Errors and residualsIn statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean).
Trend-stationary processIn the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. The trend does not have to be linear. Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots.
Line (geometry)Straight figure with zero width and depth A red line near the origin on the two-dimensional Cartesian coordinate system In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve and an idealisation of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.Unit rootIn probability theory and statistics, a unit root is a property of certain stochastic processes (such as a random walk) that can create challenges for statistical inference in time series models. A linear stochastic process contains a unit root if 1 is a solution to its characteristic equation. Processes with a unit root are non-stationary, because they do not necessarily exhibit a deterministic trend.Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.Optimization problemIn mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
DataData ( , US also ) is a collection of discrete or continuous values that conveys information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum, data value or data point is an individual value in a collection of data.
StatisticsStatistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.
Least squaresIn regression analysis, least squares is a method to determine the best-fit model by minimizing the sum of the squared residuals—the differences between observed values and the values predicted by the model. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the model functions are linear in all unknowns.
Graph theoryArea of discrete mathematicsA graph with 6 vertices and 7 edgesIn mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines).
InformationInformation is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information.
Homoscedasticity and heteroscedasticityIn statistics, a sequence of random variables is homoscedastic () if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The term originates from the Ancient Greekskedánnymi, 'to scatter'.*As an Amazon Associate I earn from qualifying purchases.