多元线性回归的中心化和标准化实验结果比较

Comparison of Centralized and Standardized Experimental Results of Multiple Linear Regression

摘要: 在讨论一元线性回归模型的时候，我们可以看出，对数据进行中心化处理后，推导计算过程会简化许多。由此想到，对于多元线性回归模型，能否也对数据进行中心化处理，或者进一步的标准化处理，以期简化计算？实际上，经过中心化和标准化处理，可得到均值为0，标准差为1的数据，从而在进行多元线性回归拟合时消除了因量纲不同或数值差异较大而引起的误差。

Abstract: When discussing the unary linear regression model, we can see that the derivation and calculation process will be much simplified after centralized data processing. Therefore, for the multiple linear regression model, can the data also be processed centrally or further standardized to simplify the calculation? In fact, data with a mean value of 0 and a standard deviation of 1 can be obtained after centralized and standardized processing, so that errors caused by different dimensions or large numerical differences can be eliminated when performing multiple linear regression fitting.