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Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various ...
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).
A piecewise linear function of two arguments (top) and the convex polytopes on which it is linear (bottom) The notion of a piecewise linear function makes sense in several different contexts. Piecewise linear functions may be defined on n-dimensional Euclidean space, or more generally any vector space or affine space, as well as on piecewise ...
If the intersection of convex hulls of the two sets is the empty set, then it is possible to use a single linear program to obtain a linear discriminant of the form, () = +. Usually, in real applications, the sets' convex hulls do intersect, and a (often non-convex) piecewise-linear discriminant can be used, through the use of several linear ...
Due to different speaking rates, a non-linear fluctuation occurs in speech pattern versus time axis, which needs to be eliminated. [31] DP matching is a pattern-matching algorithm based on dynamic programming (DP) , which uses a time-normalization effect, where the fluctuations in the time axis are modeled using a non-linear time-warping function.
Local linear regression can be applied to any-dimensional space, though the question of what is a local neighborhood becomes more complicated. It is common to use k nearest training points to a test point to fit the local linear regression. This can lead to high variance of the fitted function.
The capital asset pricing model uses linear regression as well as the concept of beta for analyzing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets.
Piecewise linear curve, a connected sequence of line segments; Piecewise linear function, a function whose domain can be decomposed into pieces on which the function is linear; Piecewise linear manifold, a topological space formed by gluing together flat spaces; Piecewise linear homeomorphism, a topological equivalence between two piecewise ...