FORECAST_LINEAR function

  • 29 June 2022
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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_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 parameter. 
  • 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 parameter 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 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


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