Does the coefficient of determination represents the percent of variation in y that is not explained by variation in x using the regression line?

No, the coefficient of determination, denoted as ( R^2 ), represents the percentage of variation in the dependent variable ( y ) that is explained by the independent variable ( x ) using the regression line. Conversely, the percent of variation in ( y ) that is not explained by ( x ) can be found by subtracting ( R^2 ) from 1 (or 100% if expressed as a percentage). Thus, ( 1 - R^2 ) indicates the portion of variation in ( y ) that remains unexplained by the model.