<s>
In	O
statistics	O
the	O
mean	B-General_Concept
squared	I-General_Concept
prediction	I-General_Concept
error	I-General_Concept
(	O
MSPE	O
)	O
,	O
also	O
known	O
as	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
of	O
the	O
predictions	O
,	O
of	O
a	O
smoothing	B-Application
,	O
curve	B-Algorithm
fitting	I-Algorithm
,	O
or	O
regression	O
procedure	O
is	O
the	O
expected	O
value	O
of	O
the	O
squared	O
prediction	B-General_Concept
errors	I-General_Concept
(	O
PE	O
)	O
,	O
the	O
square	B-General_Concept
difference	I-General_Concept
between	O
the	O
fitted	O
values	O
implied	O
by	O
the	O
predictive	O
function	O
and	O
the	O
values	O
of	O
the	O
(	O
unobservable	O
)	O
true	O
value	O
g	O
.	O
It	O
is	O
an	O
inverse	O
measure	O
of	O
the	O
explanatory	O
power	O
of	O
and	O
can	O
be	O
used	O
in	O
the	O
process	O
of	O
cross-validation	B-Application
of	O
an	O
estimated	O
model	O
.	O
</s>
<s>
If	O
the	O
smoothing	B-Application
or	O
fitting	O
procedure	O
has	O
projection	B-Algorithm
matrix	I-Algorithm
(	O
i.e.	O
,	O
hat	B-Algorithm
matrix	I-Algorithm
)	O
L	O
,	O
which	O
maps	O
the	O
observed	O
values	O
vector	O
to	O
predicted	O
values	O
vector	O
then	O
PE	O
and	O
MSPE	O
are	O
formulated	O
as	O
:	O
</s>
<s>
The	O
quantity	O
is	O
called	O
sum	O
squared	O
prediction	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
The	O
root	O
mean	B-General_Concept
squared	I-General_Concept
prediction	I-General_Concept
error	I-General_Concept
is	O
the	O
square	O
root	O
of	O
MSPE	O
:	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
squared	I-General_Concept
prediction	I-General_Concept
error	I-General_Concept
can	O
be	O
computed	O
exactly	O
in	O
two	O
contexts	O
.	O
</s>
<s>
First	O
,	O
with	O
a	O
data	O
sample	O
of	O
length	O
n	O
,	O
the	O
data	B-General_Concept
analyst	I-General_Concept
may	O
run	O
the	O
regression	O
over	O
only	O
q	O
of	O
the	O
data	O
points	O
(	O
with	O
q	O
<	O
n	O
)	O
,	O
holding	O
back	O
the	O
other	O
n	O
–	O
q	O
data	O
points	O
with	O
the	O
specific	O
purpose	O
of	O
using	O
them	O
to	O
compute	O
the	O
estimated	O
model	O
’s	O
MSPE	O
out	O
of	O
sample	O
(	O
i.e.	O
,	O
not	O
using	O
data	O
that	O
were	O
used	O
in	O
the	O
model	O
estimation	O
process	O
)	O
.	O
</s>
<s>
Second	O
,	O
as	O
time	O
goes	O
on	O
more	O
data	O
may	O
become	O
available	O
to	O
the	O
data	B-General_Concept
analyst	I-General_Concept
,	O
and	O
then	O
the	O
MSPE	O
can	O
be	O
computed	O
over	O
these	O
new	O
data	O
.	O
</s>
