Difference Between Standard Error And Residuals
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Standard Error Of Residuals In R
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Standard Error Of The Residuals In Regression
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How To Find Standard Error Of Residuals
t e For a broader coverage related to this topic, see Deviation. 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. Contents 1 Introduction 2 In univariate distributions 2.1 Remark 3 Regressions 4 Other uses of the word "error" in statistics 5 See al
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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 http://stats.stackexchange.com/questions/133389/what-is-the-difference-between-errors-and-residuals site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated http://en.citizendium.org/wiki/Errors_and_residuals_in_statistics 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 standard error works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is the difference between errors and residuals? up vote 8 down vote favorite 2 While these two ubiquitous terms are often used synonymously, there sometimes seems to be a distinction. Is there indeed a difference, or are they exactly synonymous? residuals error terminology share|improve standard error of this question edited Jan 14 '15 at 15:40 gung 73.8k19160309 asked Jan 14 '15 at 15:27 Constantin 254115 Check out Qin & Gilbert "The Error Term in the History of Time Series Econometrics" for a comprehensive treatment if you have time. Oh, but this is only for time series data. –Richard Hardy Jan 14 '15 at 15:56 add a comment| 2 Answers 2 active oldest votes up vote 6 down vote Errors pertain to the true data generating process (DGP), whereas residuals are what is left over after having estimated your model. In truth, assumptions like normality, homoscedasticity, and independence apply to the errors of the DGP, not your model's residuals. (For example, having fit $p+1$ parameters in your model, only $N-(p+1)$ residuals can be independent.) However, we only have access to the residuals, so that's what we work with. share|improve this answer edited Apr 28 '15 at 13:59 answered Jan 14 '15 at 15:40 gung 73.8k19160309 3 (+1) Residuals can be considered estimates of the errors. –Scortchi♦ Jan 14 '15 at 17:09 What is DGP ? If my model is good , shouldn't residuals follow the assumptions
under development and not meant to be cited; by editing it you can help to improve it towards a future approved, citable version. These unapproved articles are subject to a disclaimer. [edit intro] The content on this page originated on Wikipedia and is yet to be significantly improved. Contributors are invited to replace and add material to make this an original article. In statistics and optimization, the concepts of error and residual are easily confused with each other. Error is a misnomer; an error is the amount by which an observation differs from its expected value; the latter being based on the whole population from which the statistical unit was chosen randomly. The expected value, being the average of the entire population, is typically unobservable. If the average height in a population of 21-year-old men is 5 feet 9 inches, and one randomly chosen man is 5 feet 11 inches tall, then the "error" is 2 inches; if the randomly chosen man is 5 feet 7 inches tall, then the "error" is −2 inches. The nomenclature arose from random measurement errors in astronomy. It is as if the measurement of the man's height were an attempt to measure the population average, so that any difference between the man's height and the average would be a measurement error. A residual, on the other hand, is an observable estimate of the unobservable error. The simplest case involves a random sample of n men whose heights are measured. The sample average is used as an estimate of the population average. Then we have: The difference between the height of each man in the sample and the unobservable population average is an error, and The difference between the height of each man in the sample and the observable sample average is a residual. Residuals are observable; errors are not. Note that the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. The sum of the errors need not be zero; the errors are independent random variables if the individuals are chosen from the population independently. Errors are often independent of each other; residuals are not independ