The regression model was traditionally established by using the least squares (LS)method where the errors of independent variables were ignored.Although the weighted total least squares (TLS) method that captures errors of both dependent and independent variables was extensively studied for regression analysis in recent years,it still neglects the errors of independent variables when predicting the corresponding dependent variables.This paper puts forward a seamless linear regression and prediction model which estimates regression parameters and predicts dependent variables simultaneously by considering the errors of all variables.In the seamless model,the errors of independent variables in the prediction model are predicted and corrected to improve the prediction accuracy.The several existing regression models are theoretically proved to be the special cases of the proposed seamless model.The experimental results show that the proposed seamless model outperforms the other existing models in the sense of prediction accuracy,especially when the error correlation of variables is significant.%建立回归模型常采用最小二乘方法并忽略自变量观测误差。尽管同时顾及自变量和因变量观测误差的总体最小二乘方法近年来得到了广泛研究,但在模型预测时,依然忽略了待预测自变量的观测误差。对此,本文提出了一种严格考虑所有变量观测误差的无缝线性回归和预测模型,该模型将回归模型的建立和因变量预测联合处理,在建立回归模型过程中对待预测自变量的观测误差进行估计并修正,从而提高了模型预测效果。理论证明,现有的几种线性回归模型都是无缝线性回归和预测模型的特例。试验结果表明,无缝线性回归和预测模型的预测效果优于现有的几种模型,尤其在变量观测误差相关性较大时,无缝模型对预测效果的改善更为显著。
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