The Standardized Regression Line
In a 標準化後的回歸直線, the line that best summarizes the data is often called the Standardized regression line. Standardized regression lines are more useful than unstandardized ones because the coefficients (b1, b2, etc) may be measured in different units and thus direct comparison is impossible. This is similar to comparing apples and oranges. By converting all of the coefficients to a common set of statistically reasonable measurement units, standardized regression lines can be directly compared.
The slope of the Standardized regression line, which passes through the point of averages, is +SDY/(rxSDX). The rxSDX measures how much a value of X is above or below its mean. Thus, a change in a value of X that is close to its mean will result in a relatively small increase in the value of Y, while a large change in a value of X that has more distance from its mean will result in a larger increase in the value of Y.
Visualizing Relationships: Graphing the Standardized Regression Line
One way to avoid this problem is to convert the raw values of a variable into z-scores (as shown in the table below). This makes it possible to compare the size of changes in variables that are on very different scales. Another solution is to use standardized regression coefficients, which allow the effects of explanatory variables that are measured on different scales to be pooled. A standardized regression coefficient is the coefficient of a model in which all the predictors are standardized. This coefficient is interpreted in the same way as a correlation coefficient, and it is used to estimate how much a change in one of the predictors will result in a change in the dependent variable.