# Coefficient of Multiple Correlation

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Coefficient of Multiple Correlation - short version

A number between 0 and 1 that indicates the degree of the combined linear relationship predictor variables X1, X2,...,Xp to the response variable Y. It is a simple correlation coefficient between predicted and observed values of the response variable.

Coefficient of Multiple Correlation - long version

Multiple correlation is a linear relationship among more than two variables. It is measured by the coefficient of multiple determination, denoted as R^2, which is a measure of the fit of a linear regression. A regression's R^2 falls somewhere between zero and one (assuming a constant term has been included in the regression); a higher value indicates a stronger relationship among the variables, with a value of one indicating that all data points fall exactly on a line in multidimensional space and a value of zero indicating no relationship at all between the independent variables collectively and the dependent variable.