No Trend Math

Trend line in a scatter plot a line that closely fits the data points is called a trend line. If the data values of one set increases and the data values of other set decreases then the two sets of related data shows a negative trend. To formally test whether a linear trend occurs run a time series regression with a time trend as the independent variable which you can set up like so.

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Looking at the red trend lines in the examples illustrates various relationships with sets of data.

No trend math. Determining if a set of points exhibits a positive trend a negative trend or no trend at all. The returns rise and fall with no particular pattern. In mathematics if the data in a set shows no relation then that set shows no trend. The corresponding regression equation is when no trend occurs the values of the time series may rise or fall but on average they tend to return to the same level this figure shows a time series with no trend.

The trend equation is set equal to a constant which is the intercept of a regression equation. According to this figure no trend occurs in the data. If the data shows no relation then that set shows no trend.

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