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One simple method of data compression relies on the approximation of the source output by polynomial segments or "interpolators." The parameters of each polynomial are transmitted in place of the original data. This paper presents a method of theoretically analyzing such techniques. Straight line interpolation is considered specifically although the ideas can he readily generalized. It is shown that the class of compression methods considered may or may not perform well depending on the data and, thus, that in some cases more complex techniques, including possibly adaptive methods, might he used, depending on the knowledge of the data statistical model.