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Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
The lexical category determiner is the class of words described in this article. They head determiner phrases, which can realize the functions determinative, predeterminative, and modifier: determiner phrases as determinatives: the box, this hill; determiner phrases as predeterminatives: all the time, both those cars
In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or | A |. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
The Jacobian determinant is sometimes simply referred to as "the Jacobian". The Jacobian determinant at a given point gives important information about the behavior of f near that point. For instance, the continuously differentiable function f is invertible near a point p ∈ R n if the Jacobian determinant at p is non-zero.
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. [1]If A is a differentiable map from the real numbers to n × n matrices, then
However, in the case of a ring being commutative, the condition for a square matrix to be invertible is that its determinant is invertible in the ring, which in general is a stricter requirement than it being nonzero. For a noncommutative ring, the usual determinant is not defined. The conditions for existence of left-inverse or right-inverse ...
The section below provides an informal definition for the Fredholm determinant of when the trace-class operator is an integral operator given by a kernel (,). A proper definition requires a presentation showing that each of the manipulations are well-defined, convergent, and so on, for the given situation for which the Fredholm determinant is ...
For functions of three or more variables, the determinant of the Hessian does not provide enough information to classify the critical point, because the number of jointly sufficient second-order conditions is equal to the number of variables, and the sign condition on the determinant of the Hessian is only one of the conditions.