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### Standardized Regression Line

## The Role of Standardization in Multivariate Regression Analysis

標準化後的回歸直線 line (b) is an estimate resulting from a regression analysis where the underlying data have been standardized so that their variances are equal to 1. This allows for a more direct comparison of the effects of different predictor variables. It indicates how much the dependent variable will change for a one unit increase in the standardized independent variable, and it measures the effect size and direction of the relationship.

Unstandardized coefficients can be difficult to interpret because they are measured in the original units of the dependent and independent variables. By using standardized coefficients (multiplied by the ratio of the standardized independent and dependent variables’ standard deviations) the results are a measurement of how much the dependent variable will change for b units increase in the standardized independent variable.

Hence, they are much more easy to compare across studies and to different populations. Nevertheless, this standardization may be misleading since it may regress the sample dependent and independent variables against their own mean. It may also be hard to interpret the meaning of a standardized coefficient if the underlying distribution is skewed or asymmetric.

As a result, the standardized regression coefficient b has become one of the most important statistics used in machine learning and AI. In this article, we will learn how to calculate and use standardized regression coefficients. We will also discuss their advantages and disadvantages, and how they differ from unstandardized regression coefficients. Finally, we will learn how to combine the standardized and unstandardized regression coefficients in an Excel spreadsheet.