Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
Root-mean-square deviation target variable. with formula_14 and formula_15 where CDF is the quantile function. When normalizing by the mean value of the measurements, the term coefficient of variation of the RMSD, CV(RMSD) may be used to avoid ambiguity. This is analogous to the coefficient of variation with the RMSD taking the place of the standard deviation. Some researchers have recommended the use of the Mean Absolute Error (MAE) instead of the Root Mean Square Deviation. MAE possesses advantages in interpretability over RMSD. MAE is the average of the absolute values of the errors. MAE is fundamentally easier to understand than the square