Mathematik für Biologen: ZUSATZ

Quadratische Regression

Bachflohkrebs (Gammarus fosarum): Schlüpf-Erfolg der abgelegten Eier in Abhängigkeit von der Temperatur. (Dabei versteht man unter dem Schlüpf-Erfolg den Prozentsatz der abgelegten Eier, aus denen Junge schlüpften.) X Temperatur in ^{∘}C (auf jeder Temperaturstufe ca. 500 Eier) Y Schlüpferfolg in % Tabelle:

\begin{matrix}x_{i}[^{∘}C] & 2 & 4 & 6 & 8 & 10 & 12 & 16 & 20 & 24 \\ y_{i}[%] & 34, 6 & 50, 3 & 68, 3 & 75, 6 & 75, 4 & 74, 1 & 59, 0 & 46, 3 & 11, 6 \end{matrix}

Die Punkwolke:

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Als Regressions-Parabel ergibt sich:

y = 20, 76 + 9, 58 · x − 0, 42 · x^{2}

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Die Parabel zeigt: Der maximaler Schlüpf-Erfolg liegt bei 11,38 ^{∘}C.

(Beispiel aus: Alt, Bünger: Mathematik in der Biologie. Skript, Uni Bonn).