||For analyzing the data in applied research studies, continuous exposure variables are frequently partitioned into categorical variables with two levels and those categorized exposure variables is fitted in the regression model and it is called dichotomization. The dichotomization of independent variable will result in the bias on the regression coefficient and a considerable loss of information and power. Furthermore, measurement error is also a serious problem in various scientific areas. Both measurement error and dichotomization can lead to considerable loss of information, power and relative efficiency. In this thesis, we adopts the hypothesis testing on the association between response and exposures with a specified power at fixed significance level in the linear regression model in which the explanatory exposures are subject to measurement error, dichotomization or both.