校准直线拟合中的异方差性研究-以食品中苯甲酸检测为例

Study on heteroscedasticity in the fitting of calibration line-taking the detection of benzoic acid in food as an example

中文关键词:  苯甲酸  检测分析  异方差检验  最小二乘法

英文关键词:benzoic acid  detection and analysis  heteroscedasticity test  least squares method

中文摘要:

      目的 研究校准直线拟合中的异方差性问题。方法 基于液相色谱测定食品中苯甲酸的检测方法, 对半年累计的25条校准直线, 通过观察拟合残差与校准浓度之间的关系以及通过统计软件VIEWS直接检验其异方差性。结果 当拟合残差随校准浓度增加而增加时, 判定存在异方差性。在统计样本达到一定数量后, 二者检验结果一致。结论 检验异方差性, 统计样本应不低于30个数据对, 在异方差性存在的情况下, 应采用加权最小二乘法进行校准直线的拟合。

英文摘要:

      Objective To study the heteroscedasticity in the fitting of calibration line. Methods Based on the detection method for the determination of benzoic acid in food by high performance liquid chromatography, it was focused on the heteroscedasticity of the 25 calibration lines accumulated in half a year by observing the relationship between the fitting residual and the calibration concentration, as well as by testing heteroscedasticity via statistical software EVIEWS. Results When the fitting residuals increased with the calibration concentration, it was judged that there was heteroscedasticity. When statistical sample reached a certain number, the results of the two ways were consistent. Conclusion By testing heteroscedasticity, the statistical sample should be no less than 30 data pairs. In the presence of heteroscedasticity, the weighted least squares method should be used to fit the calibration line.