非常地意外，温度及降水数据（自变量）拟合NDVI（因变量）的回归模型复判定系数（Multiple Coefficient of Determination）竟然是负值，为了永远铭记这一百年不遇的发现，特此开贴记录。

在Matlab中调用regress()函数完成计算。公式如下：

nDNs=b(1)+b(2)*pDNs+b(3)*tDNs

b(1)=0；b(2)=9.001485523185693e-06；b(3)=0.028094617649913。

R²=-0.11865890，F-statistics=4.9956303>F_(1,27)=4.21（临界值），p=0.033880889<0.05，通过α=0.05的显著性检验。R²是负值，合理的解释One version of calculating R² can only give positive numbers as it is effectively the square of r. On the other hand a common method of computing R² is 1 - sum of square in model/sum of square for uncorrelated (horizontal line) - if the model is completely inappropriate it will give a worse sum of squares than a flat line.

网上一则比较全面的解释：

R² compares the fit of the chosen model with that of a horizontal straight line (the null hypothesis). If the chosen model fits worse than a horizontal line, then R² is negative. Note that R² is not always the square of anything, so it can have a negative value without violating any rules of math. R² is negative only when the chosen model does not follow the trend of the data, so fits worse than a horizontal line.

附上示例数据及代码（negativer2.rar）。

See Also

Important cases where the computational definition of R² can yield negative values, depending on the definition used, arise where the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data, and where line arregression is conducted without including an intercept. Additionally, negative values of R² may occur when fitting non-linear functions to data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion.

Note that it is possible to get a negative R-square for equations that do not contain a constant term. Because R-square is defined as the proportion of variance explained by the fit, if the fit is actually worse than just fitting a horizontal line then R-square is negative. In this case, R-square cannot be interpreted as the square of a correlation. Such situations indicate that a constant term should be added to the model.