The simple, partial, multiple and canonical correlation coefficients are useful parameters to study the inter-dependency between two and more survey variables. And, for inter-relationship, partial regression coefficients are important. Moreover, for principal component and factor analyses, the analyses of covariance or correlation matrix might be useful. In this article we suggest some estimators of simple correlation coefficient when auxiliary information about entire population is available. We have derived the true variance, up to the first order of approximation, of the convention estimator and of the ratio and difference estimators. To compare the suggested estimators empirically with the conventional estimator, a small scale Monte Carlo simulation is carried out using real data sets. The performance of these estimators as compared to conventional one is measured in terms of percentage relative bias (RB%) and relative efficiency (RE%). From the empirical study it was observed that whenever the underlying assumptions of suggested estimators are met they performed well.