This paper proposes a new approach to fit a linear regression for symbolic internal-valued variables, which improves both the Center Method suggested by Billard and Diday in \cite{BillardDiday2000} and the Center and Range Method suggested by Lima-Neto, E.A. and De Carvalho, F.A.T. in \cite{Lima2008, Lima2010}. Just in the Centers Method and the Center and Range Method, the new methods proposed fit the linear regression model on the midpoints and in the half of the length of the intervals as an additional variable (ranges) assumed by the predictor variables in the training data set, but to make these fitments in the regression models, the methods Ridge Regression, Lasso, and Elastic Net proposed by Tibshirani, R. Hastie, T., and Zou H in \cite{Tib1996, HastieZou2005} are used. The prediction of the lower and upper of the interval response (dependent) variable is carried out from their midpoints and ranges, which are estimated from the linear regression models with shrinkage generated in the midpoints and the ranges of the interval-valued predictors. Methods presented in this document are applied to three real data sets cardiologic interval data set, Prostate interval data set and US Murder interval data set to then compare their performance and facility of interpretation regarding the Center Method and the Center and Range Method. For this evaluation, the root-mean-squared error and the correlation coefficient are used. Besides, the reader may use all the methods presented herein and verify the results using the {\tt RSDA} package written in {\tt R} language, that can be downloaded and installed directly from {\tt CRAN} \cite{Rod2014}.

翻译：本文提出了一种拟合符号区间值变量线性回归的新方法，该方法改进了Billard和Diday在文献\cite{BillardDiday2000}中提出的中心法以及Lima-Neto, E.A.和De Carvalho, F.A.T.在文献\cite{Lima2008, Lima2010}中提出的中心与范围法。与中心法和中心与范围法类似，新方法在训练数据集中预测变量所假定的区间中点和半长度（范围）上拟合线性回归模型，但为完成这些回归模型中的拟合，采用了Tibshirani, R.、Hastie, T.和Zou H在文献\cite{Tib1996, HastieZou2005}中提出的岭回归、Lasso和弹性网络方法。区间响应（因变量）的下限和上限预测通过其中点和范围实现，这些中点和范围由区间值预测变量中点和范围的收缩线性回归模型估计所得。本文提出的方法应用于三个真实数据集：心脏病区间数据集、前列腺癌区间数据集和美国谋杀案区间数据集，并与中心法和中心与范围法在性能及解释便利性方面进行比较。评估采用均方根误差和相关系数指标。此外，读者可使用本文所有方法，并通过基于{\tt R}语言编写的{\tt RSDA}包验证结果，该包可直接从{\tt CRAN}\cite{Rod2014}下载安装。