A key diagnostic in the analysis of linear regression models is whether the fitted model is appropriate for the observed data. The classical lack of fit test is used for testing the adequacy of a linear regression model when replicates are available. While many efforts have been made in finding alternative lack of fit tests for models without replicates, this paper focuses on studying the efficacy of three tests: The classical lack of fit test, Utts' (1982) test, Burn and Ryan's (1983) test. The powers of these tests are computed for a variety of situations. Comments and conclusions on the overall performance of these tests are made, including recommendations for future studies.