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http://dx.doi.org/10.5351/KJAS.2021.34.4.589

Comments on the regression coefficients  

Kahng, Myung-Wook (Department of Statistics, Sookmyung Women's University)
Publication Information
The Korean Journal of Applied Statistics / v.34, no.4, 2021 , pp. 589-597 More about this Journal
Abstract
In simple and multiple regression, there is a difference in the meaning of regression coefficients, and not only are the estimates of regression coefficients different, but they also have different signs. Understanding the relative contribution of explanatory variables in a regression model is an important part of regression analysis. In a standardized regression model, the regression coefficient can be interpreted as the change in the response variable with respect to the standard deviation when the explanatory variable increases by the standard deviation in a situation where the values of the explanatory variables other than the corresponding explanatory variable are fixed. However, the size of the standardized regression coefficient is not a proper measure of the relative importance of each explanatory variable. In this paper, the estimator of the regression coefficient in multiple regression is expressed as a function of the correlation coefficient and the coefficient of determination. Furthermore, it is considered in terms of the effect of an additional explanatory variable and additional increase in the coefficient of determination. We also explore the relationship between estimates of regression coefficients and correlation coefficients in various plots. These results are specifically applied when there are two explanatory variables.
Keywords
added $R^2$ plot; added variable plot; coefficient of partial correlation; standardized regression model; variance inflation factor;
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  • Reference
1 Draper NR and Smith H (1998). Applied Regression Analysis(3rd ed.), Wiley, New York.
2 Hamilton D (1987). Sometimes R2 > r2yx1 + r2yx2: correlated variables are not always redundant, The American Statistician, 41, 129-132.   DOI
3 Montgomery DC, Peck E, and Vining GG (2006). Introduction to Linear Regression Analysis(4th ed.), Wiley, Hoboken, NJ.
4 Weisberg S (2014). Applied Linear Regression(4th ed.), Wiley, Hoboken, NJ.
5 Bring J (1994). How to standardize regression coefficients, The American Statistician, 48, 209-213.   DOI
6 Packer PE (1951). An approach to watershed protection criteria, Journal of Forestry, 49, 638-644.
7 Kahng M, Kim Y, and Ahn CH (2000). A systematic view on residual plots, The Korean Communications in Statistics, 7, 37-46.
8 Myers RH (1990). Classical and Modern Regression with Applications(2nd ed.), Duxbury Press, Belmont, CA.
9 Kahng M (2017). Some remarks on standardized regression coefficient, Journal of the Korean Data Analysis Society, 19, 151-158.   DOI