related to each other, the value of the coefficient of multiple correlation depends on the choice of dependent variable: a regression of on and will in general have a different than will a regression of on and . For example, suppose that in a particular sample the variable is uncorrelated with both and , while and are linearly related to each other. Then a regression of on and will yield an of zero, while a regression of on and will yield a strictly positive . This follows since the correlation of with its best predictor based on and is in all cases at least as large as the correlation of with its best predictor based on alone, and in this case with providing no explanatory power it will be exactly as large. References Further reading Allison, Paul D. (1998). Multiple Regression: A Primer. London: Sage Publications. Cohen, Jacob, et al. (2002). Applied Multiple Regression: Correlation Analysis for the Behavioral Sciences. Crown, William H. (1998). Statistical Models for the Social and Behavioral Sciences: Multiple Regression and Limited-Dependent Variable Models. Edwards, Allen Louis (1985). Multiple Regression and the Analysis of Variance and Covariance. Keith, Timothy (2006). Multiple Regression and Beyond. Boston: Pearson Education. Fred N. Kerlinger, Elazar J. Pedhazur (1973). Multiple Regression in Behavioral Research. New York: Holt Rinehart Winston. Stanton, Jeffrey M. (2001). "Galton, Pearson, and the Peas: A Brief History of Linear Regression for Statistics Instructors", Journal of Statistics Education, 9 (3). Correlation indicators Regression analysis