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Errors and residuals

lastmod 2018-08-17created 2018-07-262 edits

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value". The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals.

Definition of error

The difference that appears when the actual value in the population is compared with the regression line (the difference between the exact value and the observed value)

Types of error

Constant error
Error that occurs in the same direction or with the same magnitude under fixed conditions
  • Error due to physical causes
  • Error due to mechanical causes
  • Error due to personal traits
Accident error
Error that appears case by case depending on observation conditions
Mistake
Error caused by the observer's carelessness

Assumption of error in regression analysis 

y = bx + a + 오차

The regression model includes the error

Residual

  • Sometimes refers to the deviation between the mean of samples drawn from a population (the sample mean) and an individual sample value, but
  • mostly has nearly the same meaning as Estimation Error

Estimation Error

  • The difference between the expected value (estimate) computed from the sample group and the observed value of the outcome of a random trial
  • That is, the difference between the estimate obtained from a regression line (estimated curve), etc., and the actual observed value

See also

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References

  1. Gimmesilver_-_What_is_regression.pdf ↩

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