
and
1
C
in SAS, and generate a scatterplot of the new variables.
Does the fit appear linear? Do any assumptions appear to be violated? The new variables
can be defined as follows (if the dataset
original
contains the raw data):
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 Spring '08
 Staff
 Statistics, Linear Regression, Regression Analysis, residuals, new variables

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