<s>
In	O
statistics	O
,	O
the	O
residual	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
(	O
RSS	O
)	O
,	O
also	O
known	O
as	O
the	O
sum	B-Algorithm
of	I-Algorithm
squared	I-Algorithm
residuals	I-Algorithm
(	O
SSR	O
)	O
or	O
the	O
sum	O
of	O
squared	O
estimate	O
of	O
errors	O
(	O
SSE	O
)	O
,	O
is	O
the	O
sum	O
of	O
the	O
squares	O
of	O
residuals	O
(	O
deviations	O
predicted	O
from	O
actual	O
empirical	O
values	O
of	O
data	O
)	O
.	O
</s>
<s>
It	O
is	O
a	O
measure	O
of	O
the	O
discrepancy	O
between	O
the	O
data	O
and	O
an	O
estimation	O
model	O
,	O
such	O
as	O
a	O
linear	B-General_Concept
regression	I-General_Concept
.	O
</s>
<s>
It	O
is	O
used	O
as	O
an	O
optimality	B-General_Concept
criterion	I-General_Concept
in	O
parameter	O
selection	O
and	O
model	O
selection	O
.	O
</s>
<s>
In	O
general	O
,	O
total	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
=	O
explained	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
+	O
residual	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
.	O
</s>
<s>
For	O
a	O
proof	O
of	O
this	O
in	O
the	O
multivariate	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
(	O
OLS	O
)	O
case	O
,	O
see	O
partitioning	O
in	O
the	O
general	O
OLS	O
model	O
.	O
</s>
<s>
The	O
residual	O
vector	O
;	O
so	O
the	O
residual	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
is	O
:	O
</s>
<s>
where	O
is	O
the	O
hat	B-Algorithm
matrix	I-Algorithm
,	O
or	O
the	O
projection	B-Algorithm
matrix	I-Algorithm
in	O
linear	B-General_Concept
regression	I-General_Concept
.	O
</s>
