摘要
地学研究经常涉及两变量间的线性回归分析。此类线性关系可有三种情形：（１）ｘ数据的观测误差很小，数据点的离散只与ｙ数据有关；（２）ｘ和ｙ数据都有观测误差，且数据点的离散仅由观测误差所引起；（３）数据点的离散不仅与观测误差有关，而且还受到其它因素的影响（但两变量仍存在显著的线性关系）。其中第三种情形在地学中最为常见，但已有的回归分析方法只是针对前两种情形。本文对ＬＮＳ方法进行了改进，使之适用于第三型的回归分析。改进的方法在逻辑上具有一致性，在应用上适合线性关系第三型线性关系的特点。
Linear regression analysis is an important practice in earth sciences. Three types of linear relationships between two variables can be identified: (i) very small or no measuring errors are associated with the x data and deviations (due to errors of measurement alone) occur only in the y data; (ii)errors of measurement are associated with both x and y data and such errors are the only reason for any deviation from the line of best-fit; and (iii) the deviation from the equation is not because of measuring errors in x and y data alone (i.e. the deviation is real, although the linear correlation is still significant). However, existing regression models are mainly concerned with the first two types. Here, a method has been suggested for regression analysis of the third type. Such a method is better than the traditional OLS(ordinary least squares) method in that it is logically consistent and non-biased in charater.
基金
中国科学院"百人计划"(海洋沉积动力学)资助
