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Statistical model - Revision history
2026-04-04T17:16:01Z
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Prab at 13:19, 18 March 2025
2025-03-18T13:19:04Z
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2025-03-18T01:34:37Z
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Prab: CSV import
2025-02-10T21:44:20Z
<p>CSV import</p>
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2024-02-25T07:30:49Z
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<p><b>New page</b></p><div>'''Statistical model''' is a mathematical representation of a set of data. It is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but stochastically related.<br />
<br />
== Definition ==<br />
In [[statistics]], a '''statistical model''' is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.<br />
<br />
== Types of statistical models ==<br />
There are several different types of statistical models, including:<br />
* [[Parametric model|Parametric models]]<br />
* [[Non-parametric model|Non-parametric models]]<br />
* [[Semi-parametric model|Semi-parametric models]]<br />
* [[Non-parametric regression|Non-parametric regression models]]<br />
* [[Generalized linear model|Generalized linear models]]<br />
* [[Graphical model|Graphical models]]<br />
* [[Mixed model|Mixed models]]<br />
* [[Hierarchical model|Hierarchical models]]<br />
<br />
== Model specification ==<br />
Model specification involves selecting an appropriate functional form for the model and choosing which variables to include. The choice of model specification can significantly affect the conclusions drawn from the statistical analysis.<br />
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== Model estimation ==<br />
Model estimation involves estimating the parameters of the model. This is typically done using [[maximum likelihood estimation]], [[least squares estimation]], or [[Bayesian estimation]].<br />
<br />
== Model checking ==<br />
Model checking involves assessing the fit of the model to the data and checking the model's assumptions. This can be done using various [[diagnostic tests]] and [[residual analysis]].<br />
<br />
== Model selection ==<br />
Model selection involves choosing the best model from a set of candidate models. This is typically done using [[Akaike information criterion|Akaike's information criterion (AIC)]], [[Bayesian information criterion|Bayesian information criterion (BIC)]], or [[cross-validation]].<br />
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== See also ==<br />
* [[Statistical theory]]<br />
* [[Statistical inference]]<br />
* [[Statistical hypothesis testing]]<br />
* [[Regression analysis]]<br />
* [[Design of experiments]]<br />
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== References ==<br />
<references /><br />
<br />
[[Category:Statistical models]]<br />
[[Category:Mathematical modeling]]<br />
[[Category:Statistical theory]]<br />
[[Category:Statistical inference]]<br />
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Prab