Application and interpretation of linear-regression analysis

Linear-regression analysis is a well-known statistical technique that serves as a basis for understanding the relationships between variables. Its simplicity and interpretability render it the preferred choice in healthcare research, including vision science, as it enables researchers and practitioners to model and predict outcomes effectively. This article presents the fundamentals of linear-regression modeling and reviews the applications and interpretations of the main linear-regression analysis.

The primary objective of linear regression is to fit a linear equation to observed data, thus allowing one to predict and interpret the effects of predictor variables. A simple linear regression involves a single independent variable, whereas multiple linear regression includes multiple predictors. A linear-regression model is used to identify the general underlying pattern connecting independent and dependent variables, prove the relationship between these variables, and predict the dependent variables for a specified value of the independent variables. This review demonstrates the appropriate interpretation of linear-regression results using examples from publications in the field of vision science.

Simple and multiple linear regressions are performed, with emphasis on the correct interpretation of standardized and unstandardized regression coefficients, the coefficient of determination, the method for variable selection, assumptions in linear regression, dummy variables, and sample size, along with common mistakes in reporting linear-regression analysis. Finally, a checklist is presented to the editors and peer reviewers for a systematic assessment of submissions that used linear-regression models.

Medical practitioners and researchers should acquire basic knowledge of linear-regression such that they can contribute meaningfully to the development of technology by accurately interpreting research outcomes. Incorrect use or interpretation of appropriate linear-regression models may result in inaccurate results. Appointing an expert statistician in an interdisciplinary research team may offer added value to the study design by preventing overstated results.