Casestudie Breakdown prediction Contell PILOT - Transumo

Figure 5-1: Two Samples of Regression ([Bourier03], p. 167) (adapted)
5.4.1 The Determination of Regression Functions
A common approach to determine such a regression function is the method of least
squares. This method is divided into three steps: ([Bourier03], p, 167)
1. The determination of general trend from a graphical visualization or knowledge
2. The assignment of this general trend to a mathematical type of function
3. The numerical determination of the function’s parameters
The first two steps are normally trivial and have to be done as initialization part. The
third step has to determine the function’s parameters the way, the function describes
the developing of values best. To do that, the distance between determined
regression function and all available values has to be minimal, which leads to the
method of least squares in Formula 5-4. The square is necessary to avoid illegal
results. 47
Min
n
∑
i=
1
( y − yˆ
)
i
i
2
with
y = Occured value at time t = i
i
yˆ
= Value of regression function at time t = i
i
Formula 5-4: Method of Least Squares
Based on this method, a regression function can be determined for a given type of
function. Often applied types are: ([Daßler95], p. 43)
47 See ([Bourier03], p. 168-169) for details
61