AbstractAn exact procedure for the objective analysis of physical data on polymers, such as volume–temperature, near known or suspected transition points, is presented. Standard computerized linear and polynomial regression techniques are employed forY=f(X). A set of models typical of known data behavior near polymer transitions has been developed. Several sets of data for testing these models were synthesized, having a built‐in random error of 0.075. Particular emphasis is placed on the residual pattern as a function ofXwhere a residual, RES =Y(observed–Y(calculated). RES/SE, where SE is the standard error inY(calculated) is also employed. Residuals for the different models tested against the several sets of synthetic data provide discrimination or recognition patterns to apply when examining unknown bodies of data. We start on unknown data with the simplest possible models, a straight line and a quadratic. These yield residual patterns which guide one to more complex models, which in turn give new residual patterns. The correct model is approached objectively as a limit. We emphasize that these regression techniques can only describe the data but not interpret its physical meaning. These techniques are applied to a detailed analysis ofV—Tdata by Wilson and Simha on poly(cylopentyl methacrylate) which show thatV—Tdata aboveTgfollows two quadratics intersecting at 148–149°C. We identify this intersection as the liquid–liquid transition temperature,Tu, in basic agreement with the suggestion of Wi
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