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# Coefficient of determination

In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s). 

## Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

## Biometrika

Biometrika is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust.

## Confounding

In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association.

## Correlation and dependence

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.

## Correlation does not imply causation

In statistics, many statistical tests calculate correlations between variables and when two variables are found to be correlated, it is tempting to assume that this shows that one variable causes the other.

## Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

## Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

## Errors and residuals

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".

## Explained sum of squares

In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression ("SSR" – not to be confused with the residual sum of squares RSS), is a quantity used in describing how well a model, often a regression model, represents the data being modelled.

## Explained variation

In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set.

## F-test

An F-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis.

## Feature selection

In machine learning and statistics, feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction.

## Fraction of variance unexplained

In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable) Y which cannot be explained, i.e., which is not correctly predicted, by the explanatory variables X.

## Generalized least squares

In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model.

## Goodness of fit

The goodness of fit of a statistical model describes how well it fits a set of observations.

## Granger causality

The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969.

## Henri Theil

Henri (Hans) Theil (October 13, 1924 – August 20, 2000) was a Dutch econometrician, Professor at the Netherlands School of Economics in Rotterdam, known for his contributions to the field of econometrics.

## Hydrology

Hydrology is the scientific study of the movement, distribution, and quality of water on Earth and other planets, including the water cycle, water resources and environmental watershed sustainability.

## Hypothesis

A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon.

## Kitchen sink regression

Pejoratively, a kitchen sink regression is a statistical regression which uses a long list of possible independent variables to attempt to explain variance in a dependent variable.

## Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

## Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

## Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

## Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that is usually taken to apply to a binary dependent variable.

## Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

## McGraw-Hill Education

McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.

## Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and what is estimated.

## Metric prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## Multicollinearity

In statistics, multicollinearity (also collinearity) is a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy.

## Multiple correlation

In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables.

## Nash–Sutcliffe model efficiency coefficient

The Nash–Sutcliffe model efficiency coefficient (NSE) is used to assess the predictive power of hydrological models.

## Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

## Normalization (statistics)

In statistics and applications of statistics, normalization can have a range of meanings.

## Omitted-variable bias

In statistics, omitted-variable bias (OVB) occurs when a statistical model incorrectly leaves out one or more relevant variables.

## Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC, pronounced), also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC) or the bivariate correlation, is a measure of the linear correlation between two variables X and Y. It has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation.

## Proportional reduction in loss

Proportional reduction in loss (PRL) refers to a general framework for developing and evaluating measures of the reliability of particular ways of making observations which are possibly subject to errors of all types.

## Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.

## Regression validation

In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data.

## Residual sum of squares

In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data).

## Root-mean-square deviation

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) (or sometimes root-mean-squared error) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed.

## Sewall Wright

Sewall Green Wright (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis.

## Simple linear regression

In statistics, simple linear regression is a linear regression model with a single explanatory variable.

## Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

## Statistic

A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value).

## Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population.

## Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

## The American Statistician

The American Statistician is a quarterly peer-reviewed scientific journal covering statistics published by Taylor & Francis on behalf of the American Statistical Association.

## Total sum of squares

In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

## References

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