# Standardized Regression Line and Combination Rules for Multiply Imputed Data The 標準化後的回歸直線 is a linear model used to predict the values of a random variable. The variable may be an outcome or a predictor (such as a risk factor). In a meta-analysis, the standardized line is pooled across studies in order to improve the consistency of the regression coefficient estimates. A good standardized regression line will provide the best fit to the data. The slope and intercept of the line represent the estimated value of the variable, while the standard error represents its variance.

One important reason to use standardized regression coefficients is that the regression coefficients of original studies are often reported in different units of measurement. A direct comparison of these coefficients is therefore difficult. Standardized coefficients are an attempt to solve this problem by expressing the regression coefficients in the same unit of measurement.

## The Advantages of Using Standardized Variables in Regression Models

However, the standard errors of standardized regression coefficients depend on how the variables are standardized. Hence, it is necessary to consider the distribution of these variables when developing combination rules for pooled standardized regression coefficients. In this article, two sets of combination rules are proposed for pooled standardized regression coefficients in multiply imputed data. In addition, new methods for calculating and combining point estimators of the R2 in multiply imputed data are presented. Simulations show that these newly proposed combination rules produce small biases and achieve good coverage percentages.

A further aim of this article is to analyze the statistical properties of these new combination rules. For this purpose, the four conditions that have to be satisfied for a standardized regression coefficient to satisfy Condition 1 are analytically derived.