The ABC of linear regression analysis: What every author and editor should know

Abstract

Regression analysis is a widely used statistical technique to build a model from a set of data on two or more variables. Linear regression is based on linear correlation, and assumes that change in one variable is accompanied by a proportional change in another variable. Simple linear regression, or bivariate regression, is used for predicting the value of one variable from another variable (predictor); however, multiple linear regression, which enables us to analyse more than one predictor or variable, is more commonly used. This paper explains both simple and multiple linear regressions illustrated with an example of analysis and also discusses some common errors in presenting the results of regression, including inappropriate titles, causal language, inappropriate conclusions, and misinterpretation.

Determining Factors of Alarm Fatigue among Nurses in Intensive Care Units—A Polish Pilot Study

“…Independent variables with a p-value ≤ 0.1 in simple linear regression models were selected and introduced into the backward step-wise regression (the equal probability value for entry and removal was 0.05). The following assumptions for calculating multiple regression were met: a linear relationship between dependent and independent variables (based on scatterplots), multivariate normality (Shapiro-Wilk test p > 0.05), no multicollinearity (Variance Inflation Factor < 1.2), homoscedasticity (based on plotting standardized residuals against predicted values) and independence of observation (the Durbin-Watson statistic = 2) [20]. The results of all multivariable regression models were presented as standardized regression coefficients (ß) and their 95% confidence intervals (CI), and partial R 2 .…”

Factors Related to Anxiety in Paediatric Patients and Their Parents before and after a Modified Ravitch Procedure—A Single-Centre Cohort Study

“…The independent variables with a p -value ≤ 0.1 in simple linear regression models were selected and introduced into the forward stepwise regression (the equal probability value for entry and removal was 0.05). The assumptions for calculating multiple regression were met: there was a linear relationship between the dependent variable and each of the independent variables; the data did not show multicollinearity (Variance Inflation Factor < 1.5); the variance of the residuals was constant (White test p > 0.05); and the residuals were normally distributed (Shapiro–Wilk test p > 0.05) [ 26 ]. The minimum required sample size for a multiple regression study is 84, given a desired probability level of 0.05, with a maximum of four predictors in the model, a medium anticipated effect size of 0.15 and a desired statistical power level of 0.8 [ 27 ].…”

Parâmetros significativos para monitoramento e avaliação da qualidade da água, Bacia Hidrográfica do Rio Cachoeira (Joinville, Santa Catarina, Brasil)

“…Diferentemente da regressão linear simples (ou bivariada), usada para prever o valor de uma variável a partir de outra, a regressão linear múltipla é um método que utiliza mais de uma variável (Bazdaric et al, 2021).…”