Incorrect least-squares regression coefficients in method-comparison analysis.

作者：P. Joanne Cornbleet, Nathan Gochman · 发表于：Clinical Chemistry · 年份：1979 · DOI：10.1093/clinchem/25.3.432 · 被引用次数：581 · 研究领域：Advanced Statistical Methods and Models、Statistical and numerical algorithms、Spectroscopy and Chemometric Analyses

The least-squares method is frequently used to calculate the slope and intercept of the best line through a set of data points. However, least-squares regression slopes and intercepts may be incorrect if the underlying assumptions of the least-squares model are not met. Two factors in particular that may result in incorrect least-squares regression coefficients are: (a) imprecision in the measurement of the independent (x-axis) variable and (b) inclusion of outliers in the data analysis. We compared the methods of Deming, Mandel, and Bartlett in estimating the known slope of a regression line when the independent variable is measured with imprecision, and found the method of Deming to be the most useful. Significant error in the least-squares slope estimation occurs when the ratio of the standard deviation of measurement of a single x value to the standard deviation of the x-data set exceeds 0.2. Errors in the least-squares coefficients attributable to outliers can be avoided by eliminating data points whose vertical distance from the regression line exceed four times the standard error the estimate.