To make software performance prediction more powerful, execution demand functions must be measured over ranges of system parameters, preferably using scripts to automate the collection of large numbers of cases. Once data is collected it is natural to represent it by a regression function, and to interpolate using the function, to obtain parameters for models as they are needed. Although some practitioners have used linear functions, recent experience has shown that simple polynomial regression functions are often inadequate for these "resource functions". They may be very irregular, even jagged. Regression splines offer a simple representation that can adapt to very irregular functions, and which can be fitted automatically.Resource functions offer an opportunity to gather enough data to provide whatever accuracy we require, by going back for more data after doing a partial fit. However regression splines do not have a strong theory of prediction errors. This research has addressed the estimation of accuracy of fit, and the control of the additional data gathering, to provide a controlled degree of error in the fitted function. A typical example shows the power of the technique.

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