# A Method of Accuracy Increment Using Segmented Regression
## 1 Introduction  
Scientists use various models when studying different environmental phenomena. Mathematical models provide an opportunity to determine equations and dependencies to correlate the parameters of miscellaneous objects and processes. Mathematical models are built for various reasons, including the achievement of the best understanding of the objects under study, the possibility of mathematical analysis, and the possibility of conducting experimentation with the model in case it is difficult to repeat the experiment with the objects under study [1].  
The process of mathematical model building contains several steps:  
1. Experimental study and the measuring of the parameters of real-world systems and phenomena;
2. Collecting initial data for the model;
3. Mathematical formulations and fitting one or more models;
4. The statistical simulation of the model to validate it [2].  
There are general rules for building mathematical models. These rules assume the following: (1) collecting background information for the phenomenon under study, (2) using simple models at the first stage, (3) determining all parameters and the quantities and correlations between them based on data analysis, (4) complicating the model based on the nature of the phenomenon under study, (5) estimating the efficiency of the model, and (6) others [3]. The efficiency analysis involves choosing the optimal mathematical model for the problem considered.  
There are various efficiency measures for mathematical models. Generally, researchers use the following parameters:  
1. Accuracy--for the coincidence analysis of the output of a mathematical model with observed data;
2. Reliability--for the analysis of the precision of a mathematical model;
3. Transparency--for the analysis of choices and assumptions of the output expectations [4; 5].  
To analyze mathematical models, researchers can use additional criteria, such as model simplicity, calculation time, costs, depth level, and others.  
The main parameters for the efficiency level of mathematical models in terms of accuracy analysis are standard deviation [6; 7], the sum of absolute deviations between the model output and the observed data [8], a weighted sum of squared deviations [9; 10], and the maximal deviation [11]. The criterion for these parameters is the minimum value of the estimated parameter [12; 13].  
This article contains seven sections. The first section discusses the background information for the problems of mathematical model building. The second section presents a literature review regarding the topic of research and presents the statement of the problem. The third section deals with the description of mathematical tools for segmented regression building while using ordinary least squares. The fourth section proposes the step-by-step procedure for accuracy increment during segmented regression usage. The fifth section concentrates on the analysis of the proposed method based on statistical simulations. The sixth section discusses the implementation of the proposed method in real data examples, and the seventh section presents the conclusions.