This dissertation focuses on the problem of testing for a change in the regression model when errors are independently, normally distributed with constant, known or unknown variance. First we consider the regression model in which only the intercept changes at some unknown point (Model-1). Secondly, the model in which both intercept and slope change is considered (Model-2). In all cases, the likelihood ratio statistic (LRS) is of the form U = max{dollar}sb{lcub}1leq i |