1. At a computing system comprising one or more computing devices, each of the computing devices comprising one or more processors, the computing system comprising one or more storage media, the computing system having one or two data sets stored on the one or more storage media or having access to one or two data streams, the computing system maintaining a computation set size counter, the computation set size counter indicating a number of pairs of data elements in a computation set of the one or two data sets or the one or two data streams, each of said pairs of data elements containing an observation of an independent variable and an observation of a dependent variable, a computing-system-implemented method for calculating simple linear regression coefficients for data elements in the computation set, the method comprising: initialize, by the computing-device-based computing system, one or more components of simple linear regression coefficients for the computation set; accessing or receiving, by the one or more processor-based computing systems, a pair of data elements; modifying, by the computing-device-based computing system, the computation set by: adding the accessed or received pair of data elements to the computation set; modifying the computation set size counter; incrementally deriving, by the computing-device-based computing system and based at least in part on the one or more components of simple linear regression coefficients for the computation set, one or more components of simple linear regression coefficients for the modified computation set, wherein the incrementally deriving includes: accessing the one or more components; adding a contribution of the added pair of data elements to each of the one or more components mathematically; and providing, by the computing-device-based computing system and based on one or more of the incrementally derived components of simple linear regression coefficients for the modified computation set, simple linear regression coefficients for the modified computation set.