There have been differences in the use of the correlation coefficient (r) or the coefficient of determination (r2) for indexing the effect size (see Rosenthal and DiMatteo, 2001; Borenstein, 2009; Elis, 2010, for reviews). I intend to investigate this issue by considering it from the point of view of matching the findings with the implied prediction. In essence my argument follows from a simpli...

High spatial resolution soil moisture (SM) data are crucial in agricultural applications, river-basin management, and understanding hydrological processes. Merging multi-resource observations is one of the ways to improve the accuracy of high spatial resolution SM data in the heterogeneous cropland. In this paper, the Bayesian Maximum Entropy (BME) methodology is implemented to merge the follow...

Estimated daily reference crop evapotranspiration (ETo) is normally used to determine the water requirement of crops using the crop factor method. Many ETo estimation methods have been developed for different types of climatic data, and the accuracy of these methods varies with climatic conditions. In this study, pair−wise comparisons were made between daily ETo estimated from eight different E...

A theorem is presented relating the squared multiple correlation of each measure in a battery with the other measures to the unique generalized inverse of the correlation matrix. This theorem is independent of the rank of the correlation matrix and may be utilized for singular correlation matrices. A coefficient is presented which indicates whether the squared multiple correlation is unity or n...

This paper investigates whether the degree of predictability can be explained by existing asset pricing models, and provides two theoretical upper bounds on the R-square of the regression of stock returns on predictors for given classes of models of interest. Empirically, we find that the predictive R-square is significantly larger than the upper bounds permitted by well known asset pricing mod...

2 1. If shared variance (r²) is reported, correlation (r) is obtained by calculating the square root of shared variance. 2. If covariance (cov(x, y)) is reported, the correlation (r) is obtained by applying the formula r x y x y = cov(,) σ σ where σ is the standard deviation. 2 Procedure 5 and the second part of procedure 6 are described in Wolf (1986).

Social judgment data was analyzed using fuzzy least squares regression analysis based on the extension principle. The proposed analysis is new fuzzy least squares regression analysis in which input data, output data, and coefficients are represented by L-R fuzzy numbers. To evaluate data fitness, we propose a fuzzy version of a squared multiple correlation (R) and conducted an experiment to det...

The traditional coefficient of determination or R is the proportion of variation explained by a regression model versus the variation explained by the mean. This measure does not discriminate well between alternative self-referencing models such as site index curves. The traditional R compares the variation explained by a model with the variation about the mean dependent variable, a very simple...

—The use of model-predicted, local-scale habitat data as inputs in analyses intended to evaluate multiscale fish assemblage–habitat relationships in streams has become increasingly common as the scale at which such studies are conducted has increased. We used fish assemblage and habitat data from 208 wadeable streams in Wisconsin and Michigan to determine whether model-predicted habitat data wo...