Beta Coefficients

• The variation in response scale and variability across variables makes direct interpretation problematic. 
• Standardization converts variables to a common scale and variability, the most common being a mean of zero (0.0) and standard deviation of one (1.0). 
• In this way, we make sure that all variables are comparable. 
• The advantage is that they eliminate the problem of dealing with different units of measurement (as illustrated previously) and thus reflect the relative impact on the dependent variable of a change in one standard deviation in either variable. 
• Now that we have a common unit of measurement, we can determine which variable has the most impact.
  
  

(Nguồn: https://www.dataanalytics.org.uk/beta-coefficients-from-linear-models/)

Although the beta coefficients represent an objective measure of importance that can be directly compared, two cautions must be observed in their use:

• First, they should be used as a guide to the relative importance of individual independent variables only when collinearity is minimal. As we will see in the next section, collinearity can distort the contributions of any independent variable even if beta coefficients are used.
• Second, the beta values can be interpreted only in the context of the other variables in the equation. For example, a beta value for family size reflects its importance only in relation to family income, not in any absolute sense. If another independent variable were added to the equation, the beta coefficient for family size would probably change, because some relationship between family size and the new independent variable is likely.

In summary, beta coefficients should be used only as a guide to the relative importance of the independent variables included in the equation and only for those variables with minimal multicollinearity.

Nguồn:

• Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2013). Multivariate data analysis (8th ed.). Boston: Cengage.