Study on $R^2$ 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, $R^2=\sum\;{y}{^{\hat{2}}/\sum\;{y^2}$, 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 article is to provide a cautionary notice for use of the $R^2$ by pointing out its tricky aspects by means of empirical simulations.