The limitation of linear regression is that its approximation might become inaccurate when the amount of noise is relatively small (see Figure 1). The simplicity and efficiency are important advantages of linear regression over other methods and explain why it is a good choice in practice. This feature is also helpful for data visualization, since it allows us to avoid the art of manual drawing of approximation lines by naked eye. It enables us to create informative diagrams for datasets that may look chaotic at first. In data analysis, linear regression provides a clear view of data unaffected by noise. A large deviation from the line is interpreted as a sign of an important event in a system that changes its behaviour. One the reasons of its popularity is the ability to predict, which is based on the computation of the slope of the approximation line. This variant of linear regression replaces the whole dataset by a single line segment.Īs a fundamental mathematical method, linear regression is used in numerous areas of business and science. The best fitting is performed using the least-squares method. e i represents a random error term of the model. In this article, we consider simple linear regression of one independent variable x and one dependent variable y: Within this model, each value is the sum of a linear approximation in a selected point from the space of independent variables and a deviation caused by noise. Linear regression provides an optimal approximation for given data, under the assumption that the data are affected by random statistical noise. The large amount of information requires a discussion and a clarification of our approach to this problem. For an introductory explanation, refer to articles in Wikipedia. Linear regression is one of the classical mathematical methods for data analysis, which is thoroughly covered in textbooks and literature.
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