PRESS statistic

In statistics, the predicted residual sums of squares (PRESS) statistic is used in regression analysis to provide a summary measure of the fit of a model to a sample of observations. These observation were not themselves used to estimate the model. It is calculated as the sums of squares of the prediction residuals for those observations.^[1][2][3]

Having produced a fitted model, each of predictors is removed and the model is refitted to the remaining points. The predicted value is calculated at the excluded point and the PRESS statistic is calculated as the sum of all the resulting errrors.

$\sum_{i=1}^n (y_i - \hat{y}_{i, -i})^2$^[4]

References

1. ^ http://www.statsoft.com/textbook/statistics-glossary/p/button/p/ Statsoft:StatSoft.com Electronic Statistics Textbook - Statistics Glossary (Accessed September 2011)
2. ^ Allen, D. M. (1974), "The Relationship Between Variable Selection and Data Augmentation and a Method for Prediction," Technometrics, 16, 125–127
3. ^ Tarpey, Thaddeus (2000) A Note on the Prediction Sum of Squares Statistic for Restricted Least Squares, The American Statistician, Vol. 54, No. 2, May, pp. 116–118
4. ^ http://www.oga-lab.net/RGM2/func.php?rd_id=qpcR:PRESS R Graphical Manual:Allen's PRESS (Prediction Sum-Of-Squares) statistic, aka P-square (Accessed Sep 2011)

This statistics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Regression analysis Least squares Statistics stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Hawaii regional cuisine Aasaan Look at other dictionaries: Sufficient statistic — In statistics, a sufficient statistic is a statistic which has the property of sufficiency with respect to a statistical model and its associated unknown parameter, meaning that no other statistic which can be calculated from the same sample… …   Wikipedia Student's t-test — A t test is any statistical hypothesis test in which the test statistic follows a Student s t distribution if the null hypothesis is supported. It is most commonly applied when the test statistic would follow a normal distribution if the value of …   Wikipedia Statistical inference — In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation.[1] More substantially, the terms statistical inference,… …   Wikipedia Completeness (statistics) — In statistics, completeness is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of the probability distribution representing the model can all be… …   Wikipedia Effect size — In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample based estimate of that quantity. An effect size calculated from data is a descriptive statistic that… …   Wikipedia Ordinary least squares — This article is about the statistical properties of unweighted linear regression analysis. For more general regression analysis, see regression analysis. For linear regression on a single variable, see simple linear regression. For the… …   Wikipedia Control chart — One of the Seven Basic Tools of Quality First described by Walter A. Shewhart …   Wikipedia Margin of error — This article is about the statistical precision of estimates from sample surveys. For safety margins in engineering, see Factor of safety. For tolerance in engineering, see Tolerance (engineering). Not to be confused with Margin for Error. The… …   Wikipedia Sexual dimorphism measures — Although the subject of sexual dimorphism is not in itself controversial, the measures by which it is assessed differ widely. Most of the measures are used on the assumption that a random variable is considered so that probability distributions… …   Wikipedia Online gaming in the People's Republic of China — represents one of the largest and fastest growing Internet business sectors in the country. With 457 million Internet users currently active in the PRC, the country now has the largest online user base in world, of which two thirds engage in… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”