What's the difference between error and residual? What's the use?

Error: the deviation between the observed value and the true value;

Residual: the deviation between the observed value and the fitted value.

Error and residual, these two concepts are similar to some extent, and they are both indicators to measure uncertainty, but they are different. The error is related to the measurement. The magnitude of error can measure the accuracy of measurement, and the greater the error, the less accurate the measurement.

Errors are divided into two categories: systematic errors and random errors. Among them, the system error is related to the measurement scheme, which can be avoided by improving the measurement scheme. Random errors are related to the nature of observers, measuring tools and observed objects, and can only be reduced as much as possible, but cannot be avoided.

Residual-related to prediction, the residual size can measure the accuracy of prediction. The larger the residual, the less accurate the prediction. The residual is related to the distribution characteristics of the data itself and the choice of regression equation.

Error: the deviation of the average of all different sample sets from the real population average. Because the true population mean cannot be obtained or observed, it is usually assumed that the population is of a certain distribution type with n estimated means; Represents the accuracy of observation/measurement;

The large error is caused by abnormal values, which indicates that there may be serious measurement errors in the data; Or the selected model is not suitable;

Extended data:

Residual: the deviation between the average value of a sample and the average value of all sample sets; Represents the rationality of sampling, that is, whether the sample is representative;

The large residual indicates that the sample is not representative, which may be caused by the eigenvalue.

Anyway, it depends on whether a model is appropriate and how big the error is; It depends on whether the sample book is suitable or not, and whether it is disabled or not;

Residual: In mathematical statistics, residual refers to the difference between the actual observed value and the estimated value (fitting value). The "residual" contains important information about the basic assumptions of the model. If the regression model is correct, we can regard the residual as the observation value of error.

It should satisfy the assumptions of the model and have some error properties. Using the information provided by residuals to examine the rationality of model assumptions and the reliability of data is called residual analysis.

Error: Error is the measured value minus the reference value. The measured value is referred to as the measured value for short, which represents the value of the measured result. The so-called reference quantity is generally expressed by the true value or agreed quantity of the dosage. For measurement, people often take the true size of a quantity as the true value measured during observation. It is actually an ideal concept. Because only "when a quantity is perfectly determined and all defects in measurement can be eliminated, the quantity obtained through measurement" is the real value of quantity. From the measurement point of view, it is difficult to do this, so generally speaking, it is impossible to know the true value exactly.

References:

Baidu Encyclopedia-Error

Baidu encyclopedia-can