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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.
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log(x) (blue). In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale.
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.
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 sparkline is a very small line chart, typically drawn without axes or coordinates. It presents the general shape of a variation (typically over time) in some measurement, such as temperature or stock market price, in a simple and highly condensed way.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
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.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.