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Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered "tends" to increase or decrease over time. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. [1] There are two principal types of decomposition, which are outlined below.
Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. [4] This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.
For linear-algebraic analysis of data, "fitting" usually means trying to find the curve that minimizes the vertical ( y -axis) displacement of a point from the curve (e.g., ordinary least squares ). However, for graphical and image applications, geometric fitting seeks to provide the best visual fit; which usually means trying to minimize the ...
Regression-kriging is an implementation of the best linear unbiased predictor (BLUP) for spatial data, i.e. the best linear interpolator assuming the universal model of spatial variation. Matheron (1969) proposed that a value of a target variable at some location can be modeled as a sum of the deterministic and stochastic components: [2] which ...
Cochran–Armitage test for trend. The Cochran–Armitage test for trend, [1] [2] named for William Cochran and Peter Armitage, is used in categorical data analysis when the aim is to assess for the presence of an association between a variable with two categories and an ordinal variable with k categories. It modifies the Pearson chi-squared ...
A time series is very frequently plotted via a run chart (which is a temporal line chart ). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering ...
In non-parametric statistics, the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane ( simple linear regression) by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator, [1] [2] slope selection, [3] [4] the single median method, [5] the Kendall robust line-fit method, [6] and the Kendall ...