Average Absolute Error Definition
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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 − absolute error definition math y i | = 1 n ∑ i = 1 n | e i
Mean Absolute Percentage Error Definition
| . {\displaystyle \mathrm {MAE} ={\frac {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 absolute deviation average of the absolute errors | e i | = | 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 absolute error formula true value. Note that alternative formulations may include relative frequencies as weight factors. The mean absolute error used the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series using 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"
Absolute Error Calculator
is sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists 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 abs
The equation is given in the library references. Expressed in words, the MAE is the average over the verification sample of the absolute standard deviation absolute error values of the differences between forecast and the corresponding observation. The MAE define absolute error is a linear score which means that all the individual differences are weighted equally in the average. Root
Median Absolute Error
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 https://en.wikipedia.org/wiki/Mean_absolute_error 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 http://www.eumetcal.org/resources/ukmeteocal/verification/www/english/msg/ver_cont_var/uos3/uos3_ko1.htm 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.
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn http://stats.stackexchange.com/questions/131267/how-to-interpret-error-measures-in-weka-output more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How to interpret error absolute error measures in Weka output? up vote 7 down vote favorite 4 I am running the classify in Weka for a certain dataset and I've noticed that if I'm trying to predict a nominal value the output specifically shows the correctly and incorrectly predicted values. However, now I'm running it for a numerical attribute and the output is: Correlation coefficient 0.3305 Mean absolute error 11.6268 Root mean squared error 46.8547 Relative absolute error 89.2645 % Root relative squared absolute error definition error 94.3886 % Total Number of Instances 36441 How do I interpret this? I've tried googling each notion but I don't understand much since statistics is not at all in my field of expertise. I would greatly appreciate an ELI5 type of answer in terms of statistics. machine-learning error weka mse rms share|improve this question edited Jul 8 '15 at 9:25 Tim 22.2k45296 asked Jan 5 '15 at 13:54 FloIancu 138115 add a comment| 1 Answer 1 active oldest votes up vote 16 down vote accepted Let's denote the true value of interest as $\theta$ and the value estimated using some algorithm as $\hat{\theta}$. Correlation tells you how much $\theta$ and $\hat{\theta}$ are related. It gives values between $-1$ and $1$, where $0$ is no relation, $1$ is very strong, linear relation and $-1$ is an inverse linear relation (i.e. bigger values of $\theta$ indicate smaller values of $\hat{\theta}$, or vice versa). Below you'll find an illustrated example of correlation. (source: http://www.mathsisfun.com/data/correlation.html) Mean absolute error is: $$MSE = \frac{1}{N} \sum^N_{i=1} | \hat{\theta}_i - \theta_i | $$ Root mean square error is: $$RMSE = \sqrt{ \frac{1}{N} \sum^N_{i=1} \left( \hat{\theta}_i - \theta_i \right)^2 } $$ Relative absolute error: $$RAE = \frac{ \sum^N_{i=1} | \hat{\theta}_i - \theta_i | } { \sum^N_{i=1} | \overline{\theta} - \theta_i | } $$ where $\overline{\theta}$ is a mean value of $\theta$. Root relative squared error: $$RRSE = \s