How to Interpret a Standardized Regression Line

Standardized regression line

A 標準化後的回歸直線 approach to analyzing a multivariable linear-regression model is to estimate the association between a quantitative dependent variable and one focal explanatory factor. These results are often reported with their standard errors (SEs) or confidence intervals in articles reporting the findings of the regression analysis. Unfortunately, the statistical content of these unstandardized regression coefficients b varies between different studies due to differences in measurement methods and control of other potential covariates. For this reason, pooling the unstandardized regression coefficients across several studies may be impractical. Instead, standardized regression coefficients b offer a workable effect-size statistic for comparison among multiple studies.

The Importance of Standardization in Regression Analysis

A standardized regression line is a straight line that passes through the point of intersection between the original variables and their corresponding standardized versions, or their slopes. The standardized line is obtained by dividing the parameter estimates of the original variables by their sample standard deviations, a procedure performed in SAS by using the STB option in PROC REG and other SAS regression procedures.

Although standardized regression lines are very useful, the interpretation of their magnitude can be difficult, particularly when comparing a standardized predictor’s effect across studies. For example, if the sample size of population 1 is larger than that of population 2, the standardized regression line generated for the original variables x and y in population 2 will appear to be twice as large as that generated for the same variables in population 1, even though the difference is in no way caused by differences in the underlying relationship.