Key Performance Indicator Algorithms

Planning and Consolidation uses statistical analysis to determine the relationship between a KPI and the other accounts. This is not a time trend of the KPI, but a mathematical analysis of the data to determine what relationships drive the KPI.

Example Example

In this way, for example, product quality might contribute to the analysis of the customer satisfaction KPI.

End of the example.

Planning and Consolidation uses these models in two different analyses, when making predictions, and when analyzing root causes. The data relationships are calculated by mathematical algorithms. The system employs the following standard algorithms to uncover these relationships:

Linear Regression
Piecewise Linear Regression
Non-Linear (3rd-order polynomial) Regression
Multiple Linear Regression

Note
Multiple Linear Regression is not used in root cause analysis.

End of the note.

The following table provides an overview of these algorithms:

Algorithm	Explanation
Linear Regression	The simplest relationship between two variables is the linear one. Linear regression analyzes that relationship by finding the best straight line through the data. Linear regression is appropriate for many conventional relationships. It is the most efficient and fastest algorithm.
Piecewise Linear Regression	Piecewise Linear Regression is an extension to the simple linear regression. Unlike the linear regression, which seeks to draw a straight line through all available data points, Piecewise Linear Regression seeks to draw segments of straight lines in different regions of the data set. In Planning and Consolidation, each KPI measurement data set can be seen as a data series along the x axis (the independent variable). The segmentation is performed starting on the whole dataset, recursively partitioning the series until a good fit is achieved. This model is useful for relationships, which might be discontinuous.
Non-linear (3rd order polynomial) regression	Some relationships are non-linear. In this case, you may find it necessary to fit data points along a curve. This objective is accomplished by a non-linear regression. Planning and Consolidation uses the 3rd-order polynomial as the preset fitting model. This model smooths out the line into a curve. This model is good for the following relationships: Relationships that change continuously Relationships that can change direction Example Up to a certain point, an increase in rainfall results in a greater crop yield. However, once a saturation point is reached, the crops start to drown and the yield decreases. End of the example.
Multiple Linear Regression	Multiple regression is not easy to convey in a graph. Multiple Linear Regression is based on the assumption that more than one variable drives the KPI. This model is better for KPIs, which are likely to be driven by a set of unrelated variables. However, the model is limited by assuming all relationships are linear. Example Consider a common scenario, in which customer satisfaction is driven by quality and price. The analysis could also include headcount, legal fees, and shares outstanding. This would result in a 5-dimensional graph. The analysis, though, might reveal that customer satisfaction rises when quality improves but drop as price increases. So the prediction made for customer satisfaction can be based on both the quality and the price. End of the example.