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BENG449 – Problem Set 6, Question 2
Alex Lemon
March 11, 2008
1 Part A
The plot of
S
(
b
1
, b
2
) is a threedimensional graph in which the height of the
graph above the
b
1

b
2
plot gives the value of the residual sum of squares if
the noisy data is estimated using the doubleexponential model with the given
parameter values. On the speciFed region,
S
(
b
) appears to be globally convex
with a minimum corresponding to the OLS estimates for
β
1
and
β
2
. In the Frst
trial, this optimization point was found to be at
b
1
= 0
.
0490 and
b
2
= 0
.
0200;
in the second trial, the OLS estimates were
b
1
= 0
.
0520 and
b
2
= 0
.
0190.
2 Part B
There are two ways to think about whether or not
S
(
b
) is a noisy function. On
the one hand,
S
(
b
) is a smooth function of
b
1
and
b
2
, so the threedimensional
plot of the residual sum of squares versus the parameter values is a smooth
function. When we generate noisy data, we usually expect to see random vari
ation around some underlying relationship with the result that a plot of the
noisy data is not in general a smooth function. However, the plot of
S
(
b
) is a
smooth function of the parameter values,
b
1
and
b
2
. On the other hand,
S
(
b
)
is a function of the noisy data that was generated, and in this sense, the graph
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 Spring '08
 RichardCarson

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