Description

Calculates the slope, offset, and detrended standard deviation for a given data series.

Formula

First calculates the mean x (time) and y (data) values of the entire series.

Calculates sums of data and time multiplied by time re-centered around the mean time:

$$ s_{data} = \Sigma_{i=0}^n data_{i} * (time_{i} - time_{mean}) \\ s_{time} = \Sigma_{i=0}^n (time_{i} - time_{mean})^2 \\ $$

Then calculates series slope and offset:

$$ slope = \frac {s_{data}} {s_{time}} \\ offset = data_{mean} - slope * time_{mean}\\ $$

And calculates the standard deviation from the detrended data:

$$ s = \Sigma_{i=0}^n (data_{i} - offset - slope*time{i})^2 \\ \sigma = \sqrt{\frac{s}{n}} $$

Source


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Tags: algorithm qc