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Net interest margin ( NIM) is a measure of the difference between the interest income generated by banks or other financial institutions and the amount of interest paid out to their lenders (for example, deposits), relative to the amount of their (interest-earning) assets.
Net interest income ( NII) [1] is the difference between revenues generated by interest-bearing assets and the cost of servicing (interest-burdened) liabilities. For banks, the assets typically include commercial and personal loans, mortgages, construction loans and investment securities.
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. [1] .
- 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.This illustrates the relationship a + b a = a b = φ. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if.
In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic .
Definition. The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
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