Abstarct: Regression models are mostly used in various sciences, including medicine, natural sciences, social sciences, economics, and environmetrics. In cases where the response variable is non-normal, generalized linear models are usually used instead of linear ones. A basic assumption in these models is the independence between observations. However, in many situations we are encountered with some sort of dependency structure; e.g. longitudinal data, time series, and spatial data analysis. In these cases, the dependence of responses should be introduced into the model. Different approaches have been proposed for this task. The usual approach is to use generalized linear mixed models. Statistical inference in this class of models (in both frequentist and Bayesian approaches) faces serious computational problems. A new alternative solution to account for the dependency of responses is to use copula regression models. In this thesis, we first introduce Gaussian copula marginal regression model. Then, we establish the statistical inference of the model and goodness of fit criteria, and we use Hunsman's test to determine the correctness of the copula model selection as well. Our inference approach is baxsed on the likelihood function. We evaluate the performance of model by using simulated and real examples.