Standardized Regression Line

The 標準化後的回歸直線 line is a method used to calculate the slope of a linear relationship between a dependent variable and one or more predictor variables. The slope is usually reported in terms of the number of standard deviations that the dependent variable will change when the corresponding unit increase occurs in the predictor variable. Standardized regression slopes are often viewed as more interpretable than unstandardized regression slopes.

The term standardized is used because the slope estimates are obtained by multiplying the sample regression coefficient by the ratio of the standard deviations of the independent and dependent variables. This results in a value that is free of the units of the variable and allows it to be directly compared across different variables with differing units.

Common Misconceptions About Standardized Regression in Statistics

There are several things to keep in mind when working with standardized regression slopes. First, it is important to note that a standardized regression slope will not provide you with an estimate of the true value of the dependent variable or its slope. This is because the standardized regression slope assumes that the variable has a normal distribution with a mean of 0 and a standard deviation of 1.

Also, when comparing standardized regression slopes it is important to remember that the standard t-test is insensitive to standardization. Therefore, the same t-test statistic that was applied to the original model (M1) should be applied to the standardized regression models, as long as we use alternative combination rules for t-tests testing standardized coefficients that take into account the fact that these coefficients are unbiased estimators of the parameter estimates and have standard errors that are identical to those of the unstandardized coefficients.