Researchers are often interested in studying the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship, and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology. However, the primary form of the regression analysis, ordinary least squares (OLS) is not suitable for actuarial applications because the relationships are often nonlinear, and the probability distribution of the response variable may be non-Gaussian distribution. One of the methods that have been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the response variable have a distribution from the exponential family. In this research work, we study copula regression as an alternative method to OLS and GLM. The significant advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. The first part of this study, we will briefly discuss copula regression by using several varieties of marginal copula functions and copula regression is the most appropriate method in a non-Gaussian variable (violated normality assumption) regression model fitting. Also, we validated our results by using real-world example data and random generated (50000 observations) data.