Regression Analysis For Intervals

Regression analysis is a very common method of data analysis to determine the relationships between variables through observation data. Traditionally, regression analysis take point data as research object, and the predicted results are also single value. However, the real data is often changes within a certain range, rather than a exactly point data. Confidence interval forecasts are proposed to make up for the lack of point forecasts. The defect of confidence intervals forecasts is the problem of information loss.Interval regression analysis is a data analysis method which take intervals as research object. Intervals can reflect changes in the scope of the data, and are more in line with reality. Interval symbolic data is one kind of intervals. It is formed through the "data package" procedure. As a result, the interval symbolic data can contain not only the endpoint information, but also the individual information with the interval. Based on the existence of individuals within Intervals, this dissertation researched in two aspects.When the individuals with interval are unknown, information that can be used includes the interval endpoints, the midpoint and the radius. Many literatures are proposed based on these special data. some methods are based on the midpoints and radius of intervals, such as the center and range method, the constrained center and range method as well as model M etc. When the errors range is large while the radius is relatively small, these methods may not perform well. This dissertation improves the defects by add some constrains to the center and range method. Monte Carlo experiments show that the new constrained method can perform well when the errors range is relatively high. Finally, the new constrained method is applied to predict the CSI 300 index.When the individuals within the interval are known, the individual information can be used. The descriptive statistics based method(DSM) made full use of the individual information. However, the lower bound of the predict interval may be higher than the upper bound. The extend descriptive statistics based method(e DSM) is proposed to solve the problem. On one hand, this dissertation give derivation of the coefficient estimating equation, based on some assumptions. On the other hand, two predicting strategies are proposed to improve the prediction accuracy. One is predicting some special value to form the interval. The other one is predicting the individuals within interval, and then form the interval through "data package". Under the proposed assumption, OLS model can also be used to estimate the coefficients. Four methods are formed and these methods are compared with the original DSM and CCRM. Monte Carlo simulation experiments show that the proposed e DSM perform well in all cases. Suppose the error range is same, when the absolute value of the coefficient is large, predicting special value performs best, otherwise predicting individuals to form interval will be the best choise. Finally, each of the comparison method is applied to predict changes of the stock index and to predict credits of taobao shops.