<s>
In	O
statistics	O
and	O
data	B-General_Concept
analysis	I-General_Concept
,	O
the	O
application	B-Application
software	I-Application
SegReg	B-Language
is	O
a	O
free	O
and	O
user-friendly	O
tool	O
for	O
linear	O
segmented	O
regression	O
analysis	O
to	O
determine	O
the	O
breakpoint	O
where	O
the	O
relation	O
between	O
the	O
dependent	O
variable	O
and	O
the	O
independent	O
variable	O
changes	O
abruptly	O
.	O
</s>
<s>
SegReg	B-Language
permits	O
the	O
introduction	O
of	O
one	O
or	O
two	O
independent	O
variables	O
.	O
</s>
<s>
The	O
breakpoint	O
is	O
found	O
numerically	O
by	O
adopting	O
a	O
series	O
tentative	O
breakpoints	O
and	O
performing	O
a	O
linear	B-General_Concept
regression	I-General_Concept
at	O
both	O
sides	O
of	O
them	O
.	O
</s>
<s>
The	O
tentative	O
breakpoint	O
that	O
provides	O
the	O
largest	O
coefficient	O
of	O
determination	O
(	O
as	O
a	O
parameter	O
for	O
the	O
fit	O
of	O
the	O
regression	B-General_Concept
lines	I-General_Concept
to	O
the	O
observed	O
data	O
values	O
)	O
is	O
selected	O
as	O
the	O
true	O
breakpoint	O
.	O
</s>
<s>
To	O
assure	O
that	O
the	O
lines	O
at	O
both	O
sides	O
of	O
the	O
breakpoint	O
intersect	O
each	O
other	O
exactly	O
at	O
the	O
breakpoint	O
,	O
SegReg	B-Language
employs	O
two	O
methods	O
and	O
selects	O
the	O
method	O
giving	O
the	O
best	O
fit	O
.	O
</s>
<s>
SegReg	B-Language
recognizes	O
many	O
types	O
of	O
relations	O
and	O
selects	O
the	O
ultimate	O
type	O
on	O
the	O
basis	O
of	O
statistical	O
criteria	O
like	O
the	O
significance	O
of	O
the	O
regression	B-General_Concept
coefficients	I-General_Concept
.	O
</s>
<s>
The	O
SegReg	B-Language
output	O
provides	O
statistical	O
confidence	O
belts	O
of	O
the	O
regression	B-General_Concept
lines	I-General_Concept
and	O
a	O
confidence	O
block	O
for	O
the	O
breakpoint	O
.	O
</s>
<s>
To	O
complete	O
the	O
confidence	O
statements	O
,	O
SegReg	B-Language
provides	O
an	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
and	O
an	O
Anova	B-General_Concept
table	O
.	O
</s>
<s>
A	O
list	O
of	O
publications	O
in	O
which	O
SegReg	B-Language
is	O
used	O
can	O
be	O
consulted	O
.	O
</s>
<s>
where	O
BP	O
is	O
the	O
breakpoint	O
,	O
Y	O
is	O
the	O
dependent	O
variable	O
,	O
X	O
the	O
independent	O
variable	O
,	O
A	O
the	O
regression	B-General_Concept
coefficient	I-General_Concept
,	O
B	O
the	O
regression	O
constant	O
,	O
and	O
RY	O
the	O
residual	O
of	O
Y	O
.	O
</s>
<s>
where	O
,	O
additionally	O
,	O
BPX	O
is	O
BP	O
of	O
X	O
,	O
BPZ	O
is	O
BP	O
of	O
Z	O
,	O
Z	O
is	O
the	O
second	O
independent	O
variable	O
,	O
C	O
is	O
the	O
regression	B-General_Concept
coefficient	I-General_Concept
,	O
and	O
D	O
the	O
regression	O
constant	O
for	O
the	O
regression	O
of	O
RY	O
on	O
Z	O
.	O
</s>
<s>
As	O
an	O
alternative	O
to	O
regressions	O
at	O
both	O
sides	O
of	O
the	O
breakpoint	O
(	O
threshold	O
)	O
,	O
the	O
method	O
of	O
partial	O
regression	O
can	O
be	O
used	O
to	O
find	O
the	O
longest	O
possible	O
horizontal	O
stretch	O
with	O
insignificant	O
regression	B-General_Concept
coefficient	I-General_Concept
,	O
outside	O
of	O
which	O
there	O
is	O
a	O
definite	O
slope	O
with	O
a	O
significant	O
regression	B-General_Concept
coefficient	I-General_Concept
.	O
</s>
<s>
However	O
,	O
the	O
fit	O
of	O
the	O
data	O
beyond	O
the	O
threshold	O
is	O
not	O
as	O
well	O
as	O
in	O
the	O
blue	O
figure	O
that	O
has	O
been	O
made	O
using	O
the	O
principle	O
of	O
minimization	O
of	O
the	O
sum	O
of	O
squares	O
of	O
deviations	O
of	O
the	O
observed	O
values	O
from	O
the	O
regression	B-General_Concept
lines	I-General_Concept
over	O
the	O
whole	O
domain	O
of	O
explanatory	O
variable	O
X	O
(	O
i.e.	O
</s>
