In the Present Book Chapter-I is an introductory one. It contains the general introduction about the methods of Diagnostic Tests in statistical modeling besides the objectives and organization of the present study. It also brings out the chapter scheme. Chapter-II describes the various selection criteria for statistical model building. Under the criteria of model selection among a large number of potentially important regressors, only a subset of explanatory variables may be finally chosen. Chapter-III proposes how to specify the Nested and Non-Nested models in statistics. It also gives the test procedure for selection of Nested and Non-Nested models in statistics.Chapter-IV proposes some Diagnostics tests in statistical model building. It also describes the importance of Diagnostic tests in statistical model building.Chapter-V gives the conclusions of the present research study. It also brings out the suggestions for future research in the time of present study. Several relevant articles regarding the statistical modeling and Diagnostics tests have been presented under the title ‘BIBLIOGRAPHY’.