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The properties of the estimators of population mean arising from the ratio and product methods of estimation in the context of sample surveys have been analyzed in this paper when the observations on both the study and auxiliary variables are contaminated with measurement errors. The measurement errors in both the variables are also correlated. The properties of the ratio and product estimators along with the sample mean under the influence of measurement errors are derived and studied. The properties of the estimators in finite samples are studied through Monte-Carlo simulation and its findings are reported.

The coefficient of determination (R 2 ) is used for judging the goodness of fit in a linear regression model. It gives valid results only when the observations are correctly observed without any measurement error. The R 2 provides invalid results in the presence of measurement errors in the data in the sense that sample R 2 becomes an inconsistent estimator of population multiple correlation coefficient between the study variable and explanatory variables. The corresponding variants of R 2 which can be used to judge the goodness of fit in multivariate measurement error model have been proposed in this paper. These variants are based on the utilization of information on known covariance matrix of measurement errors and known reliability matrix associated with explanatory variables. The asymptotic properties of the traditional R 2 and proposed R 2 have been studied.

In this article, we consider the estimation of population mean when some observations on the study characteristic are missing in the bivariate sample data. In all, ve estimators are presented and their e ciency properties are discussed. One estimator arises from the the amputation of incomplete observations while the remaining four estimators are formulated using inputed values obtained by the ratio method of estimation.