Note on Use of $R^2$ for No-intercept Model

There have been some controversies on the use of the coefficient of determination for linear no-intercept model. One definition of the coefficient of determination, $R^2={\sum}\;{\widehat{y^2}}\;/\;{\sum}\;y^2$, is being widely accepted only for linear no-intercept models though Kvalseth (1985) demonstrated some possible pitfalls in using such $R^2$. Main objective of this note is to report that $R^2$ is not a desirable measure of fit for the no-intercept linear model. In fact it is found that mean square error(MSE) could replace $R^2$ efficiently in most cases where selection of no-intercept model is at issue.