Explainable Linear and Generalized Linear Models by the Predictions Plot

Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of a specific case is unusually high or low? To assist with this the so-called predictions plot is proposed. Its simplicity makes it easy to interpret, and it combines much information. Its main benefit is that it helps explainability of the prediction formula as it is, without depending on how the formula was derived. The input variables can be numerical or categorical. Interaction terms are also handled, and the model can be linear or generalized linear. Another display is proposed to visualize correlations and covariances between prediction terms, in a way that is tailored for this setting.

多元线性回归是一类基础的统计工具，可生成包含输入变量、斜率与截距项的预测公式。但我们能否直观地识别出影响权重最高的变量项，或是解释为何某一特定样本的预测值出现异常偏高或偏低的情况？为解决这一痛点，本文提出了所谓的预测图（predictions plot）。该方法凭借简洁的形式便于解读，且可整合多维度信息。其核心优势在于，能够直接对现有预测公式进行可解释性分析，且无需依赖公式的推导过程。输入变量可分为数值型与分类型两类，该方法同样支持交互项的处理，且适配线性模型与广义线性模型。此外，本文还提出了另一可视化工具，用于呈现预测项之间的相关性与协方差，其设计完全贴合该场景的特定需求。