## Description

Computes a linear regression by fitting a straight line to the data and taking seasonality into account.

## Syntax

`SEASONAL_LINEAR_REGRESSION(Input Block, Seasonality [, Ranking Dimension])`

## Arguments

Argument | Type | Dimensions | Description |
---|---|---|---|

(required) | Number | Any Dimensions | This is the data source on which the seasonal linear regression is computed, and must be a Metric with data points as an expression of Integer or Number type. This Metric must include the same Dimension that is used in the `Ranking Dimension` argument. |

(required) | Integer | No Dimension or Dimensions of Text 1 | Length of the seasonality. It must be greater than 1, for example, if you observe a quarterly on a Metric defined by month, the Seasonality length is 3. If you observe a yearly seasonality on a Metric defined by month, the Seasonality length is 12. |

(optional) | Dimension | Not applicable | This is a Dimension applied to the time series taken in the `Input Block` . This is optional if it’s a datetime Dimension from the calendar. If this is not the case, then this is mandatory. It’s also mandatory if the Metric is defined on several time Dimensions. |

## Returns

Type | Dimensions |
---|---|

Number | Dimensions of Input Block |

With N being the Seasonality length of the serie, the function returns:

- Blank for value before the first non blank value.
- (
*A** x +*B*) **SeasonalityFactor*(x) after the first non blank value

To compute *SeasonalityFactor*, *A *and *B*, we use the classical decomposition method, called multiplicative decomposition, over historical data.

Notes:

- Blank observations (in the input Block) between the first non-blank value and the last non-blank values are considered as 0.
- The function requires 2 times the seasonality in terms of datapoint between the first non-blank value and the last non-blank values.

## Examples

Formula | Description |
---|---|

`SEASONAL_LINEAR_REGRESSION(Actuals, 4, Quarter)` | Computes a yearly seasonality over a metric defined by quarter. |

`SEASONAL_LINEAR_REGRESSION( Actuals, 12, Month)` | Computes a yearly seasonality over a metric defined by month. |

`SEASONAL_LINEAR_REGRESSION( Actuals, 3, Month)` | Computes a quarterly seasonality over a metric defined by month. |

Example using `SEASONAL_LINEAR_REGRESSION(Actuals, 4)`

:

## Using SEASONAL_LINEAR_REGRESSION as Forecasting Function

A common use case for using the SEASONAL_LINEAR_REGRESSION function is to prepare a forecast. It’s a good method when your observation series shows a linear trend** **and a seasonality.

## See also

Related articles: FORECAST ETS , FORECAST_LINEAR

[References: Multiplicative decomposition , wikipedia]