其中 nn 表示样本大小，σ^\hat{\sigma} 定义为误差项的标准差，tr⁡(S)\operatorname{tr}(\boldsymbol{S}) 是帽子矩阵的迹。选定带宽后，可以进一步计算权重，并在每个校准位置拟合 GWR 模型，以获得一组局部系数。通过取每个校准位置的局部 R2R^{2} 的平均值，可以获得 GWR 模型的总体 R2R^{2} 值。

【原 文】 Fotheringham, A. Stewart and Yang, Wenbai and Kang, Wei. Multiscale Geographically Weighted Regression (MGWR) 2017. Annals of the American Association of Geographers , Vol. 107, No. 6 p. 1247-1265.

【阅后感】 本文作者是地理加权回归方法的提出者之一，也是《地理加权回归：空间可变关系的分析》一书的作者。在提出地理加权回归十余年后，作者发现原来的方法对于尺度缺乏建模能力（即解释变量可能来自于不同尺度的空间数据），进而深入研究了与尺度结合的地理加权回归，提出了自己的一套新方法。

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