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If the data points are normally distributed with mean 0 and variance , then the residual sum of squares has a scaled chi-squared distribution (scaled by the factor ), with n − 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.
Beyond its application to distance comparison, squared Euclidean distance is of central importance in statistics, where it is used in the method of least squares, a standard method of fitting statistical estimates to data by minimizing the average of the squared distances between observed and estimated values, [18] and as the simplest form of ...
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. [33] Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional ...
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value.
Decimal degrees (DD) is a notation for expressing latitude and longitude geographic coordinates as decimal fractions of a degree.DD are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices.
The starting point is on the line (,) =only because the line is defined to start and end on integer coordinates (though it is entirely reasonable to want to draw a line with non-integer end points).
In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences.
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,