Spring 2012
STAT 512
HW 3 Key
1
Homework 3 (15 pts. + 1 pt. BONUS)
due Feb. 3
A reminder – Please do not hand in any unlabeled or unedited SAS output. Include in your writeup only
those results that are necessary to present a complete solution (what you want the grader to grade). In
particular, questions must be answered in order (including graphs), and all graphs must be fully labeled
(main title should include the question number, and all axes should be labeled). Don’t forget to put all
necessary information (see course policies) on the first page. Include the SAS input for all questions at
the very end of your homework; this could be important even though it won’t be graded. You will often
be asked to continue problems on successive homework assignments so save all your SAS code.
1. (8 pts.) Consider the following data set that describes the relationship between the rate
of an enzymatic reaction (V) and the substrate concentration (C). A common model used
to describe the relationship between the rate and the concentration is the Michaelis
Menten model
°
=
±
?
²
±
?
+
²
, where
1
is the maximum rate of the reaction and
2
describes
how quickly the reaction will reach its maximum rate. The equation can be rearranged so
that
?
°
can be written as a linear model with explanatory variable
?
²
:
?
°
=
?
±
?
+
±
?
±
?
?
²
The data set is as follows:
Concentratio
n
Rate
Concentratio
n
Rate
0.02
49
0.22
159
0.02
47
0.22
152
0.06
97
0.56
191
0.06
107
0.56
201
0.11
123
1.10
207
0.11
139
1.10
200
Even though we know theoretically what the final equation „should‟ be, let‟s see if we can
generate this.
SAS Code:
data
HW3MM;
input
c v @@;
cards
;
0.02 49 0.02 47 0.06 97 0.06 107
0.11 123 0.11 139 0.22 159 0.22 152
0.56 191 0.56 201 1.10 207 1.10 200
;
run
;
proc
print
data
=HW3MM;
*a;
title1
'Problem 1: Transformation of Y'
;
data
transformY;
set
HW3MM;
vinv =
1
/v;
*ai scatterplot;
title2
'1/v vs c'
;
symbol1
v
=circle
i
=sm77;
proc
gplot
data
=transformY;
plot
vinv*c;
run
;
*aii residual plot;
proc
reg
data
=transformY;
model
vinv=c;
output
out
=tYout
r
=residtY;
run
;
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STAT 512
HW 3 Key
2
title2
'residual plot'
;
symbol1
i
=
none
;
proc
gplot
data
=tYout;
plot
residtY*c /
vref
=
0
;
run
;
*aiii normality of residuals;
title2
'normal plots of residuals'
;
proc
univariate
data
=tYout
normal
plot
;
var
residtY;
histogram
residtY /
normal
kernel
(
L
=
2
);
qqplot
residtY /
normal
(
L
=
1
mu
=est
sigma
=est);
run
;
* b *;
title1
'Problem 1: Transform X and Y'
;
*transform x;
data
transformXY;
set
transformY;
cinv =
1
/c;
proc
print
data
=transformXY;
run
;
*bi;
title2
'1/v vs. 1/c'
;
symbol1
v
=circle
i
=sm77;
proc
gplot
data
=transformXY;
plot
vinv*cinv;
run
;
*bii residual plot;
proc
reg
data
=transformXY;
model
vinv=cinv;
output
out
=tXYout
r
=residtXY
p
=predtXY;
run
;
title2
'residual plot'
;
symbol1
i
=
none
;
proc
gplot
data
=tXYout;
plot
residtXY*cinv /
vref
=
0
;
run
;
*biii normality of residuals;
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 Normal Distribution, Regression Analysis, residuals

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