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In finance, a trend line is a bounding line for the price movement of a security. It is formed when a diagonal line can be drawn between a minimum of three or more price pivot points. A line can be drawn between any two points, but it does not qualify as a trend line until tested. Hence the need for the third point, the test.
All have the same trend, but more filtering leads to higher r 2 of fitted trend line. The least-squares fitting process produces a value, r-squared (r 2), which is 1 minus the ratio of the variance of the residuals to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line.
A market trend is a perceived tendency of the financial markets to move in a particular direction over time. [1] Analysts classify these trends as secular for long time-frames, primary for medium time-frames, and secondary for short time-frames. [2]
Google provides tool Google Trends to explore how particular terms are trending in internet searches. On the other hand, there are tools which provide diachronic analysis for particular texts which compare word usage in each period of the particular text (based on timestamped marks), see e.g. Sketch Engine diachronic analysis (trends).
A trend line could simply be drawn by eye through a set of data points, but more properly their position and slope is calculated using statistical techniques like linear regression. Trend lines typically are straight lines, although some variations use higher degree polynomials depending on the degree of curvature desired in the line.
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
See Michaelis–Menten kinetics for details . In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables.
The above equations are efficient to use if the mean of the x and y variables (¯ ¯) are known. If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the α ^ and β ^ {\displaystyle {\widehat {\alpha }}{\text{ and }}{\widehat {\beta }}} equations.