Casestudie Breakdown prediction Contell PILOT - Transumo

A graphical form like this allows an easy validation of the obtained regression
function. But there is also a mathematical measure that offers a quality factor. It is
called coefficient of determination and defined by Formula 5-7. The general idea is to
2
2
split the total variance ( Var
y
) into the variance caused by regression (
ŷ
)
2
residual variance (
u
)
Var and the
Var . 50 ( )
R
2
Var
=
Var
2
yˆ
2
y
with
Var
Var
Var
2
y
2
yˆ
2
u
= Var
1
=
n
1
=
n
2
yˆ
n
∑
i=
1
n
∑
i=
1
+ Var
u
i
2
i
2
u
yˆ
− y
2
Formula 5-7: Coefficient of Determination
The coefficient of determination is a value between 0 and 1. If regression does not
offer any additional information than the mean value, no variance is caused by
regression. This leads to a coefficient of 0. By contrast, a coefficient of 1 would be
caused by a regression variance that is of same magnitude like total variation.
Hence, every occurred value is actually part of the determined regression function.
([Eckey02], p. 181)
In practice, a coefficient of determination of at least 0.8 is demanded. In case of time
sequences, an even higher coefficient like 0.9 is demanded ([Eckey02], p. 181). A
regression function with such a high coefficient can be used for prediction purposes
by just calculating regression values for the near future.
Section 5.10.2 will introduce a promising appliance of regression to determine a
trend, which indicates a change in behavior. In contrast to that, prediction of an
upcoming malfunction is not possible by using regressing, because every significant
temperature rising would be predicted as upcoming malfunction. As most risings are
caused by external influences and not by changes of general behavior, a usage of
regression for prediction purposes would lead to at least the same high quantity of
false alarms.
50 See ([Eckey02], p. 180-181) for details
64