残差 Residual-学英语学统计！

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Residual
残差类型

Regular  常规型

The difference between the observed values and predicted or fitted values. The residual is the part of the observation that is not explained by the fitted model. You can analyze residuals to determine the adequacy of the model.
= response - fit

是观测值与预测值/拟合值之间的差异。残差是观测中不能用拟合模型解释的部分。可以通过分析残差来确定拟合模型是否适当。
值为：响应值-拟合值

Standardized  标准化型

Also known as the Studentized residual or internally Studentized residual. The standardized residual is the residual, ei, divided by an estimate of its standard deviation. This form of the residual takes into account that the residuals may have different variances, which can make it easier to detect outliers. Standardized residuals greater than 2 and less than -2 are usually considered large and Minitab labels these observations with an R in the table of unusual observations or fits and residuals.
= (residual) / (standard deviation of the residual).  

也就是所说的学生化残差或是内部学生化残差。标准化残差是残差ej除以残差群的标准差估计值后得到的数值。这种形式的残差用来说明残差间可能存在的变动，而通过残差间变动可以很容易发现异常点。大于2或小于-2的标准化残差通常被认为是过大的，Minitab用异常观测/拟合与残差表中的R来标注这些异常的观测。
值为：残差/残差的标准差。


Deleted Studentized    学生化的去除型

Also called externally Studentized residual. Studentized deleted residuals are useful for identifying outliers because the ith residual is calculated when the fitted regression is based on all of the cases except the ith one. The residual is then divided by its estimated standard deviation. Since the Studentized deleted residual for the ith observation estimates all quantities with this observation deleted from the data set, the ith observation cannot influence these estimates. Therefore, unusual Y values clearly stand out. Studentized deleted residuals with large absolute values are considered large.

也称作外部学生化残差。学生化去除残差对于识别异常点是有用的，因为第i个残差的计算是在回归模型涵盖了除第i个实例外所有的实例的基础上进行的。然后，再用残差除以此时的残差群标准差的估计值。由于第i个观测的学生化去除残差估计了剔除第i个观测后的数据集中的所有点，第i个观测就不会影响第i个残差的估。因此，毫无疑问地会突出异常的Y值。绝对值大的学生化去除残差被认为是大的。

If the regression model is appropriate, with no outlying observations, each Studentized deleted residual follows the t distribution with n - 1 - p degrees of freedom.
= (residual) / (standard deviation of the residual). The ith Studentized residual is computed with the ith observation removed.

如果回归适当，即没有异常观测，每个学生化去除残差服从自由度为(n-1-p)的t分布。
值为：残差/残差的标准差。第i个学生化残差在计算时会剔除第i个观测。

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