## The median …

EstimLab brings an important innovation to the relation between the cost and the variables – particularly for the quantitatives, but without forgetting the qualitatives – selected as being the real “cost drivers”. This innovation allows tomake up for all the inconveniences of the ordinary least squares method. Remember :

- The ordinary least squares method introduces a bias that can be very high if the cost data are scattered, to the point that this method was eventually called ” linear regression “: concretely the found relation “regresses” towards the average of the costs. Practically it implies that the found relation underestimates the “heavy” products (greater than the average, the average being defined here as the gravity centre of the data) and overestimates the “light” products (lower than the average)

- It also tends to neglect the light products, in the sense that it favors the “heavy” products to the detriment of the others. This results from the fact that, concerning costs, the data precision of costs is never given in value but in percent; strong costs therefore have a less good absolute precision. Now the method tries to minimize the squares of the distances: it thus is more naturally interested in the high costs.

- Finally the « outliers» can seriously modify the found relation. The outliers are points for which the cost is generally (but not always) very different from the others: they present, compared to the others, important distances that the method tries to reduce, and therefore “pulls” the relation’s curve towards these points..

Regarding costs – unless the costs are well aligned (which doesn’t happen very often) – the ordinary least squares method has serious inconveniences, that many authors tried to minimize by bringing mathematical corrections (these exist in EstimLab for persons who really want to use this method). Our idea was, rather than to look for palliatives, to replace it by a method that the computer facilitates nowadays. This method – generalized in the median space – consists in not minimizing the squares of the distances, but the absolute distances between the data and the relation we are looking for. This new method is only interested in the position of the costs in regard to the relation instead of the cost values . With this method, the inconveniences mentioned above disappear automatically and the palliatives become totally useless!

And the found relation is better than the one produced by the OLS method, in the sense that it is closer to data …

This method leads to mathematical procedures (used in EstimLab) completely different to the previous ones. For example: for the OLS method, Gauss showed that the deviations (between the cost data and the relation) must be distributed according to the curve known under the name of “bell curve” (or in more mathematical terms of ” curve of Gauss »), while the new method has to see the deviations distributed according to a curve with a ” witch’s hat ” form (or Laplace » curve ). Consequently the deviations, on average, are lower. This also leads to a different calculation of the confidence intervals for the estimated costs (and all this is in EstimLab).

EstimLab thus brings a better solution regarding the search for the relation between costs and significant variables, and therefore estimated values of better quality for new products.