On the Interpretation of Large Datasets by a New Method of Regression Analysis Based on Reverse Discretization

Abstract

Abstract The discrete data points of a Dataset are replaced by continuous functions. These functions have finite derivatives and their integration from minus to plus infinity is equal to unity. The employment of these functions renders the Sum-Square-Error (SSE) a continuous function of x and y. The optimization of this SSE yields a Regression Line called in this article Dynamic Regression Line. The proposed algorithm yields a regression line that does not simply indicate the trend but also provides an interpretation of the data by revealing the underline law that generated them. In two examples given in this article the data points are distributed randomly around the segments of a broken line, which was the generating law. Only the x and y coordinates and the intensity of the information carried by each point were used in the Analysis. The regression line obtained by this method revealed, with acceptable accuracy, the line that generated the data points. It is suggested that the interpretive potential of this method can have applications in several disciplines like Engineering, Statistics, Artificial Intelligence, Economics, Marketing, Polling, and others.