The simple linear regression model with measurement errors are linear relationship between two random variate in which both of the variate are subject to measurement errors . Sometime the explanatory and response variable cannot be observed. In this work we will focus on this model when the error in the explanatory variable is correlated with the error in the regression equation. Specifically, we are Interested in the comparison between the ordinary errors-in-variables estimator of the regression coefficient and the estimator that Take account of the correlation between the errors. Based on large sample approximations, we compare the estimators and find That the estimator that takes account of the correlation should be preferred in most situations. We also compare the estimators in small sample situations. This is done by stochastic simulation.
