In a review of the literature on unit weights, Bobko, Roth, and Buster ( 2007 ) noted that " unit weights and regression weights perform similarly in terms of the magnitude of cross-validated multiple correlation, and empirical studies have confirmed this result across several decades " ( p . 693 ).
12.
The coefficient of multiple correlation takes values between 0 and 1; a higher value indicates a better predictability of the independent variables, with a value of 1 indicating that the predictions are exactly correct and a value of 0 indicating that no linear combination of the independent variables is a better predictor than is the fixed mean of the dependent variable.
13.
The coefficient of multiple correlation is computed as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been derived from a model-fitting procedure.
14.
The square of the coefficient of multiple correlation can be computed using the vector \ mathbf { c } = { ( r _ { x _ 1 y }, r _ { x _ 2 y }, \ dots, r _ { x _ N y } ) } ^ \ top of correlations r _ { x _ n y } between the predictor variables x _ n ( independent variables ) and the target variable y ( dependent variable ), and the correlation matrix R _ { xx } of correlations between predictor variables.
15.
Moreover, it could be established that the multiple correlation ( " R " ) between the two types of variables reaches its maximum ( " R " is about 0.80 ) if the neumatic elements are evaluated according to the following rules of duration : ( a ) neume elements that represent short notes in neumes consisting of at least two notes have duration values of 1 time; ( b ) neume elements that represent long notes in neumes consisting of at least two notes have duration values of 2 times; ( c ) neumes consisting of only one note are characterized by flexible duration values ( with an average value of 2 times ), which take over the duration values of the syllables to match.
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