Deming Regression: Least-Squares Analysis with Errors in Both X and Y Data, and a Simple Spreadsheet Implementation

Almost every system or device capable of computation contains a linear least-squares parametric analysis program by which to fit a set of dependent y-data against a set of independent x-data to a straight line. Such programs are used in fields as diverse as finance and sport and are of especial significance in science. Although widely – and appropriately – applied in many circumstances it is not always recognised that it is required that the x-data be without error (or, at least, of small error) and that the fitted values are sensitive to outliers. If this is not the case, the slope and intercept parameters fitted to the line may have significant error. We briefly mention “median of medians” non-parametric procedures by which effects of outliers may be considerably reduced. Errors-in-Variables (EIV) methods, of which Deming Regression is the most popular, provide a remedy by recognising that both x- and y-data may contain significant error and so yielding more reliable fitted parameters. Unfortunately, software for Deming Regression is not generally available except by purchase or subscription. Here, we describe the statistics of Deming Regression and provide an Excel spreadsheet which applies the program to user-supplied data. The Excel spreadsheet is compatible with the free Open Office spreadsheet, and may also be used with Google Online Sheets but with some loss of functionality.