This paper establishes a central limit theorem (CLT) for R2 statistics in a moderately high- dimensional asymptotic framework. The underlying population accommodates a general independent components model, by virtue of which our result unifies the two CLTs proposed separately in Zheng et al. (2014) and Guo and Cheng (2021). Beyond this, the new CLT demonstrates and quantifies a non-negligible impact of kurtosis parameters of the latent independent components on the fluctuation of R2 statistics. As an application, a novel confidence interval is constructed for the coefficient of multiple correlation in a high-dimensional linear regression.