Absolute Error Statistics Definition
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Mean Absolute Error Definition
WolframResearch Probability and Statistics>Error Analysis> History and Terminology>Disciplinary Terminology>Religious Terminology> Absolute Error The difference between the absolute error definition physics measured or inferred value of a quantity and its actual value , given by (sometimes with the absolute value taken) is called the absolute error. The margin of error statistics definition absolute error of the sum or difference of a number of quantities is less than or equal to the sum of their absolute errors. SEE ALSO: Error Propagation, Percentage Error, Relative Error REFERENCES: Abramowitz, M. and Stegun, I.A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New
Standard Error Statistics Definition
York: Dover, p.14, 1972. Referenced on Wolfram|Alpha: Absolute Error CITE THIS AS: Weisstein, Eric W. "Absolute Error." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbsoluteError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Language» Knowledge-based programming for everyone. Contact the MathWorld
close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by M A E = 1 n ∑ i = 1 n | f i − y i | = 1 n sampling error statistics definition ∑ i = 1 n | e i | . {\displaystyle \mathrm {MAE} ={\frac measurement error statistics definition {1}{n}}\sum _{i=1}^{n}\left|f_{i}-y_{i}\right|={\frac {1}{n}}\sum _{i=1}^{n}\left|e_{i}\right|.} As the name suggests, the mean absolute error is an average of the absolute errors | e i |
Absolute Error Formula
= | f i − y i | {\displaystyle |e_{i}|=|f_{i}-y_{i}|} , where f i {\displaystyle f_{i}} is the prediction and y i {\displaystyle y_{i}} the true value. Note that alternative formulations may include relative frequencies as http://mathworld.wolfram.com/AbsoluteError.html weight factors. The mean absolute error is on same scale of data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series on different scales.[1] The mean absolute error is a common measure of forecast error in time [2]series analysis, where the terms "mean absolute deviation" is sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists https://en.wikipedia.org/wiki/Mean_absolute_error more generally. Related measures[edit] The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error (MASE) and the mean squared error. These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference. Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares approach is related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2011) (Learn how and when to remove this template message) This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2011) (Learn how and when to remove this template message) See also[edit] Least absolute deviations Mean absolute percentage error Mean percentage error Symmetric mean absolute percentage error References[edit] ^ "2.5 Evaluating forecast accuracy | OTexts". www.otexts.org. Retrieved 2016-05-18. ^ Hyndman, R. and Koehler A. (2005). "Another look at measures of forecast
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The equation is given in the library references. Expressed in words, the MAE is the average over the verification sample of the absolute values of the differences between forecast and the corresponding observation. The MAE is a linear score which means that all the individual differences are weighted equally in the average. Root mean squared error (RMSE) The RMSE is a quadratic scoring rule which measures the average magnitude of the error. The equation for the RMSE is given in both of the references. Expressing the formula in words, the difference between forecast and corresponding observed values are each squared and then averaged over the sample. Finally, the square root of the average is taken. Since the errors are squared before they are averaged, the RMSE gives a relatively high weight to large errors. This means the RMSE is most useful when large errors are particularly undesirable. The MAE and the RMSE can be used together to diagnose the variation in the errors in a set of forecasts. The RMSE will always be larger or equal to the MAE; the greater difference between them, the greater the variance in the individual errors in the sample. If the RMSE=MAE, then all the errors are of the same magnitude Both the MAE and RMSE can range from 0 to ∞. They are negatively-oriented scores: Lower values are better. Loading Questions ... You read that a set of temperature forecasts shows a MAE of 1.5 degrees and a RMSE of 2.5 degrees. What does this mean? Choose the best answer: Feedback This is true, but not the best answer. If RMSE>MAE, then there is variation in the errors. Feedback This is true too, the RMSE-MAE difference isn't large enough to indicate the presence of very large errors. Feedback This is true, by the definition of the MAE, but not the best answer. Feedback This is the best answer. See the other choices for more feedback.