The multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and a set of covariates.
Testing whether the MCC differs significantly from zero or not is of interest in multiple correlation analysis. For high-dimensional data, due to the singularity of the sample covariance matrix, the classical testing procedures are no longer usable. In this paper, under the multivariate normality assumption, a simple testing procedure was proposed to test zero MCC using the random projection and union intersection methodologies. Some simulations were carried out to study the performance evaluation of the procedure. The results were found to be very convincing. Lastly, the experimental validation of the proposed approach was carried out on mice tumor data.