LINEAR REGRESSION ANALYSIS FOR INTERVAL-VALUED DATA

This study deals with regression analysis using data where the observations are given as interval values. Regression analysis of interval-valued data aims to estimate the upper and lower boundaries of the interval of the target variable for a given interval of the explanatory variable. Conventional methods use the centre and range of the interval of the explanatory variable and the interval of the target variable to obtain the estimated upper and lower regression lines. However, this method provides good estimates only when the slopes of the upper and lower regression lines are the same, making interpretation of the estimation results difficult. To deal with this problem, we define errors in interval-valued data and propose a method to minimize them. From simulation results, it is found that the proposed method provides good estimation with high interpretability and minimizes the problems of conventional methods.