基于层次结构数据的多元线性回归问题分析

Multiple Linear Regression Problem Based on Hierarchical Structure Data

针对传统多元线性回归分析(Multiple linear regression,MLR)在处理大数据时,特别是具有层次结构的数据,提出了基于层次结构数据的偏回归系数计算模型。该模型通过计算下层中每个部分的偏回归系数及上、下层之间的层次结构矩阵,来计算上层的总体偏回归系数。从理论研究和实际数据试验验证了在计算回归系数时新模型与传统MLR模型具有等效性。同时,新模型能有效解决隐私数据的保护问题,实现计算的并行处理,提高了大数据处理能力。

Multiple linear regression(MLR)is widely used in statistical analysis.Based on common tools of the multiple linear regression in big data research,especially in the research of hierarchical structure data,a partial regression coefficient model is proposed here.The total partial regression coefficient is calculated by using each partial regression coefficient at the lower part and the hierarchical matrix between the lower and upper parts.It is validated that the new model is equivalent to the common models of multiple linear regression by the theoretical research and the real data.The new method can effectively solve the problem of privacy data in privacy protection research.Moreover,the new model can realize the parallel computation,which improves the capability of big data processing.