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Determining whether a given graph = (,) is an interval graph can be done in (| | + | |) time by seeking an ordering of the maximal cliques of that is consecutive with respect to vertex inclusion. Many of the known algorithms for this problem work in this way, although it is also possible to recognize interval graphs in linear time without using ...
A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope. [3] [4] Points where concavity changes (between concave and convex) are inflection points. [5]
Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimally small, such that becomes and becomes , the result is the instantaneous velocity at time , or the derivative of the ...
A confidence interval for the slope estimate may be determined as the interval containing the middle 95% of the slopes of lines determined by pairs of points [13] and may be estimated quickly by sampling pairs of points and determining the 95% interval of the sampled slopes. According to simulations, approximately 600 sample pairs are ...
Graph of points and linear least squares lines in the simple linear regression numerical example. The 0.975 quantile of Student's t-distribution with 13 degrees of freedom is t * 13 = 2.1604, and thus the 95% confidence intervals for α and β are
For example, f(x) might be the proportion of people of a particular age x who support a given candidate in an election. If x is measured at the precision of a single year, we can construct a separate 95% confidence interval for each age. Each of these confidence intervals covers the corresponding true value f(x) with confidence 0.
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]
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 ...