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This is a list of countries by external debt: it is the total public and private debt owed to nonresidents repayable in internationally accepted currencies, goods or services, where the public debt is the money or credit owed by any level of government, from central to local, and the private debt the money or credit owed by private households or private corporations based on the country under ...
2024 list by the United Nations Population Fund Rank Country Total Fertility rate in 2024 (births/woman) 1 Niger 6.6 2 Chad 6.0 3 DR Congo 6.0 4 Somalia 6.0 5 Central African Republic 5.7 6 Mali 5.7 7 Angola 5.0 8 Nigeria 5.0 9 Burundi 4.8 10 Benin 4.7 11 Burkina Faso
- Definitions
- Interpretation
- Extensions
- Comparison with Norm of Residuals
- History
- See Also
- Further Reading
A data set has n values marked y1,...,yn (collectively known as yi or as a vector y = [y1,...,yn]T), each associated with a fitted (or modeled, or predicted) value f1,...,fn (known as fi, or sometimes ŷi, as a vector f). Define the residuals as ei = yi − fi (forming a vector e). If y ¯ {\displaystyle {\bar {y}}} is the mean of the observed data: 1....
R2 is a measure of the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression predictions approximate the real data points. An R2of 1 indicates that the regression predictions perfectly fit the data. Values of R2 outside the range 0 to 1 occur when the model fits the data w...
Adjusted R2
The use of an adjusted R2 (one common notation is R ¯ 2 {\displaystyle {\bar {R}}^{2}} , pronounced "R bar squared"; another is R a 2 {\displaystyle R_{\text{a}}^{2}} or R adj 2 {\displaystyle R_{\text{adj}}^{2}} ) is an attempt to account for the phenomenon of the R2 automatically increasing when extra explanatory variables are added to the model. There are many different ways of adjusting. By far the most used one, to the point that it is typically just referred to as adjusted R, is the cor...
Coefficient of partial determination
The coefficient of partial determination can be defined as the proportion of variation that cannot be explained in a reduced model, but can be explained by the predictors specified in a full(er) model.This coefficient is used to provide insight into whether or not one or more additional predictors may be useful in a more fully specified regression model. The calculation for the partial R2 is relatively straightforward after estimating two models and generating the ANOVA tables for them. The c...
Generalizing and decomposing R2
As explained above, model selection heuristics such as the Adjusted R 2 {\displaystyle R^{2}} criterion and the F-test examine whether the total R 2 {\displaystyle R^{2}} sufficiently increases to determine if a new regressor should be added to the model. If a regressor is added to the model that is highly correlated with other regressors which have already been included, then the total R 2 {\displaystyle R^{2}} will hardly increase, even if the new regressor is of relevance. As a result, the...
Occasionally, the norm of residuals is used for indicating goodness of fit. This term is calculated as the square-root of the sum of squares of residuals: 1. norm of residuals = S S res = ‖ e ‖ . {\displaystyle {\text{norm of residuals}}={\sqrt {SS_{\text{res}}}}=\|e\|.} Both R2 and the norm of residuals have their relative merits. For least square...
The creation of the coefficient of determination has been attributed to the geneticist Sewall Wrightand was first published in 1921.
Nash–Sutcliffe model efficiency coefficient (hydrological applications)Gujarati, Damodar N.; Porter, Dawn C. (2009). Basic Econometrics (Fifth ed.). New York: McGraw-Hill/Irwin. pp. 73–78. ISBN 978-0-07-337577-9.Hughes, Ann; Grawoig, Dennis (1971). Statistics: A Foundation for Analysis. Reading: Addison-Wesley. pp. 344–348. ISBN 0-201-03021-7.Kmenta, Jan (1986). Elements of Econometrics (Second ed.). New York: Macmillan. pp. 240–243. ISBN 978-0-02-365070-3.Lewis-Beck, Michael S.; Skalaban, Andrew (1990). "The R-Squared: Some Straight Talk". Political Analysis. 2: 153–171. doi:10.1093/pan/2.1.153. JSTOR 23317769.Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler.
A plot of normal distribution (or bell-shaped curve) where each band has a width of 1 standard deviation – See also: 68–95–99.7 rule. Cumulative probability of a normal distribution with expected value 0 and standard deviation 1 In statistics, the standard deviation is a measure of the amount of variation of a random variable expected about its mean.
Four UN members (Cuba, Liechtenstein, Monaco and North Korea) do not belong to the IMF hence their economies are not ranked below. Kosovo, despite not being a member of the United Nations, is a member of IMF. Taiwan is not a IMF member but it is still listed in the official IMF indices. Several leading GDP-per-capita (nominal) jurisdictions may ...
The demographics of Israel, monitored by the Israel Central Bureau of Statistics, encompass various attributes that define the nation's populace. Since its establishment in 1948, Israel has witnessed significant changes in its demographics. Formed as a homeland for the Jewish people, Israel has attracted Jewish immigrants from Europe, Asia ...
