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Purpose. Coefficient of determination (R-squared) indicates the proportionate amount of variation in the response variable y explained by the independent variables X in the linear regression model. The larger the R-squared is, the more variability is explained by the linear regression model.
The great value of the coefficient of determination is that through use of the Pearson R statistic and the standard error of the estimate, the researcher can construct a precise estimate of the interval in which the true population correlation will fall.