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series_fit_2lines()

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

Applies a two segmented linear regression on a series, returning multiple columns.

Takes an expression containing dynamic numerical array as input and applies a two segmented linear regression in order to identify and quantify a trend change in a series. The function iterates on the series indexes. In each iteration, the function splits the series to two parts, fits a separate line (using series_fit_line()) to each part, and calculates the total r-square. The best split is the one that maximized r-square; the function returns its parameters:

Parameter	Description
rsquare	R-square is standard measure of the fit quality. It's a number in the range [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, which 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 mainly used for charting.
right_rsquare	R-square of the line on the right side of the split, see series_fit_line().
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().
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.

Note

This function returns multiple columns an so cannot be used as an argument for another function.

Syntax

project series_fit_2lines(series)

Learn more about syntax conventions.

• Will return all mentioned above columns with the following names: series_fit_2lines_x_rsquare, series_fit_2lines_x_split_idx etc.

project (rs, si, v)=series_fit_2lines(series)

• Will return the following columns: rs (r-square), si (split index), v (variance) and the rest will look like series_fit_2lines_x_rvariance, series_fit_2lines_x_line_fit and etc.

extend (rs, si, v)=series_fit_2lines(series)

• Will return only: rs (r-square), si (split index) and v (variance).

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 make-series operator.

Examples

Run the query

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
    (Slope, Interception, RSquare, Variance, RVariance, LineFit)=series_fit_line(y),
    (RSquare2, SplitIdx, Variance2, RVariance2, LineFit2)=series_fit_2lines(y)
| project id, x, y, LineFit, LineFit2
| render timechart