The previous chapter addressed the problem of fitting a mathematical function through a given set of data points and approximating the value of a smooth curve between the given data points by an interpolation function. The techniques work well for data points which have been evaluated from some known function or computer algorithm or for data points with zero or negligible random errors in the data values. For experimental data and thus for a wide range of engineering problems, a given set of data has some uncertainty in the data points or values, i.e. the data with some randomness. There are several things that one might want to do with such data. First, one might just want to plot the data and draw a “smooth” curve through the data to aid the user in visualizing the functional dependency. Second, one might want to fit a particular mathematical model to the data and analyze the “goodness” of the fit of the model to the data. Third, one might want to fit a particular physical model with unknown parameters to the data and determine the “best” values of some set of physical parameters when fitted to the data. All of these approaches to data analysis and plotting are considered in this chapter under the heading of Curve Fitting and Data Plotting. The general difference from the previous chapter is that in this chapter the data is assumed to have some randomness so that one does not necessarily want to fit a function “exactly” through the given set of data points, but a curve or function is desired that “best” represents the data. The terms in quotes in the above discussion are not well defined at this point, but hopefully they will become better defined as this chapter progresses.
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