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Zeichnen einer Potenzregressionsfunktion (
y = a·x
b
)
Die Potenzregression beschreibt die abhängige Variable y als Potenzfunktion von x. Die Potenz-
regression kann verwendet werden, wenn y proportional zur Potenz x
b
ist. Die Standardformel
für die Potenzregression lautet y = a · x
b
, sodass man ln(y) = ln(a) + b · ln(x) erhält, wenn beide
Seiten der Modellgleichung logarithmiert werden. Falls man dann die Transformationen X =
ln(x), Y = ln(y), and A = ln(a) benutzt, erhält man die Formel Y = A + X für die lineare
Regression (quasilineare Regression).
u Operationen auf dem ClassPad
(1) Beginnen Sie mit der grafischen Darstellungsoperation vom Grafikfenster oder dem
Listenfenster des Statistik-Menüs.
Vom Grafikfenster
Tippen Sie auf [Calc] [Power Reg] [OK] [OK] ".
Vom Listenfenster
Tippen Sie auf [SetGraph][Setting...], oder tippen Sie auf G.
(2) In dem erscheinenden Dialogfeld „Set StatGraphs“ konfigurieren Sie ein StatGraph-
Setup mit der nachfolgend aufgeführten Einstellung. Tippen Sie danach auf [Set].
Type: PowerR
(3) Tippen Sie auf y, um die Grafik zu zeichnen.
7-5-12
Berechnungen und grafische Darstellungen mit einer zweidimensionalen Stichprobe
Nachfolgend ist die Modellformel für die Potenzregression aufgeführt.
y = a·x
b
a : Regressionskoeffizient
b :Regressionsexponent
r : Korrelationskoeffizient (der quasilinearen Regression)
r
2
: Bestimmtheitsmaß (der quasilinearen Regression)
MSe : Mittlerer quadratischer Fehler (Restvarianz bei der Streuungszerlegung)
• MSe =
Σ
1
n2
i=1
n
(ln (y
i
) – (ln (a) + ln (x
i
)))
2
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