Standardized Regression Line


A 標準化後的回歸直線 line consists of a regression coefficient b and its standard error SE(b). Regression models are commonly used in medical research to analyze the associations between a quantitative dependent variable (such as an outcome measure) and a set of explanatory variables. The regression coefficient b describes the effect of one unit change in the variable on the dependent variable, and its standard error gives information about its reliability. In the original articles reviewed in this article, unstandardized regression coefficients b and their standard errors SE(b) are often reported. Because they are in different measurement units, comparing these regression coefficients directly without first standardizing them is like comparing apples and oranges.

Understanding the Standardized Regression Line: A Comprehensive Guide

In this article, four conditions have been defined that need to be met in order for a statistic to be considered a standardized regression coefficient. Two new procedures for pooling standardized regression coefficients and their confidence intervals are proposed and investigated, and their properties are discussed. Two improved point estimators of R2 in multiply imputed data are also proposed and investigated, and simulation results show that they produce very small biases.

For both of the new methods for pooling standardized regression coefficients and confidence intervals, the standardization of both the predictor and outcome variables takes place at the level of the individual imputed dataset m. In both cases, a regression analysis is applied to the standardized predictors and outcome variable, and the resulting regression coefficients and their correct standard errors are pooled according to Rubin’s rules for point estimates. Neither of the new procedures meets all of the defined conditions, but both meet three of them and produce pooled estimates that are close to those in the original articles in most situations.

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