# Coefficient of determination

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## Coefficient of determination

A measure of the goodness of fit of the relationship between the dependent and independent variables in a regression analysis; for instance, the percentage of variation in the return of an asset explained by the market portfolio return. Also known as R-square.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.

## R Square

In statistics, the percentage of a portfolio's performance explainable by the performance of a benchmark index. The R square is measured on a scale of 0 to 100, with a measurement of 100 indicating that the portfolio's performance is entirely determined by the benchmark index, perhaps by containing securities only from that index. A low R square indicates that there is no significant relationship between the portfolio and the index. An R Square is also called the coefficient of determination. See also: Beta.
Farlex Financial Dictionary. © 2012 Farlex, Inc. All Rights Reserved
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An error analysis demonstrated the high accuracy of our pecScreen models, giving respectively a mean absolute error and a coefficient of determination [R.sup.2] of 0.115 bar and 0.9995 for square woven, and 0.294 bar and 0.9996 for Dutch weave screens.
Graphing the data added quantity versus quantity recovered gives a coefficient of determination of 0.999 and slope of 0.9931, and the ordinate to the origin passes through zero (Figure 9).
j) The general hypothesis was tested, based on the results obtained with the Coefficient of Determination ([R.sup.2.sub.Adj.]): X1.1 Quality standards 0.909, XI.2 Quality control systems 0.56, and X1.3 Quality inspection systems 0.511.
According to the results in Figure 1, it is possible that the separation of leaves into size class can contribute to maximize the coefficient of determination ([R.sup.2]) when leaves are grouped into a single size class.
The selection of the best model took place by using the coefficient of determination ([R.sup.2]), the mean squared error (MSE) and Akaike
Coefficient of determination ([r.sup.2]) was 0.684 which implies 68.4% change in BAZ can be attributed to BFP.
The proposed model was selected through the highest coefficient of determination ([R.sup.2]).Schumacher equation model, in this case, was selected as the proposed model for predicting height growth of dominant trees and site index..
The coefficient of determination [R.sup.2] = 0.194 [R.sup.2] = 0.194, and the Durbin-Watson statistics reach the value of 1.49.
CurveExpert calculated the coefficient of determination and standard error among 33 common trends/models available and found that The MMF regression models for all wetland components provided satisfactory accuracy with highest coefficients of determination (R2) and lowest standard error (S).
Several goodness-of-fit criteria (coefficient of determination (R2%), adjusted coefficient of determination (Adj.R2%), coefficient of variation (CV%), SD ratio, Root Mean Square Error (RMSE), Relative Approximation Error (RAE), Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE), and Pearson correlation between actual and predicted values were estimated for describing the most suitable algorithm in terms of the predictive performance.
The coefficient of determination of (3) is 0.993684, which indicates high degree of fitting, namely, high reliability of the trend.
Comparison of Linear Coefficient of Determination, [R.sup.2], for Different Adsorption Isotherm Model.

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