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 square root of the average of squared errors. The effect of each error on RMSD is proportional to the size of the squared error; thus larger errors have a disproportionately large effect on RMSD. Consequently, RMSD is sensitive to outliers. The RMSD of an estimator formula_1 with respect to an estimated parameter formula_2 is defined as the square root of the mean square error: For an unbiased estimator, the RMSD is the square root of the variance, known as the standard deviation. The RMSD of predicted values formula_4 for times "t" of a regression's dependent variable formula_5 with variables observed