Hello
everyone.
My
name
is
Micol Tresoldi.
Today
my
talk
will
be
about
coding
with
continuous
and
mixture
variables
to
explore
more
of
the
input
space.
Before
I
jump
into
the
topic
though,
I'd
like
to
give
your
brief
outline
of
what
my
presentation
would
look
like.
I'll
start
by
sharing
and
presenting
to
you
a
little
bit
of
a
general
idea
of
what
the
object
of
the
project
was
and
the
objective
that
was
driving
it,
and
then
I'll
pass
on
to
present
the
initial
approach
that
we
took
initially
to
pursue
this
objective.
I'll
then
show
you
though,
that
following
this
initial
approach,
we
do
encounter
some
problem.
At
that
point
at
the
problem
stage,
we'll
need
to
go
back
to
the
beginning
of
the
problem
setting,
and
try
to
look
at
that
from
a
slightly
different
perspective,
in
a
way
that
we
can
figure
out
an
alternative
way
of
looking
at
our
input
variables.
In
doing
this,
we'll
be
altering
our
data
structure.
But
I'll
show
you
how
we
can
actually
build
an
equivalent
to statistical
model
in
a
way
that
we
will
not
be
in
need
of
going
and
collect
any
additional
data,
but
actually
we'll be
able
to
re-analyse
exact
same
data,
and
still
be
able
to
hopefully
overcome
our
initial
problem
and
find
some
useful
directions
to
go.
This
is
the
overview
of
the
presentation.
Let
me
start
by
giving
you
the
general
idea
of
the
project.
When
the
clients
first reach
out
to
us,
they
had
something
in mind
in
terms
of
having
some
ingredients
they
needed
to
mix
together,
in
a
way
that
the
final
formulation
exhibited
some
optimal
properties.
More
specifically,
any
formulation
was
going
to
be
judged
upon
two
properties,
and
each
of
these
properties
had
to
meet
some
certain
optimality
criteria.
As
I
just
stated,
the
problem
itself,
is
pre-
general
in
its
nature
.
We'll
have
some
ingredients,
using
the
common
analogy,
we
can
think
about
ourselves
in
the
kitchen
having
some
ingredients
and
having
to
figure
out
a
way
to
mix
them.
In
way
that,
at
the
end,
our
cake
will
look
nice
and
also
taste
good.
This
is
the
general
framework.
Now,
let
me
give
you
some
more
details
about
this
specific
cake.
The
recipe
calls
for
four
ingredients,
Factor
A,
Factor
B,
Factor
C,
and
Factor
D.
For
Factor
A,
B,
and
C,
actually
the
amount
to
put
in
the
recipe
is
being
predetermined.
We
don't
have
freedom
there.
On
the
other
hand,
what
we
need
to
decide
though
is
how
we're
going
to
make
those
ingredients,
if
you
like.
There
are
multiple
ways
of
making
those
ingredients
because
we
have
multiple
raw
materials
that
we
can
employ
to
arrive
to
those
ingredients.
Then
only
after
having
these
ingredients
ready
for
using,
we
can
actually
employ
them
in
the
final
recipe.
This
is
for
Factor
A,
B, and C.
For
Factor
D
on
the
other
hand,
there
is
only
one
raw
material
we
can
use.
Only
one
way
of
making
it.
What
we
need
to
decide
is
how
much
we're
going
to
put
a
factor
D
in
the
final
recipe.
Just
to
recap,
in
terms
of
decision
-making
problem,
we'll
need
to
decide
four
things,
how
we
make
Factor
A,
how
we
make
Factor
B,
how
we
make
Factor
C,
and
how
much
of
Factor
D
we're
going
to
put
in
the
recipe.
Okay,
now
I'll
need
to
be
a
little
more
specific
in
giving
you
some
more
details
about
how,
what
were
these
ways
of
making
Factor
A,
B,
and
C.
The
client,
when
they
came
to
us,
they
had
relatively
few
options
in
mind
for
this.
For
Factor
A,
they
wanted
to
consider
two
raw
materials.
either
only
using
raw
material
A1,
or
only
using
raw
material A2.
For
factor
B,
once
again,
only
two
raw
materials,
B
1
and
B
2.
The
possible
ways
of
making
factor
B,
it
was
either
the
two
pure
blends
of
B
1
and
B
2,
or
a
50-50
blend
of
B
1
and
B2.
Factor
C
we are
now
three
row
materials
are
available
for
making
it.
Again, either
the
three
pure
blends,
C
1,
C
1,
C3,
or
as
a
fourth
options,
are
50-50
blend
of
C
1
and
C
2.
With
respect
to
the
Factor
D
quantity,
which
I'm
going
to
denote
by
from
now
on,
by
X
1,
they
wanted
to
test
four
possible
levels.
Four
possible
amounts,
five,
10,
15,
and
20.
Regarding
the
response
variables,
those
are
slightly
more
straightforward
in
the
sense
that
we
only
have
two
of
them,
both
our
continuous
variables.
Each
of
them,
as
I
was
mentioned
in
the
beginning,
had
to
meet
certain
optimality
threshold,
optimality
criteria.
For
Y1
had
to
be
above
17.
For
Y2
had
to
be
above
2.6.
Now
we
have
on
our
left,
our
input
variables
that
we
need
to
decide
how
to
maneuver
and
vary
in
making
the
recipe.
On
the
right
side,
we
have
the
properties
that
we're
interested
in.
What
we
decided
to
do
was
to
propose
our
clients
to
do
designed
experiment
in
a
way
that
we
would
go
out
and
make
some
of
these
recipes,
make
some
of
these
formulations
and
be
able,
from
the
collected
data,
after
recording
the
properties
for
[inaudible 00:06:32]
,
actual
observed
formulation,
to
understand
and
infer
the
relationships
undergoing
that
were
linking
the
input
variables.
How
we
were
making
our
recipe
and
response
variables.
How
the
properties
actually
were
executing
themselves
for
different
combinations
of
the
inputs.
Ultimately
that
the
objective
of
the
project
was
in
fact,
to
figure
out
whether
there
was
an
optimal
recipe,
meaning
a
recipe
that
whose
properties
both
met
their
respective
optimality
criteria.
Given
this
framework,
given
this
setting,
now
it's
pretty
clear
that
X
1
is
going
to
be
a
quantitative
variable.
But
how
about
Factor
A,
B,
and
C?
Given
the
fact
that
we
can
mix
these
raw
materials
.
Are
we
going
to
treat
them
as
categorical
or
are
we
going
to
treat
them
as
numeric?
At
this
stage,
because
the
client
was
particularly
interested
in
observing
the
performance
of
these
specific
compositions
of
the
raw
materials
for
making
the
various
Factors
A,
B,
and
C,
we
decided
to
accommodate
their
requests
and
coded
them
as
categorical
variables
in
a
way
that
we
were
sure
that
those
specific
compositions
were
going
to
show
up
in
the
design
of
experiment.
Again,
categorical
variables
means
that,
and
in
this
case,
each
level
of
the
categorical
correspond
to
a
possible
way
of
making
the
ingredient
or
factor.
We
end
up
with
three
categorical
variables
with
two,
three,
and
four
levels
respectively.
Now,
turns
out
that
actually
this
categorical
coding
approach
was
also
pretty
helpful
in
the
discussion
of
how
we
wanted
to
specify
the
statistical
model
that,
in
principle,
was
supposed
to,
or
at
least
assumed
to
be
comprehensive
enough
to
describe
and
capture
the
relationship
undergoing
between
the
factors
and
the
responses,
the
properties.
For
the
client,
was
particularly
easy
for
having
this
categorical
coding
to
identify
and
specify
what
kind of interaction
turns
who
they
were
expecting
to
see
in
terms
of
explaining
and
be
relevant
in
explaining
the
relationships.
The
final
statistical
model
that
we
ended
up
specifying
the
design
of
experiment,
comprised
of
main
effects,
two
-way
interactions,
all
of
them,
quadratic
and
cubic
terms
for
the
continuance
variable
with
the
addition
of
the
interaction
of
the
quadratic
with
one
of
the
factors.
Now,
of
course,
we
also
had
some
constraint
in
the
number
of
experiments
available.
Because
we
obviously
don't
have
infinite
amount
of
resources,
so
we
put
a
constraint
of
51
runs,
and
this
is
the
DOE
that
JMP
gave
us
able
to
estimate
the
statistical
model
we
just
specified,
and
also
be
able
to
be
within
the
constraints
that
on
our
resources.
Now
with
this,
the
only
thing
that
was
left
to
do
was
go
and
make
this
51
formulations.
Imagine
that
we're
super
quick,
and
everything
is
magic,
and
we
have
already
got
gun
and
made
all
of
our
relations
collected
data
.
Now
we
are
in
good
shape
for
estimating
the
Gaussian
model
that
we
specified.
These
are
the
results
for
the
first property, Y
1.
We
can
see
that
there
is
a
pretty
good
fit
between
predicting
and
actual
values.
A
lso,
if
we
look
at
the
metrics,
the
reporting,
the
model
summary,
those
look
pretty
satisfactory.
The
same
is
true
if
we
look
at
now
at
the
second
property
Y2,
again,
pretty
good
fit.
We
are
happy
with
our
models,
and
we
think
we
did
a
good
job
in
capturing
the
relationship.
Now
remember
that
what
we
really
want
to
discover
is,
in
fact,
there
is
any
optimal
recipe
that
can
meet
both
criteria
for
our
properties.
How
are
we
going
to
do
this?
How
are
we
going
to
establish
if
such
a
optimal
recipe
exists
or
not?
Well,
in
JMP Pro 16,
this
is
a
super
easy
task,
because
we
can
simulate
thousands
of
potential
alternatives
recipes
by
using
the
Profiler
Feature
options.
For
each
of
these
hypothetical
recipes,
we
can
automatically
have
in
the
same
table
the
predicted
mean
value
for
the
two
properties,
so
that
it
comes
super natural
and
super
easy
to
see
if
there
is
any
optimal
recipe.
Just
to
give
you
an
idea
how
quick
that
is,
I
want
to
show
you
live,
how
we
can
do
this.
This
is
my
DOE
categorical
table,
where
I
have
my
Factor
A,
B,
and
C.
X1
is
my
only
quantitative
input
variables.
I
have
my
recorded
values
for
the
two
properties,
Y1
and
Y2.
Imagine now
that
we
have
already
run
the
model,
estimated
model
and
saved
the
prediction
formulas
for
the
two
variables
here.
We
can
go
here
and
highlight
these
two
columns.
Go
to
graph,
select
Profiler,
and
then
put
those
two
prediction
formulas
in
the
Y
prediction
formula
box
and
click
OK.
This
is
the
usual
way
we
get
a
profiler
dialogue
box.
In
fact,
we
can
,
easily
play
around
and
changing
the
various,
but
levels
of
the
inputs
in
a
way
that
we
can
actually
see
how
this
impacts
our
predictions
for
the
two
properties.
However,
what
I
want
to
show
you
today
is
how
we
can
actually
ask,
going
to
the
red
triangle,
ask
JMP
to
output
a
random
table,
and
we
can
make
it
as
big
as
we
like.
I'm
going
to
start
with
30,000
rows,
just
to
start,
I'll
show
you,
see,
didn't
really, took
no
time
for
JMP
to
give
us
this
30,000
rows
where
each
table,
where
each
row
corresponds
to
a
hypothetical
recipe
that
we
haven't
necessarily
seen
in
the
DOE.
This
is
the
power
of
having
this
feature
in
JMP,
that
we
can
explore
the
input
space
in
literally
no
time.
Now,
if
we
are
interested
in
seeing
whether
there
is
one
recipe
that
is
optimal,
then
we
can
go
here,
Graph
Builder,
and
put
the
predictive
values
for
Y1,
predictive
values
for
Y2.
And
then
just
to
aid
our
visualization,
I'm
going
to
put
a
vertical
axis
in
correspondence
of
the
optimal
threshold
for
Y2,
and
likewise
horizontal
line
marking
the
optimal
threshold
for
Y1.
This
upper
quadrant
denotes
the
optimal
region,
because
both
properties
are
satisfying
the
optimality
criteria.
Unfortunately,
that
we
can
see
from
here
that
we
don't
find
any
recipe
that
is,
in
fact,
able
to
satisfy
both
the
criteria.
This
is
like,
okay,
not
very
good
news.
Now
let
me
go
back
to
my
presentation
very
quick.
We
can
see,
in
fact,
that
we
don't
have
any
properties
line
this
quadrant
with
the
happy
green
smiley.
What
do
we
do
at
this
point?
Do
we
give
up?
Of
course
not.
What
we
can
do
is,
in
fact,
go
back
to
the
beginning
of
the
problem
and
try
to
see
if
we
can
change
any
of
our
initial
choices
that
we
first made
in
approaching
the
problem.
In
particular,
you
might
be
remembering
that
we
were
undecided
whether
we
would
treat
the
Factor
A,
B,
and
C
as
categorical
or
as
numeric.
So
far
we
have
treated
them
as
categorical.
So
far,
factor
A
as
being
a
categorical
variable,
with
two
levels,
either
only
using
A1
or
only
using
A2.
However,
because
in
fact,
the
client
were
open
to
mix
the
raw
materials
to
make
Factor
A.
So
that
was
an
option.
Then
what
we
can
think
of
is
substituting
this
Factor
A
with
variable
that
now
I
call
A1 Content,
which
is
a
quantitive
variable,
which
represents
how
much
of
A1
I'm
going
to
put
into
the
mixture
of
A1
and
A2 for
making
Factor
A.
The
translation,
the
conversion
between
categorical
levels
and
numerical
values,
it's
almost
immediate
.
If
I'm
only
using
A1,
I'm
going
to
use
100% of
A1
in
my
mixture.
so
I
can
code
A1
Content
to
be
equal
to
one.
On
the
opposite
side,
if
I'm
only
using
A2,
this
means
that
I
have
zero A1
Content
in
my
mixture,
and
therefore
A1
Content
is
going
to
be
equal
to
zero.
You
might
have
guessed
that
implicitly,
we
are
also
defining
A2
Content
to
be
equal
to
1 -
A1
Content.
But
we
don't
really
need
that
because
we
are
only
looking
at
two
mixture
variables.
Why
are
we
doing
this?
Well,
the
advantage
is
clear
.
With
Factor A,
we
were
constrained
in
looking
at
either
A1
Content
to
be
equal
to
zero
or
one.
Now
that
we're
considering
continuance
coding,
the
A1
Content
can
take
any
value
between
zero
and
one.
This,
of
course,
represents
an
enormous
jump
in
the
flexibility
of
our
model
and
an
infinite
in
the
sense
that
now
we
are
open
to
literally
infinite
more
mixtures
and
infinite
more
ways
of
making
Factor A.
Likewise,
Factor
B
is
categorical
with
three
levels.
So
far
it's
been
this
way,
coded
only
B1,
only
B2
or
50-50
blend.
But
following
the
similar
logic,
we
can
now
introduce
a B1
Content,
continuous
variable.
A
gain,
the
conversion
is
going
to
be
exactly
the
same.
50-50
blend
of
B
1
and
B
2
will
be
converted
in
0.5
because
I'm
using
50
%
of
B
1
and
50
%
of
B
2.
Again,
B
2 Content
is
1 - B
1 Content.
A
gain,
the
advantage
is
that
we're
not
bound
to
jump
from
zero
to
0.5,
or
to
zero
to
one
necessarily,
but
we
can
explore
the
whole
spectrum
of
values
from
zero
to
one.
Factor
C
is
likely
more
tricky,
because
we
do
have
three
possible
raw
materials
to
mix
up.
A
t
this
stage,
we
need
to
introduce
not
just
one,
but
actually
three
continuous
variables
that
besides
being
continuous,
have
also
the
mixture
constraints.
Meaning at
all
times,
they
need
to
be
something
to
one.
But
the
conversion
between
the
levels
of
Factor
C
and
the
three
new
mixture
variables
follows
exactly
the
same
logic.
That's
super
easy.
This
is
just
a
visualization
of
how
we
do
the
conversion
of
the
levels.
This
is
how
the
DOE
points
that
we
already
have
the
data
on.
We
don't
need
anything
else.
Are
seat
within
the
continuous
coding
space.
Now,
the
only
more
involved
steps
in
passing
from
the
categorical
coding
to
use
a
continuous
coding
is
how,
in
fact,
we
convert
this
the
statistical
model
that
we
use
to
design
the
experiment
and
then
to
analyze
the
data.
How
are
we
going
to
do
this?
Well,
the
easier
way
is
to
just
do
it
in
many
small
steps.
What
we're
going
to
do
is
start
with
our
main
effects
model,
a
little
by
little
at
the
different
factors.
We
start
with
Factor A,
which
had
only
two
levels.
Now
in
the
continuous
coding,
what
we're
going
to
put
is
A1
Content.
We're
only
going
to
put
the
linear
term
of
this
A1
Content.
In
fact,
we
only
had
one
coefficient
for
Factor A
in
the
category
coding
model.
Likewise,
now
we're
going
to
have
one
single
coefficient
for
A1
content.
Now
if
you
don't
believe
me,
this,
it's
an
equivalent
model.
I'm
going
to
show
you
a
couple
of
examples.
Imagine that
we
want
to
figure
out
the
impact
of
using
only
A2
for
making
Factor A,
then
that
means
that
A1
content
is
zero.
Fine.
From
the
categorical
coding
model,
we're
going
to
just
look
at
the
intercept
term,
because
this
extra
term
refers
to
when
we
use
A1.
On
this
other
side,
for
continuous
coding
model,
we're
going
to
put
the
intercept,
of
course,
and
then
the
A1
Content
coefficient,
but
now
we
will
multiply
it
by
zero
because
A1
Content
is
zero.
Not
even
doing
any
math,
you
can
really
see
that
these
two
numbers
are
exactly
the
same.
Similarly,
if
we
want
to
see
,
what's
the
impact
of
using
only
A1
now
at
this
time,
A1
content
is
going
to
be
equal
to
one.
Now
for
categorical,
I'm
going
to
sum
up
the
intercept
term
plus
the
Factor A
coefficient
accord
accounting
for
the
difference
and
the
levels
of
the
factor.
On
this
other
side though,
we
are
going
to
always
include
the
intercept.
A
t
this
point,
we'll
multiply
the
A1
Content
coefficient
by
one
because
the
content
is
one.
Again, not
even
any
math,
the
two
numbers
here
are
the
same
as
the
two
numbers
here.
Exactly
equivalent.
Now
with
Factor
B,
we
had
three
levels.
How
are
we
going
to
do
that?
Well,
because
it
has
three
levels,
now
we
can't
just
add
the
linear
term,
but
we
also
need
to
add
the
quadratic
term.
We
had
two
coefficients
before,
and
we're
going
to
have
two
coefficients
also now
with
the
continuous
coding.
A
gain,
if
you
don't
believe
me,
this
is
an
equivalent
model,
we can
work
out
at
least
one
example,
which
works
exactly
as
befor
e.
If
I
only
have
B2, B
1 Content
in
zero,
means
that
two
coefficients
are
going
to
have
zero
weight
in
computing
the
impact.
Therefore
the
two
numbers
are
only
just
two
that
are,
in
fact
the
same.
I'm
not
going
to
go
into
this
again,
only
B
1
is
equivalent
to
B1 Content
equal
to one.
The
most
interesting
is,
this
that
at
least
requires
you
to
do
some
summation.
Where
B
1
Content
is
going
to
be
0.5,
because
we
are
considering
50-50
blend.
You
can
verify
easily
that
these
two
numbers
here
summed
up
are
equivalent
to
this
other
side
of
the
equation
where
we
put
0.5
and
0.5
squared,
because
now
our
B
1 Content
is
equal
to
0.5.
Now
for
Factor
C,
we
had
four
levels.
We
particularly
remember,
we
had
three
possible
raw
materials.
We
had
to
introduce
three
mixture
variables.
Every
time
we
do
have
to
deal
with
mixture
variables
things,
it's
slightly
complicated
because
they
become
perfectly
cleaner
with
any
constant
term.
In
putting
the
C
1,
C
2,
and
C
3,
the
sum
of
them
deletes
or
requires
us
to
delete
the
constant
term.
But
other
than
that,
everything
follows
pretty
much
the
same.
We
had
three
coefficients
here,
and
we're
still
going
to
have
three
coefficient
here
because
we
have
four,
but
we
are
getting
rid
of
the
intercept.
So
still
the
same
balance.
A
gain,
I'm
not
going
to
go
through
all
of
the
examples,
but
you're
more
than
welcome
to
look
at
the
slides
offline
and
check
that
those
are,
in
fact,
gives
you
always
the
same
answers.
These
are
all
the
examples.
Now
with
so
much
work,
we
have
found
the
conversion
of
the
main
effects.
How
we
actually
convert
each
separate
factors
into
using
the
new
continuous
variables?
Now
our
original
model,
though,
included
more
than
just
main
effects.
In
fact,
we
had
the
two
-way
interactions.
Now
the
idea
here
is
that
every
time
Factor A
appears,
I'm
going
to
substitute
it with
A1
Content.
Every
time
Factor
B
appears,
I'm
going
to
substitute
it
with
the
two B1
Content
and
B
1
Content
squared.
Likewise
for
Factor
C,
I'm
going
to
substitute
it
with
the
four
terms
that
I've
put
here.
The
same
holds
when
I'm
interacting
with
X
1,
and
everything
is
very
much
in
the
same
flavor,
logically
follows
the
same
scheme.
The
only
caution
that
you
want
to
be
aware
of
and
be
particularly
attentive
about
is
that
every
time
you
interact
a three
mixture
variables,
where
those
are
your
three
mixture
variables,
those
main
effects
that
you
originally
had
now
need
to
be
excluded
from
the
model,
otherwise,
the
model
won't
be
feasible.
That's
the
only
caution
that
you
need
to
be
careful
about.
Other
than
that,
we're
ready
to
go.
We've
got
our
equivalent
continuous
model.
Now
what
we
can
do
is,
in
fact,
again,
verify
that
everything
is
still
same.
I
get
exactly
the
same
predictions,
either
using
the
categorical
coding
or
going
and
using
the
continuous
coding.
Now
you
might
ask
myself,
why
are
you
going
into
so
much
trouble
and
going,
doing
so
much
mess
if
things
are
exactly
the same?
Well,
the
advantage
is
immediate
to
see,
and
you
can
really
appreciate
it
if
you
start
looking
at
the
profilers.
This
is
the
profilers,
how
it
looks,
when
you
use
the
categorical
coding
.
You
have
to
jump
between
the
different
levels.
You
don't
have
the
faintest
idea
what
can
happen
in
between.
With the
continuous
coding
on the
other
hand,
that's
exactly
what
you
can
do.
You
can
explore
way
more
of
the
different
possible
ways
of
making
the
various
ingredients
Factor A,
B,
and
C
in
a
way
that
before
it
was
just
out
of
bounds.
In
technical
terms,
means
that
we
have
way
more
power
of
interpolation.
This
doesn't
come
free,
of
course.
What
you
pay,
the
price
of
is
in
fact,
that
you
are
implicitly
making
some
assumptions.
The
assumptions
regards
the
way
that
the
various
new
continuous
variables
that
we
have
introduced
are
related
to
the
responses.
In
a
way,
we
are
implicitly
assuming
that
the
relations
between
A
1 Content
and
our
properties
is
linear.
The
relationship
between
B1 C
ontent
is
quadratic and
so
forth.
If
you
think
that
those
assumptions
don't
really
hold
in
your
case,
then
of
course,
the
whole
procedure
is
questionable.
You
don't
want
to
pursue
this.
But
if
you
don't
have
any
reason
why
you
wouldn't
believe
this,
or
at
least
why
you
wouldn't
at
least
explore
this
possibility,
then,
now
we
can
go
back
and
do
the
same
exercise
and
explore
again
the
input
space,
but
with
way
more
flexibility.
Again,
let's
see
if
we
can
find
that
an
optimal
recipe
with
this
new
continuous
mixture
coding.
How
we're
going
to
do?
Well,
exactly
same
ways.
I'm going to
use
the
JMP
profiler
feature
and
use
the
simulation
and
see
if
we
can
find
anything.
Now
let
me
go
here.
This
is
my
DOE
continuous
table.
Continuous,
because
now
you
can
see
that
these
are
all
coded
as
continuous
variables
.
They
have
the
blue
triangle
next
to
themselves
.
The
C
1,
C
2,
C
3
are
also
these
stars,
indicating
that
they're
coded
as
mixture
variables
in
JMP.
Now
imagine
that
again,
we
have
already
fitted
our
model
with
the
fit
model
platform.
We
saved
our
prediction
formulas
now
with
the
continuous
coding.
What
we're
going
to
do
same
thing,
Graph
Profiler,
select
those,
and
here
we
go.
Here
is
our
prediction
profiler.
Now
we
can
play
way
more
with
the
profiler
and
see
all
different
combinations
without
having
to
jump
between
different
options.
Now,
once
again,
red
triangle,
output
random
table.
Just
for
making
things
fair,
I'm
going
to
ask
3,000
rows.
Again,
no
time,
literally
blink
of
an
eye.
JMP
gives
you
3,000
row
tables
where
now
every recipe is again, sorry.
Every row
is
again,
a
potential
hypothetical
recipe
that
we
haven't
really
seen,
necessarily
seen
in
our
DOE
but
it
still
feasible,
because
it
still
respects
the
constraint
that
we
had
at
the
beginning.
Once
again,
to
figure
out
whether
something
good
is
happening,
or
at
least
whether
within
this
30,000
formulation,
we
do
find
something
that
is
optimal.
I'm
going
to
construct
the
same
graph.
Now
you
can
see
that
our
points
are
all
disperse
and
are
not
aligned
anymore.
Again,
fitting
the
axis
just
to
aid
our
visualization.
This
is
the
nice
thing.
With
this
way
of
coding
and
looking
at
more
of
the
input
space,
we
do
find
few
formulations
that
seem
to
be
promising.
Of
course,
we
need
to
keep
in
mind
that
this
our
predictive
values.
Everything
is
still
relying
on
our
data,
on
our
statistical
model
analysis,
but
is
still
more
promising
than
before.
We
do
find
something
in
the
optimal
region
defined
by
these
two
axis.
Quickly,
going
back
to
my
presentation,
I
want
to
draw
a
final
conclusion
here,
which
is,
in
fact,
that,
using
the
categorical
coding,
we
couldn't
find
any
recipe
that
at
least
on
the
predictive
side,
could,
in
fact,
meet
both
the
optimality
criteria.
Well,
once
we
turn
to,
figuring
out
how
to
code
these
different
categorical
variables
into
continuous
and
mixture
variables
and
exploit
the
JMP
power
of
giving
us
thousands
and
thousands
of
formulations,
we
do
find
a
few
that
in
fact
meet
the
specs.
We
were
happy
that
at
least
we
could
go
back
to
our
clients
say,
look,
instead
of
giving
up
on
your
project,
try
to
make
these
formulations
and
see
how,
in
fact,
whether
the
actual
properties
do
meet
your
criteria
or
not,
but
at
least
it
gives
us
some
directions
of
improvement
where
to
go.
With
this,
I'd
like
to
end
my
presentation.
Thank
my
colleague,
Xinjie Tong
and
all
of
my
collaborators
at
Dow
Chemical.
Thank
you,
all
of
you
for
watching
my
presentation.
I'll
be
more
than
happy
to
answer
any
questions
you
might
have
at
this
point.
Thank
you.
