Angle of rotation Angle of rotation In mathematics, the angle of rotation is a measurement of the amount, namely the angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since , a full rotation (turn)). A counterclockwise rotation of more than one complete turn is normally measured modulo 360°, meaning that 360° is subtracted off as many times as possible to leave a non-negative measurement less than 360°. For example, the
Degrees of freedom (statistics) the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error, also called residual degrees of freedom. Perhaps the simplest example is this. Suppose are random variables each with expected value μ, and let be the "sample mean." Then the quantities are residuals that may be considered estimates of the errors "X" − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any "n" −