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Prolate spheroidal coordinates μ and ν for a = 1.The lines of equal values of μ and ν are shown on the xz-plane, i.e. for φ = 0.The surfaces of constant μ and ν are obtained by rotation about the z-axis, so that the diagram is valid for any plane containing the z-axis: i.e. for any φ.
A representation of a tree in terms of its orthogonal components. l represents an internal node, an element of the orthonormal basis. This is a precursor to using the tree as a scaffold for the ilr transform
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
An accelerometer measures proper acceleration, which is the acceleration it experiences relative to freefall and is the acceleration felt by people and objects. [2] Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame. [4]
In statistics, Deming regression, named after W. Edwards Deming, is an errors-in-variables model that tries to find the line of best fit for a two-dimensional data set. It differs from the simple linear regression in that it accounts for errors in observations on both the x - and the y - axis.
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes ( Greek : Προκρούστης ) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.
Directly below the accelerometer's geometry is a flex cavity that allows the mass in the cavity to flex or move in direction that is orthogonal to the surface of the accelerometer. Accelerometers based upon piezoelectricity are constructed with two piezoelectric transducers.
The theorem also implies that the secondary regression used for obtaining is unnecessary when the predictor variables are uncorrelated: using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.