PIECEWISE NONLINEAR REGRESSION
SigmaPlot’s nonlinear regression is based on a powerful transform language. This allows multi-line fit equations to be defined over different independent variable (x) intervals. An excellent example is the analysis of cell growth data. This data measures the number of viable cells as a function of time. The shape of a cell growth curve consists of the four segments shown in the following graph.
The data in this graph has five replicates that are graphed using SigmaPlot’s replicate data format. It is graphed using a log y-axis scale to display with straight lines the exponential growth and (possibly) death behavior. The multi-line equation for the four-segment piecewise-linear growth curve f is
f = if(t <= T1, region1(t),
if(t <= T2, region2(t),
if(t <= T3, region3(t), region4(t))))
region1(t) = (x1*(T1-t) + x2*(t-t1))/(T1-t1)
region2(t) = (x2*(T2-t) + x3*(t-T1))/(T2-T1)
region3(t) = (x3*(T3-t) + x4*(t-T2))/(T3-T2)
region4(t) = (x4*(t4-t) + x5*(t-T3))/(t4-T3)
The transform language "if" statement is used to create the four x intervals defined by the time points t1
Download the self-extracting file piecewise_curve_fitting.exe and double click on it to obtain the SigmaPlot notebook with this example and the piecewise-linear curve fit definition.
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