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series_fit_2lines_dynamic()

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Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Applies two segments linear regression on a series, returning a dynamic object.

Takes an expression containing dynamic numerical array as input and applies two segments linear regression in order to identify and quantify trend changes in a series. The function iterates on the series indexes. In each iteration, it splits the series to two parts, and fits a separate line using series_fit_line() or series_fit_line_dynamic(). The function fits the lines to each of the two parts, and calculates the total R-squared value. The best split is the one that maximizes R-squared. The function returns its parameters in dynamic value with the following content:

  • rsquare: R-squared is a standard measure of the fit quality. It's a number in the range of [0-1], where 1 is the best possible fit, and 0 means the data is unordered and don't fit any line.
  • split_idx: the index of breaking point to two segments (zero-based).
  • variance: variance of the input data.
  • rvariance: residual variance that is the variance between the input data values the approximated ones (by the two line segments).
  • line_fit: numerical array holding a series of values of the best fitted line. The series length is equal to the length of the input array. It's used for charting.
  • right.rsquare: r-square of the line on the right side of the split, see series_fit_line() or series_fit_line_dynamic().
  • right.slope: slope of the right approximated line (of the form y=ax+b).
  • right.interception: interception of the approximated left line (b from y=ax+b).
  • right.variance: variance of the input data on the right side of the split.
  • right.rvariance: residual variance of the input data on the right side of the split.
  • left.rsquare: r-square of the line on the left side of the split, see [series_fit_line()].(series-fit-line-function.md) or series_fit_line_dynamic().
  • left.slope: slope of the left approximated line (of the form y=ax+b).
  • left.interception: interception of the approximated left line (of the form y=ax+b).
  • left.variance: variance of the input data on the left side of the split.
  • left.rvariance: residual variance of the input data on the left side of the split.

This operator is similar to series_fit_2lines. Unlike series-fit-2lines, it returns a dynamic bag.

Syntax

series_fit_2lines_dynamic(series)

Learn more about syntax conventions.

Parameters

Name Type Required Description
series dynamic ✔️ An array of numeric values.

Tip

The most convenient way of using this function is applying it to the results of the make-series operator.

Example

print
    id=' ',
    x=range(bin(now(), 1h) - 11h, bin(now(), 1h), 1h),
    y=dynamic([1, 2.2, 2.5, 4.7, 5.0, 12, 10.3, 10.3, 9, 8.3, 6.2])
| extend
    LineFit=series_fit_line_dynamic(y).line_fit,
    LineFit2=series_fit_2lines_dynamic(y).line_fit
| project id, x, y, LineFit, LineFit2
| render timechart

Series fit 2 lines.