Discussion on regression analysis with small determination coefficient in human-environment researches

Area of Science:

• Environmental Science
• Social Science
• Statistics

Background:

• The determination coefficient (R-squared) is crucial for evaluating regression model explanatory strength in human-environment research.
• A debate exists on whether to use or discard regression models with low R-squared values.
• Human-environment research is characterized by numerous variables, large sample sizes, and polynomial regression models.

Purpose of the Study:

• To address misconceptions regarding the application of regression models with small R-squared values in human-environment studies.
• To provide guidance on selecting determination coefficients, considering independent variables, and applying regression models.
• To encourage the appropriate use of regression analysis despite potentially low R-squared values.

Main Methods:

• Theoretical analysis of the mathematical mechanisms of regression analysis.
• Case studies to illustrate practical applications and potential pitfalls.
• Examination of three key aspects: determination coefficient selection, independent variable consideration, and model application.

Main Results:

• Regression models passing significance tests can quantitatively explain variable impacts even with low R-squared.
• Low R-squared values limit comprehensive and accurate prediction of dependent variable values.
• Increasing sample size enhances the interpretation of dependent variables in local models, approximating ideal model behavior.

Conclusions:

• Small R-squared values should not excessively restrict the application of statistically significant regression models in human-environment research.
• Understanding the nuances of R-squared and sample size is vital for accurate interpretation and application.
• This study aims to improve the application of regression analysis in the human-environment field.