In the book an attempt has been made to develop some new diagnostic tests for statistical model building in the context of linear regression models. Diagnostics of outliers has been described and a test for identifying outliers by using predicted residuals has been proposed in the present study. Besides outliers, a measure of influence for diagnostics has been developed in the study. Some new modified R2 and criteria for model selection have been developed along with modified mean square prediction error criteria; and modified information criteria for model selection. A test for exogeneity in model specification by using augmented regression model; and a test for stability of regression parameters in model specification have been proposed under diagnostic tests. A new test for misspecification of the linear regression model has been derived along with a modified Rainbow Test by using Internally studentized residuals. The problem of misspecification of non-nested linear regression models, has been discussed together with a diagnostic test for functional form between loglinear and linear regression models.

In the present book, Chapter-I is an introductory one. It gives general introduction about the nonlinear regression models. A brief review about the existing inferential procedures for nonlinear regression models has been give in Chapter-II. It contains various nonlinear methods, of estimation based on nonlinear least squares and maximum likelihood methods, besides the methods by using some numerical analysis procedures.Chapter-II and IV describe the specification and estimation of some important nonlinear production function models such as Cobb-Douglas, Constant Elasticity of Substitution (CES), Variable Elasticity of Substitution (VES) and Transcedental Logarithmic (Translog) Production functions. Some new Inferential procedures for certain nonlinear regression models have been proposed and developed in Chapter V. The directions for further research along with the conclusions have been presented in Chapter-VI. General selected references regarding nonlinear regression models have been documented under Bibliography.