Testing for heteroscedasticity and series  correlation among error terms are basic problems in linear regression model  diagnostics. In this talk, we will present simple tests for heteroscedasticity  and series correlation that are applicable in both low and high dimensional  linear regression models. The test statistics are based on the regression  residuals and design  matrix. The test procedures are robust under different distributions of random  errors. The asymptotic distributions of the proposed statistics are derived via  newly established joint central limit theorems the delta method. Good  performance of the proposed tests is demonstrated by simulation  results.