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The coefficient of determination is the ratio of the explained variation to the total variation. The coefficient of determination is such that 0 < r 2 < 1, and. Coefficient of Determination. The coefficient of determination is the percent of the variation that can be explained by the regression equation. The coefficient of determination can never be negative. it is bounded by 0 ≤ r² ≤ 1 and this is because the coefficient of determination is the square of the correlation. CiteSeerX - Document Details (Isaac Councill, Lee Giles): For statistical design of an optimal filter, it is probabilistically advantageous to employ a large number of observation. A measure of the correlation between the dependent and independent variables in a regression analysis.