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.