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In multiple regression analysis, the population multiple correlation coefficient (PMCC)  is widely used to    measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero  PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero  PMCC  based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A  simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data.

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Maximum entropy copula theory is a combination of copula and entropy theory. This method obtains the maximum entropy distribution of random variables by considering the dependence structure. In this paper, the most entropic copula based on Blest's measure is introduced, and its parameter estimation method is investigated. The simulation results show that if the data has low tail dependence, the proposed distribution performs better compared to the most entropic copula distribution based on Spearman's coefficient. Finally, using the monthly rainfall series data of Zahedan station, the application of this method in the analysis of hydrological data is investigated.

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This paper addresses the limitations of classical correlation measures when data are imprecise, inherently vague, or affected by measurement uncertainty. We develop a new method for computing the correlation coefficient and conducting the corresponding hypothesis test for intuitionistic fuzzy data. Using the  $(alpha, beta)$-cut approach and formulating an associated nonlinear programming problem, we derive the intuitionistic fuzzy correlation coefficient and generalize the related test statistic. We demonstrate the effectiveness of the method through two numerical examples and an extensive simulation study across three uncertainty levels and various sample sizes. Simulation results indicate that under high uncertainty, the proposed method substantially reduces the Type I error rate and achieves higher power than the approach based on conventional fuzzy sets. Furthermore, by enabling separate modeling of membership and non-membership degrees, the proposed method allows for evaluating the distinct influence of each component on the final outcomes, leading to more realistic analyses in imprecise environments.