Normal Distribution Of Error Term
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 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 does the distribution of the error term affect the distribution of the response? up vote 11 down vote favorite 6 So when I assume that the error terms are normally distributed in a linear regression, what does it mean for the response variable, $y$? regression distributions share|improve this question edited May 27 '11 at 18:37 chl♦ 37.6k6125243 asked May 27 '11 at 16:14 MarkDollar 1,59082747 add a comment| 4 Answers 4 active oldest votes up vote 7 down vote accepted Maybe I'm off but I think we ought to be wondering about $f(y|\beta, X)$, which is how I read the OP. In the very simplest case of linear regression if your model is $y=X\beta + \epsilon$ then the only stochastic component in your model is the error term. As such it determines the sampling distribution of $y$. If $\epsilon\sim N(0, \sigma^2I)$ then $y|X, \beta\sim N(X\beta, \sigma^2I)$. What @Aniko says is certainly true of $f(y)$ (marginally over $X, \beta$), however. So as it stands the question is slightly vague. share|improve this answer answered May 27 '11 at 23:07 JMS 3,4651224 I like all comments! And they all seem to be right. But I was just searching for the easiest answer :) What happens when you assume that the errer term is normal distributed. That this occurs now very often in reality gets clear from the other answers! Thanks a lot! –MarkDollar May 29 '11 at 7:57 add a comment| up vote 15 down vote The short answer is that you cannot conclude anything about the distribution of $y$, because it depends on the distribution of the $x$'s and the strength and shape of the relationship. More formally, $y$ will have a "mixture of normals" distribution, which in practice can be pretty
is Inference After fitting a model to the data and validating it, scientific or engineering questions about the process are usually answered by computing statistical intervals for relevant process quantities using the model. These intervals give the range of plausible values for the process parameters based on the data and the underlying assumptions about the process. Because of the statistical nature of the process, however, the intervals cannot always be guaranteed to include the true process parameters and still be narrow enough http://stats.stackexchange.com/questions/11315/how-does-the-distribution-of-the-error-term-affect-the-distribution-of-the-respo to be useful. Instead the intervals have a probabilistic interpretation that guarantees coverage of the true process parameters a specified proportion of the time. In order for these intervals to truly have their specified probabilistic interpretations, the form of the distribution of the random errors must be known. Although the form of the probability distribution must be known, http://www.itl.nist.gov/div898/handbook/pmd/section2/pmd214.htm the parameters of the distribution can be estimated from the data. Of course the random errors from different types of processes could be described by any one of a wide range of different probability distributions in general, including the uniform, triangular, double exponential, binomial and Poisson distributions. With most process modeling methods, however, inferences about the process are based on the idea that the random errors are drawn from a normal distribution. One reason this is done is because the normal distribution often describes the actual distribution of the random errors in real-world processes reasonably well. The normal distribution is also used because the mathematical theory behind it is well-developed and supports a broad array of inferences on functions of the data relevant to different types of questions about the process. Non-Normal Random Errors May Result in Incorrect Inferences Of course, if it turns out that the random errors in the process are not normally distributed, then any inferences made about the process may be incorrect. If the true distribut
Επιλέξτε τη γλώσσα σας. Κλείσιμο Μάθετε περισσότερα View this message in English Το YouTube εμφανίζεται https://www.youtube.com/watch?v=0L2MgeQyhnU στα Ελληνικά. Μπορείτε να αλλάξετε αυτή την προτίμηση παρακάτω. Learn more You're viewing YouTube in https://explorable.com/normal-distribution-assumptions Greek. You can change this preference below. Κλείσιμο Ναι, θέλω να τη κρατήσω Αναίρεση normal distribution Κλείσιμο Αυτό το βίντεο δεν είναι διαθέσιμο. Ουρά παρακολούθησηςΟυράΟυρά παρακολούθησηςΟυρά Κατάργηση όλωνΑποσύνδεση Φόρτωση... Ουρά παρακολούθησης Ουρά __count__/__total__ VII: The Error Term is Normally Distributed Henry Khoo ΕγγραφήΕγγραφήκατεΚατάργηση εγγραφής11 Φόρτωση... normal distribution of Φόρτωση... Σε λειτουργία... Προσθήκη σε... Θέλετε να το δείτε ξανά αργότερα; Συνδεθείτε για να προσθέσετε το βίντεο σε playlist. Σύνδεση Κοινή χρήση Περισσότερα Αναφορά Θέλετε να αναφέρετε το βίντεο; Συνδεθείτε για να αναφέρετε ακατάλληλο περιεχόμενο. Σύνδεση Μεταγραφή Στατιστικά στοιχεία 260 προβολές 0 Σας αρέσει αυτό το βίντεο; Συνδεθείτε για να μετρήσει η άποψή σας. Σύνδεση 1 2 Δεν σας αρέσει αυτό το βίντεο; Συνδεθείτε για να μετρήσει η άποψή σας. Σύνδεση 3 Φόρτωση... Φόρτωση... Μεταγραφή Δεν ήταν δυνατή η φόρτωση της διαδραστικής μεταγραφής. Φόρτωση... Φόρτωση...
blank: Or log in with... Search over 500 articles on psychology, science, and experiments. Search this site: Leave this field blank: Home Overview ResearchMethods Experiments Design Statistics FoundationsReasoning Philosophy Ethics History AcademicPsychology Biology Physics Medicine Anthropology Self-HelpSelf-Esteem Worry Social Anxiety Sleep Anxiety Write Paper Assisted Self-Help For Kids Your Code Home > Research > Statistics > Normal Distribution Assumptions Normal Distribution Assumptions Siddharth Kalla 59.4K reads Comments Share this page on your website: Normal Distribution Assumptions Normal distribution assumptions are important to note because so many experiments rely on assuming a distribution to be normal. In most cases, the assumption of normality is a reasonable one to make. This article is a part of the guide: Select from one of the other courses available: Scientific MethodResearch DesignResearch BasicsExperimental ResearchSamplingValidity and ReliabilityWrite a PaperBiological PsychologyChild DevelopmentStress & CopingMotivation and EmotionMemory & LearningPersonalitySocial Psychology ExperimentsScience Projects for KidsSurvey GuidePhilosophy of ScienceReasoningEthics in ResearchAncient HistoryRenaissance & EnlightenmentMedical HistoryPhysics ExperimentsBiology ExperimentsZoologyStatistics Beginners GuideStatistical ConclusionStatistical TestsDistribution in Statistics Discover 17 more articles on this topic Don't miss these related articles: 1Calculate Standard Deviation2Standard Error of the Mean3Variance4Standard Deviation5Normal Distribution Browse Full Outline 1Frequency Distribution 2Normal Distribution2.1Assumptions 3F-Distribution 4Central Tendency4.1Mean4.1.1Arithmetic Mean 4.1.2Geometric Mean 4.1.3Calculate Median 4.2Statistical Mode 4.3Range (Statistics) 5Variance5.1Standard Deviation5.1.1Calculate Standard Deviation 5.2Standard Error of the Mean 6Quartile 7Trimean 1 Frequency Distribution2 Normal Distribution2.1 Assumptions3 F-Distribution4 Central Tendency4.1 Mean4.1.1 Arithmetic Mean4.1.2 Geometric Mean4.1.3 Calculate Median4.2 Statistical Mode4.3 Range (Statistics)5 Variance5.1 Standard Deviation5.1.1 Calculate Standard Deviation5.2 Standard Error of the Mean6 Quartile7 Trimean However, there are important special scenarios when this is not the case. An understanding of the normal distribution assumptions will help researchers know the limitations of their experiment and also help them understand their own study and where it breaks down. Norm