## Description

Forecasts a variable by fitting a straight line to the data. It is a model that relates a response variable *Y* to an input variable *x* by the equation

`Y=a+bx`

The quantities *a* (slope) and *b* (intercept) are arguments of the regression model. The fitting is done using the *ordinary least squares method*.

## Syntax

`FORECAST_LINEAR(Source Metric [, Ranking Dimension] [, Alternate Metric])`

`Source Metric`

is the data source on which the 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.`Ranking Dimension`

is the dimension by which the regression is computed. If left undefined, the ranking dimension defaults to a Calendar Dimension from`Source Metric`

. If`Source Metric`

is defined on multiple Calendar Dimensions, you must define which dimension to use. If you want to use a dimension outside of time, you must define it here.-
`Alternate Metric`

is an optional argument that allows you to forecast`Source Metric`

based on another metric.`Alternate Metric`

must be another metric with the exact same dimensionality as`Source Metric`

The last 2 arguments, `Ranking Dimension`

and `Alternate Metric`

are optional.

## Return type

All the time series cells will be filled by an integer or decimal value starting from the first empty cell until the last value of the `Ranking Dimension`

(as it is sorted).

**Note:** If the regression is against an `Alternate Metric`

, the forecast will only compute a value on non-empty X values.

## How the slope is calculated across dimensions

The quantities *a* (slope) and *b* (intercept) are arguments of the regression model. The fitting is done using the *ordinary least squares method*. The slope a and intercept b are computed on all the dimensions that are not designed as the `Ranking Dimension`

. This calculation will be performed on all items within the dimensions outside of the `Ranking Dimension`

.

It means that when performing a linear regression on time on a metric based on Month and Country, the resulting metric will have a different equation on all country items.

For example, let's say you have a metric with Month, Country, and Product, and you use Month as the `Ranking Dimension`

the linear regression would be performed for each item in the Country and Product dimensions.

**Note**: If `Source Metric`

has empty values, they won't be taken into account to compute a and b.

**Note: **If the `Source Metric`

has only one data point, the linear regression will return a constant function equal to the only available data point

## Examples

Metric `Sales`

defined on 1 Dimension

Month | Nov | Dec | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Sales | 1 | 3 | 5 | 4 | 9 | 13 | 16 | 17 |

Forecasted Sales =`FORECAST_LINEAR('Sales','Month’)`

Metric `Sales`

defined on 2 Dimensions

Month | Nov | Dec | Jan | Feb | Mar | Apr | May | Jun | Nov | Dec | Jan | Feb | Mar | Apr | May | Jun |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Country | FR | FR | FR | FR | FR | FR | FR | FR | US | US | US | US | US | US | US | US |

Sales | 1 | 3 | 5 | 4 | 9 | 13 | 16 | 17 | 1 | -1 | -3 | -5 | -4 | -9 | -13 | -16 |

Forecasted Sales =`FORECAST_LINEAR('Sales','Month’)`

aggregated on Countries

Forecasted Sales =`FORECAST_LINEAR('Sales','Month’)`

not aggregated on Countries

Metric `Cost of sales`

against Metric `Sales`

.

Sales | 1 | 3 | 5 | 4 | 9 | 13 | 16 | 17 | 20 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cost of sales | -2.5 | -1.5 | -0.5 | -1 | 1.5 | 3.5 | 5 | 5.5 | 7 |

Forecasted Salary =`FORECAST_LINEAR('Cost of sales actuals’,'Month','Sales per month')`

## References

https://www.sciencedirect.com/topics/mathematics/simple-linear-regression

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