If the coefficient of determination (R²) between two financial series is calculated as 0.64, which of the following statements is mathematically true?

The coefficient of determination is defined as R² = Explained variation/Total variation. R² = 0.64 therefore means that 64% of the variation in the dependent variable is explained by its regression on the independent variable. Option (B): in simple regression R² = r², so r = ±√0.64 = ±0.80, with the sign being that of the slope. It is not 0.64. Option (C): the unexplained proportion is 1 - R² = 0.36, i.e. 36%. Option (D): the Spearman coefficient is based on ranks and need not be equal to Pearson’s r, so it cannot be obtained from R². Option (E): the standard error of estimate is measured in the units of Y and depends on the residual variance. It is not equal to 1 - R². Hence the correct option is (A).