multiple correlation coefficient

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Noun1.multiple correlation coefficient - an estimate of the combined influence of two or more variables on the observed (dependent) variable
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
coefficient of correlation, correlation coefficient, correlation - a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation); "what is the correlation between those two variables?"
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CCL2 levels at radiotherapy end could be modelled using linear regression including the following variables: baseline CCL2 (coefficient = 1.15, p = 0.0001), age (coefficient = -3.26, p = 0.004), abdominal surgery (coefficient = 23.3, p = 0.09), hypertension (coefficient = 29.6, p = 0.02), and use of anticoagulants (coefficient = 41.0, p = 0.05) and multiple correlation coefficient = 0.89 (see plot).
We sort the multiple correlation coefficient of individual by multiple regression in statistical methods [23, 24]; the greater the multiple correlation coefficient is, the more repeated the information should be, the smaller the information utilization should be, and the smaller the weight should be.
Shieh (2013) is highly critical of Equation 1, claiming that it is insufficiently accurate and that only computationally intensive simulation-based computer programs should be used to determine sample size requirements for the squared multiple correlation coefficient. Shieh also claimed that Bonett and Wright (2011) did not evaluate the accuracy of Equation 1 under a sufficiently wide range of conditions.
The multiple correlation coefficient (R) is 0.756 and the coefficient of determination (R2) equal to 0.572.
Multiple correlation coefficient is .308 and explained .095 of the technical skill, i.e., the four variables in the table combine to explain 9.5% of technical skill.
For the full PSAT/NMSQT scale, the addition of a quadratic term improved model fit; however, the effect size was small as indexed by the change in the squared multiple correlation coefficient (R2) of 0.001.
r = Multiple correlation coefficient; a = intercept; b1 +- S.E and b2 +- S.E = regression coefficient; r2 = proportion of variance due to regression; VIF = Variance inflation factor, *** P less than 0.001; N.S.
Multiple regression analysis was also performed with CF1, CF2, and GR as variables, and SI3 and RT3 as predictor variables, r, R, and r' denote simple correlation coefficient, standard multiple correlation coefficient, and standard partial regression coefficient, respectively.
As a result, the power of the test of significance for an independent variable [X.sub.1] is reduced by a factor of (1-[r.sup.2.sub.(1|2,3,....)]), where [r.sub.(1|2,3,....)] is defined as the multiple correlation coefficient for the model [X.sub.1] = f([X.sub.2],[X.sub.3],...), and all [X.sub.i] are independent variables in the larger model (3,4).
3.20 Distribution of the Sample Multiple Correlation Coefficient From Multivariate Normal Distribution
(a) R is the multiple correlation coefficient of overall tests for each motivational style.
(15) Correlations between on- and off-line measurements (as determined by linear regression analysis) and 95% confidence intervals were depicted in graph form; multiple correlation coefficient ([R.sup.2]) values ranged between 0.95 and 0.98 (figure 2).

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