How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions derived from them. But when these parameters have strong mutual dependencies, as is the rule rather than the exception in chemical data analysis, a more sophisticated approach to the statistical imprecision is required than is described in most chemistry textbooks. For the analysis of data from a typical kinetic experiment in physical chemistry, this is illustrated numerically as well as graphically. (Contains 2 tables and 13 figures.)