This paper came with the aim of knowing the causal mediation analysis and estimation methods in addition to the study data. Mediation is the basis for many fields, where at the present time the use of mediation analysis has become increasingly common in many areas of scientific research as well in other fields such as economic and social as well as medical sciences. Causal mediation analysis is one of the important methods in order to know the mechanism of influence between variables, which has had a large role among researchers in recent times. In order to arrive at a model that leads to accurate estimates, it is necessary to find or search for the method by which the important variables are chosen in order to be included in the model, especially when the study data suffers from the presence of the problem of linearity. Therefore, many methods of estimating the mediation variables have been used, which are the least squares method and Ridge method. In order to apply the estimation methods, a simple random sample of (50) women were drawn to study the factors affecting the number of births (response variable). The study data were analyzed using programming in R language.