As we study the equations of motion however, we often deal with experimental trails which produce a large number of related data points. During the course of a one-second free fall for instance, we may measure the location of an object at forty or fifty different times. We could treat each of those distance-time measurements as a separate “trial,” comparing each individual distance value to the one predicted by our theory at that time. However, that approach is not only time consuming, but it overlooks the fact that each data pair is a part of a larger, overarching relationship. It is the characteristics of that relationship, not the “accuracy” of the individual data pairs, which the experiment was designed to explore.
The best tools for examining the overall patterns found
in large data sets are the data plot and the statistical regression.