Example 1: Hop growth
Hops, which are required for the production of beer, are a fast growing creeper. In order to make statements about hop growth, the following series of measurements was taken during an investigation.
|Time t (in weeks)||0||2||4||6||8||10||12||16|
|Height (in m)||0.6||1.2||2.0||3.3||4.1||5.0||5.5||5.8|
(Example from Lambacher Schweizer: Leistungskurs Analysis, Edition Baden-Wuerttemberg, 1st edition 2000)
Data from: "hopfenwachstum.csv" Saturation limit: 6 Dark figure: 1 4,0189 ƒ(x) = ———————————————— 0,66981 + 5,3302 · e^(-0,35622·t) Inflection point W(5,8226/3) Maximum growth rate ƒ'(xw) = 0,53433 8 Values Coeff.of determin. = 0,99383916 Correlation coeff. = 0,99691482 Standard deviation = 0,16172584
As in the book, the value 6 was assumed as the saturation limit. Nevertheless, the results differ from those of the template. However, no curve fitting is carried out there, but the proportionality factor k is calculated using an arbitrary data pair, for example with ( 12 | 5.5 ). The data for this example are stored in the file hopfenwachstum.csv .