As the main indicator for assessing the explanatory strength of regression model, there is no denying that a bigger value of determination coefficient (R-squared, R²) is the consistent pursuit of researchers in human-environment field, but whether to abandon or apply the model with a small value of R² is an ongoing argument. This paper summarizes three characteristics of human-environment researches (large number of various variables, large mathematical sample size, and polynomial regression model). Based on the mathematical mechanism of regression analysis, theoretical analysis and case study are combined to point out the misconceptions that are easy to step into and the corresponding suggested methods from three perspectives: selection of determination coefficients, consideration of independent variables, and application of regression models. An extraordinary important point is, if the regression model passes the significance test, even with a small coefficient of determination, it can still quantitatively explain the impact extent of independent variables on dependent variables, but cannot comprehensively and accurately predict the specific value of dependent variable based on existing independent variables; moreover, the larger the sample size, the closer the interpretation of dependent variables in local model to ideal model. It is expected that these cases and lessons could help researchers to better apply regression analysis in human-environment researches, and that the small value of R² would not be an excessive restriction affecting the development of scientific research in this field.

中文翻译：

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人与环境研究中小决定系数回归分析的探讨

作为评估回归模型解释强度的主要指标，决定系数（R -squared，R ²）取值越大是人类-环境领域研究者的一贯追求，但究竟是放弃还是应用R ²值较小的模型是一个持续的争论。本文总结了人与环境研究的三个特点（变量众多、数学样本量大、多项式回归模型）。基于回归分析的数学机理，将理论分析与案例研究相结合，从决定系数的选择、自变量的考虑、回归的应用三个角度指出容易踏入的误区和相应的建议方法楷模。非常重要的一点是，如果回归模型通过了显着性检验，即使决定系数很小，仍然可以定量说明自变量对因变量的影响程度，但不能根据已有的自变量来全面准确地预测因变量的具体取值；此外，样本量越大，局部模型对因变量的解释越接近理想模型。期望这些案例和教训能够帮助研究人员更好地将回归分析应用于人-环境研究，并且小的价值R ²不会成为影响该领域科学研究发展的过度限制。