This article presents a framework for measurement errors in order to analyze the properties of estimators in survey sampling and therefrom to examine the effect of measurement errors. We consider a simple case in which information on merely one auxiliary characteristic is available and the regression method of estimation is used. First, we present two estimators of regression coefficient - one arising from direct regression and the other from reverse regression. Both the estimators are known to be inconsistent in the presence of measurement errors but when they are used to formulate estimators of population mean of study characteristic, consistent estimators are obtained even when measurement errors are present. The large sample approximations for the biases and mean squared errors are derived and a comparison of the estimators that incorporate the auxiliary information is made with the traditional estimator that ignores the auxiliary information. The influence of measurement errors is also studied.