# 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

```
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
```