Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 2. Simulation Never heard of it > Why correlated variables?

Risk Analyst

Why correlated variables?

In statistics, the correlation coefficient is a measure of the strength of the relationship between two variables, and it varies between -1 and 1. In business, for instance, there is typically a negative correlation between price and demand: when the price goes up the likelihood is high that the demand goes down. On the other hand, there may be a positive correlation between the number of phone calls made by sales representatives and the number of appointments set. No correlation is found in most events, such as between the temperature of the cup of coffee on my desk and the colour of the next car driving past my office building.

In modelling scenarios, there are cases when it is important to take correlation into account, for instance, when estimating market share as shown in example 3 of this help chapter. Products where the purchase is driven by strictly utilitarian principles, such as pharmaceuticals and industrial products, supply perhaps the best examples of market share being influenced by technical attributes of the product. When one process has an impact on another we can reasonably believe they are correlated. If the relationship is relevant it should be measured and included in the simulation model.

Risk Analyst uses the function mmCORREL to generate correlated variables according to the Scheuer-Stoller method (read also the material concerning the function mmCORREL in this help file). The following tables have been made from the file example mmCORREL.xls accompanying the Risk Analyst tool of MM4XL software. In the first table we have target values. These are values entered by the user and they specify the desired level of correlation between variables.

 Monte Carlo Simulation Software: Management Process Risk Analysis

In the range C16:E16 of the following table we entered the array formula:


 Monte Carlo Simulation Software: Management Process Risk Analysis

While in row 17 we entered the formulae:

=mmNORMAL(10, 1, C16)
=mmNORMAL(10, 1, D16)
=mmNORMAL(10, 1, E16)

Finally, in row 18 of the table above we entered the formulae below and we ran 1000 simulations:


From the Sensitivity page of the Preview window we exported the charts below, which show the level of correlation between the three variables object of the simulation.

 Monte Carlo Simulation Software: Management Process Risk Analysis

 Monte Carlo Simulation Software: Management Process Risk Analysis

 Monte Carlo Simulation Software: Management Process Risk Analysis

The returned values are remarkably close to the target values. This means that the variables generated in B23:D1022 follow a correlation pattern very close to the desired one. When modelling processes where accuracy plays an important role, the mmCORREL function can be a great help.

The correlation coefficient is reliable only where there are linear relationships. If the relationship between two variables follows a non-linear pattern, then the correlation coefficient becomes a weak estimator and may lead to wrong conclusions.

MM4XL software offers two tools called Smart Mapping and Benchmark Map to draw bubble maps, which are very effective charts for detecting correlation. Read more about these tools in the corresponding help chapter.

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