北京航空航天大学学报 ›› 2007, Vol. 33 ›› Issue (04): 500-504.

• 论文 • 上一篇    

多元线性回归的预测建模方法

王惠文, 孟洁   

  1. 北京航空航天大学 经济管理学院, 北京 100083
  • 收稿日期:2006-05-30 出版日期:2007-04-30 发布日期:2010-09-19
  • 作者简介:王惠文(1957-),女,辽宁大连人,教授,wanghw@vip.sina.com.
  • 基金资助:

    国家自然科学基金资助项目(70531010;70371007);创新研究群体科学基金资助项目(70521001)

Predictive modeling on multivariate linear regression

Wang Huiwen, Meng Jie   

  1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2006-05-30 Online:2007-04-30 Published:2010-09-19

摘要: 根据历史的样本数据,建立多元线性回归的预测模型;从而在不需要未来样本数据的情况下,预测未来时刻多元线性回归模型中的回归参数,以及主要的模型精度评估指标.对多元线性回归模型参数的预测,转化为对其变量集合的增广矩阵的叉积阵的预测.对叉积阵进行谱分解,利用高维群点主轴旋转的预测建模方法,通过Givens变换得到特征向量矩阵的转角值,对自由取值的转角以及特征值建立预测模型.仿真实验例示了该方法的主要计算步骤;计算结果显示,利用本模型得到的拟合值精度较高,预测值真实可信.最终计算结果和实验结果吻合较好,表明这种方法可以用于分析和预测众多领域中因变量对自变量的回归关系问题.

Abstract: Based on the historical data, predictive method of multivariate linear regression model was discussed, where both future multivariate regression parameters and the performance evaluation statistics were estimated without future data. Prediction to the regression parameters was converted to predict cross product matrix of the variable augmented matrix. By applying spectral decomposition, cross product matrix was decomposed of eigenvectors and eigenvalues. Predictive method of orthonomal matrix based on rotations of principal axes was adopted to predict eigenvector matrix, where rotated angles from Givens transformation were obtained, and regular predictive models were built on both the angles and eigenvalues, respectively. The experimental simulation illustrates main computational procedures of the predictive model. Besides, the results show a high precise of the fitted values and a statistical validity of the predictive values. The agreement of the final computation results with the experimental data indicates this method could be used to analyze and forecast regression relationships of dependent variable to independent variables in many application fields.

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