Prediction Intervals of Simple Linear Regression for Interval-Valued Data  

Oleh:

Wakatsuki, Issei ; Yasui, Seiichi ; Ojima, Yoshikazu

Jenis: Article from Proceeding
Dalam koleksi: 12th ANQ Congress in Singapore, 5-8 Agustus 2014, page 1-11.
Topik: Interval-Valued Data; Prediction Intervals; Linear Regression; Midpoint; Vertex
Fulltext: QP2-2.2-P0266.pdf (622.79KB)

Isi artikel

Regression analysis is a well-known classical method. It deals with classical data, but new method is required to deal with symbolic data nowadays. Symbolic data is the aggregated data. The form of the aggregated data can be a range, list, histogram, distribution, etc. Symbolic data are developed as a method to analyze large datasets. A new method which can deal with symbolic data is needed, because classical method can’t deal directly with symbolic data. We focus on interval-valued data. Regarding interval-valued data, Billard and Diday (2006) introduced a method using the interval midpoints and another method using interval midpoints and length. However, there is no method which focuses on prediction intervals of interval-valued data. So, we compared results of regression analysis of classical data with results of regression analysis of interval-valued data. Based on the results, we proposed methods of correction of regression analysis of interval-valued data. We generated classical data and interval-valued data from the classical data which depend on the number of interval, interval length and the number of classical data in an interval. In the proposed approach, it is five linear regression methods related to the interval midpoints and the vertex of interval. These results provide that the method using weighted interval midpoints and vertex of interval and the method using the points between interval midpoint and vertex of interval can predict prediction intervals of simple linear regression of classical data approximately

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