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  1. The double sovereign is a gold coin of the United Kingdom with a nominal value of two pounds sterling (£2). It features the reigning monarch on its obverse and, most often, Benedetto Pistrucci 's depiction of Saint George and the Dragon on the reverse (pictured). It was rarely issued in the first century and a half after its debut in 1820 ...

  2. 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...

  3. Linearity. The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination. of the two state vectors where a and b are any complex numbers. [13] : 25 Moreover, the sum can be extended for any number of state vectors.

  4. en.wikipedia.org › wiki › CarCar - Wikipedia

    Car. A car, or an automobile, is a motor vehicle with wheels. Most definitions of cars state that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people, not cargo. [1] [2]

    • 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.
  5. History of the automobile. The Ford Model T (foreground) and Volkswagen Beetle (background) are among the most mass-produced car models in history. Crude ideas and designs of automobiles can be traced back to ancient and medieval times. [1] [2] In 1649, Hans Hautsch of Nuremberg built a clockwork-driven carriage.

  6. 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.