For statistical inference about the parameters of the regression model, it is necessary to assume a specific distribution for
 the random error term. A basic assumption in the linear regression model is that the random error term follows a normal
 distribution. However, in statistical research, sometimes the distribution of the data display both skewness and bimodality,
 and in such situations, it is inappropriate to use the normal distribution for statistical analysis. A conventional approach
 to overcome this problem is to use a mixture of normal models. But in such models, the number of parameters increases
 substantially, which makes it difficult to fit these models to the data. In addition, the mixed models suffer from the non
identifiability issues. In this case, a suitable solution is to use flexible distributions which can simultaneously handle the
 skewness and bimodality of the data in the modeling structure. So far, various methods have been proposed, which were
 created based on the development of the skew-normal distribution. In this article, these asymmetric bimodal distributions are
 used to build and introduce a flexible regression model compared to the regression models based on the normal distribution
 as well as a mixture of two normal distributions. Their performance is evaluated using a simulation example. Then, the
 usefulness of the method is demonstrated through a practical example related to the horse data set.