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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 or is influenced by changes in an external factor.
If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis, as described in Trend estimation. If the trends have other shapes than linear, trend testing can be done by non-parametric methods, e.g. Mann-Kendall test, which is a version of Kendall rank correlation coefficient.
The trend-cycle component can just be referred to as the "trend" component, even though it may contain cyclical behavior. [3] For example, a seasonal decomposition of time series by Loess (STL) [ 4 ] plot decomposes a time series into seasonal, trend and irregular components using loess and plots the components separately, whereby the cyclical ...
If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the ^ ^ equations. These expanded equations may be derived from the more general polynomial regression equations [ 7 ] [ 8 ] by defining the regression polynomial to be of order 1, as follows.
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.
The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier . The filter was popularized in the field of economics in the 1990s by economists Robert J. Hodrick and Nobel Memorial Prize winner Edward C. Prescott , [ 1 ] though it was first proposed much earlier by E. T. Whittaker in 1923. [ 2 ]
Smoothed analysis — measuring the expected performance of algorithms under slight random perturbations of worst-case inputs; Symbolic-numeric computation — combination of symbolic and numeric methods; Cultural and historical aspects: History of numerical solution of differential equations using computers
Trend line can refer to: A linear regression in statistics; The result of trend estimation in statistics; Trend line (technical analysis), a tool in technical analysis