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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 previous two examples have suggested how we should define the measure formally. In short, the coefficient of determination or r-squared value, denoted r2, is the regression sum of squares divided by the total sum of squares. 1  Since r2 is a proportion, it is always a number between 0 and 1.  If r2 = 1, all of the data points fall perfectly on the regression line.