# SEASONAL_LINEAR_REGRESSION function

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## 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

Input Block

(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.

Seasonality

(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.

Ranking Dimension

(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.