In this thesis, a panel data regression model with heteroskedastic as well as spatially correlated disturbances is considered, and a joint LM test for homoskedasticity and no spatial correlation is derived. In addition, a conditional LM test for no spatial correlation given heteroskedasticity, as well as a conditional LM test for homoskedasticity given spatial correlation, are also derived. These LM tests are compared with marginal LM test that ignore heterokedasticity in testing for spatial correlation, or spatial correlation in testing for homoskedasticity.