python - 在 Python 中计算决定系数

Question

我正在尝试计算 coefficient of determination (R^2) 在 Python 中，但在某些情况下我得到负值。这是否表明我的计算有误？我认为 R^2 应该限制在 0 和 1 之间。

这是我用于计算的 Python 代码，直接改编自 WP 文章:

>>> yi_list = [1, 1, 63, 63, 5, 5, 124, 124]
>>> fi_list = [1.7438055421354988, 2.3153069186947639, 1002.7093097555808, 63.097699219524706, 6.2635465467410842, 7.2275532522971364, 17.55393551900103, 40.8570]
>>> y_mean = sum(yi_list)/float(len(yi_list))
>>> ss_tot = sum((yi-y_mean)**2 for yi in yi_list)
>>> ss_err = sum((yi-fi)**2 for yi,fi in zip(yi_list,fi_list))
>>> r2 = 1 - (ss_err/ss_tot)
>>> r2
-43.802085810924964

Answer 1

维基百科文章中所示的计算实现对我来说没问题。

根据维基百科文章:

Values of R2 outside the range 0 to 1 can occur where it is used to measure the agreement between observed and modelled values and where the "modelled" values are not obtained by linear regression and depending on which formulation of R2 is used.

查看您的数据，预期模型对 63 和 1002.7093097555808 可能是大方差的主要来源。