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 parameters of the regression model. The fitting is done using the ordinary least squares method.
Syntax
FORECAST_LINEAR(Source_metric [, Ranking_dimension, Alternate_metric])
Source_metricis 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 theRanking_Dimensionparameter.Ranking_Dimensionis the dimension by which the regression is computed. If left undefined, the ranking dimension defaults to a Calendar Dimension fromSource_metric. IfSource_metricis 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_metricis an optional parameter that allows you to forecastSource_metricbased on another metric.Alternate_metricmust be another metric with the exact same dimensionality asSource_metric
The last 2 parameters, 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 parameters 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