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World War II deaths by country World War II deaths by theater Soviet soldiers killed during the Toropets–Kholm Offensive, January 1942. Officially, roughly 8.6 million Soviet soldiers died in the course of the war, including millions of POWs. Einsatzgruppen murder Jewish civilians outside Ivanhorod, Ukraine, 1942. Over 6 million Jews were ...
Largest economies in the world by GDP (nominal) in 2024 according to International Monetary Fund estimates[n 1][1] Countries by estimated nominal GDP in 2024.[n 2] > $20 trillion $10–20 trillion $5–10 trillion $1–5 trillion $750 billion – $1 trillion $500–750 billion $250–500 billion $100–250 billion $50–100 billion $25–50 ...
Game of Thrones is an American fantasy drama television series created by David Benioff and D. B. Weiss for HBO. It is an adaptation of A Song of Ice and Fire, a series of fantasy novels by George R. R. Martin, the first of which is A Game of Thrones.
- 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 da...
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 R2 criterion and the F-test examine whether the total R2 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 R2will hardly increase, even if the new regressor is of relevance. As a result, the above-mentioned heuristics will ignore relevant regressors when cross...
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.Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by ...
List of countries by population (United Nations) This is a list of countries and other inhabited territories of the world by total population, based on estimates published by the United Nations in the 2022 revision of World Population Prospects. It presents population estimates from 1950 to the present. [2]
When civil war broke out in Spain, Hitler and Mussolini lent military support to the Nationalist rebels, led by General Francisco Franco. Italy supported the Nationalists to a greater extent than the Nazis: Mussolini sent more than 70,000 ground troops, 6,000 aviation personnel, and 720 aircraft to Spain. [36]
