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Final
Exam
Review
 Model
vs
Data
December
15,
2006
Model
vs.
Data
In
most
experiments
we
can
control
a
set
of
independent
variables
x
and
can
measure
the
value
of
the
dependent
variable
y
.
For
such
a
system
we
can
propose
a
model
which
relates
the
value
of
the
dependent
variable
to
the
values
of
the
independent
variables
as
shown
in
Equation(1)
y
=
f
(x;
Θ)
(1)
The
aim
of
the
generating
a
model
for
the
system
is
to
obtain
an
answer
to
the
following
three
questions
For
what
value
of
Θ
is
the
deviation
between
model
and
data
minimum?
•
Is
the
model
consistent
with
the
data?
•
•
What
are
the
error
bars
on
the
values
of
parameters?
In
the
context
of
models
we
classify
models
as
linear
or
nonlinear.
Linear
models
depend
on
the
parameters
Θ
linearly.
For
example
the
log
of
the
rate
of
an
arrhenius
reaction
is
linear
in
the
parameters
log(
A
)
and
E
R
a
.
This
model
is
linear
even
tough
log(
A
)
is
not
linearly
dependent
on
the
dependent
variable
temperature
T
.
E
a
log(
k
)
=
log(
A
)
−
(2)
RT
Usually
in
solving
these
problems
we
make
the
following
two
assumption
1.
The
dependent
variable
y
,
that
is
being
measured
is
distributed
nor±
mally
(a
gaussian
distribution)
around
its
mean
value.
This
distri±
bution
can
be
due
to
many
factors
which
are
not
in
control
of
the
experimentalist.
2.
On
the
other
hand
the
independent
variables
x
are
known
exactly.
1
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 Fall '04
 ClarkColton

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