搜尋結果
TSMC. Taiwan Semiconductor Manufacturing Company Limited ( TSMC; also called Taiwan Semiconductor) [4] [5] is a Taiwanese multinational semiconductor contract manufacturing and design company. It is the world's second most valuable semiconductor company, [6] the world's largest dedicated independent ("pure-play") semiconductor foundry, [7] and ...
- 73,090 (2022)
- US$73.67 billion (2022)
Quantum System One, a quantum computer by IBM from 2019 with 20 superconducting qubits A quantum computer is a computer that takes advantage of quantum mechanical phenomena.On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports ...
Fibonacci sequence. A tiling with squares whose side lengths are successive Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13 and 21. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn .
- 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.In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in ...
Monte Carlo method. The approximation of a normal distribution with a Monte Carlo method. Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in ...
History The distribution was first introduced by Siméon Denis Poisson (1781–1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile (1837).: 205-207 The work theorized about the number of wrongful convictions in a given country by focusing on certain random variables N that count, among ...
