<s>
In	O
statistics	O
,	O
the	O
fraction	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
unexplained	I-General_Concept
(	O
FVU	B-General_Concept
)	O
in	O
the	O
context	O
of	O
a	O
regression	O
task	O
is	O
the	O
fraction	O
of	O
variance	O
of	O
the	O
regressand	O
(	O
dependent	O
variable	O
)	O
Y	O
which	O
cannot	O
be	O
explained	O
,	O
i.e.	O
,	O
which	O
is	O
not	O
correctly	O
predicted	O
,	O
by	O
the	O
explanatory	O
variables	O
X	O
.	O
</s>
<s>
We	O
define	O
the	O
fraction	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
unexplained	I-General_Concept
(	O
FVU	B-General_Concept
)	O
as	O
:	O
</s>
<s>
Alternatively	O
,	O
the	O
fraction	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
unexplained	I-General_Concept
can	O
be	O
defined	O
as	O
follows	O
:	O
</s>
<s>
where	O
MSE(f )	O
is	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
of	O
the	O
regression	O
functionƒ	O
.	O
</s>
<s>
It	O
is	O
useful	O
to	O
consider	O
the	O
second	O
definition	O
to	O
understand	O
FVU	B-General_Concept
.	O
</s>
<s>
In	O
this	O
case	O
,	O
no	O
variation	O
in	O
Y	O
can	O
be	O
accounted	O
for	O
,	O
and	O
the	O
FVU	B-General_Concept
then	O
has	O
its	O
maximum	O
value	O
of	O
1	O
.	O
</s>
<s>
More	O
generally	O
,	O
the	O
FVU	B-General_Concept
will	O
be	O
1	O
if	O
the	O
explanatory	O
variables	O
X	O
tell	O
us	O
nothing	O
about	O
Y	O
in	O
the	O
sense	O
that	O
the	O
predicted	O
values	O
of	O
Y	O
do	O
not	O
covary	O
with	O
Y	O
.	O
</s>
<s>
But	O
as	O
prediction	O
gets	O
better	O
and	O
the	O
MSE	O
can	O
be	O
reduced	O
,	O
the	O
FVU	B-General_Concept
goes	O
down	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
perfect	O
prediction	O
where	O
for	O
all	O
i	O
,	O
the	O
MSE	O
is	O
0	O
,	O
SSerr	O
=	O
0	O
,	O
SSreg	O
=	O
SStot	O
,	O
and	O
the	O
FVU	B-General_Concept
is	O
0	O
.	O
</s>
