One fitted regression, seven lenses: Durbin–Watson for first-order autocorrelation, Breusch–Godfrey for higher-order (its auxiliary regression zero-fills the pre-sample residuals, the Greene convention), Ljung–Box on the residual autocorrelations, Breusch–Pagan and White for heteroskedasticity, Jarque–Bera for normality, and the influence trio of leverage, Cook's distance and DFFITS.
The thresholds are the standard ones: leverage above 2k/n, |DFFITS| above 2√(k/n), Cook's distance near 1 as a danger sign. The p-values come from the exact χ² and t distribution functions, not tables.
Frequently asked questions
Which test decides between robust errors and GLS?
Breusch–Pagan or White rejecting heteroskedasticity points to HC standard errors (or WLS with known weights); Breusch–Godfrey rejecting points to HAC or the AR(1) GLS option in the linear regression tool.
Does a high Cook's distance mean I should delete the row?
No — it means the row deserves inspection. Deleting valid extreme observations biases results; first check whether it is a data-entry error, then decide.
中文说明
一次拟合、七重视角：一阶自相关看 Durbin–Watson，高阶自相关看 Breusch–Godfrey（辅助回归对样本前残差零填充，Greene 惯例），残差自相关看 Ljung–Box，异方差看 Breusch–Pagan 与 White，正态性看 Jarque–Bera，强影响点看杠杆值、Cook 距离与 DFFITS 三件套。
阈值均取标准值：杠杆值高于 2k/n、|DFFITS| 高于 2√(k/n)、Cook 距离接近 1 视为危险信号。p 值来自精确的 χ² 与 t 分布函数，而非查表。
常见问题
这些检验如何指导选稳健标准误还是 GLS？
Breusch–Pagan 或 White 拒绝同方差 → 用 HC 稳健标准误（或已知权重时用 WLS）；Breusch–Godfrey 拒绝无自相关 → 用 HAC 或线性回归工具里的 AR(1) GLS。
Cook 距离大就要删行吗？
不——它只说明该行值得检查。删除有效的极端观测会引入偏差；先确认是否录入错误，再决定。