Regional Potentials using the RCR Index

What is the RCR Index, and what can it do? 

RCR (Residential Construction Renovation) is a statistical measure of the market potentials in the residential construction and renovation sectors. The index is based on statistical data for both local and 5-figure post code levels. The RCR index shows the positive and negative deviations from the average market potential in the respective countries.    

Thus the RCR index can be used for:

• Calculating regional market potentials
• Regional optimisation of the  distribution channels
• Logistical planning 

How does the RCR model work?

The model on which the RCR is based, is a so-called ‘non-linear multiple regression model‘ (see Toolbox 1).  This process looks for a relationship between the market potential and the statistical factors of influence. This relationship is held constant in the form of an equation, which is calibrated on a known control sample.

• Toolbox 1: Multiple Regression Models 

Statistical models which describe the connection between a variable which is to be explained and several factors of influence (factors) which are independent of one another. Here, a regression equation (the model) is calibrated on a set of data. For multiple, non-linear models like the RCR index, this is done using an iterative algorithm, i.e. a method which progressively approximates the correct result. The goodness of fit is described by a multiple correlation coefficient (R²). Whether an R² is significant for a given control variable or not is determined by a hypothesis test (F-Test). The result of the hypothesis test is with what probability (probability of error) a correct hypothesis has been proposed.
 
Market potential is of course dependent on a very large number of statistical factors of influence. However, not all of these factors can or should be taken into account in the calculation of the RCR. There needs to be a reduction of the data in order to keep the most important factors of influence. It is particularly important that several factors which exert the same influence are replaced by one single factor. The statistical process of this data reduction is called ‘factor analysis‘ (see Toolbox 2).

• Toolbox 2: Factor Analysis 

The method of data reduction by which classes of variables of influence are merged into factors. Factor analysis solves the Eigen value problem, and is needed in order to extract factors which are independent of one another. Factor analyses are used in order to ensure the independence of the input variables in a multiple regression model such as the RCR.
 
There are also factors of influence on to which others are statistically ‘attached‘, without needing to be assessed individually. This means that the actual factors which are assessed by the RCR include a multiplicity of other influences which are not explicitly listed. 

The factors of analysis on which the RCR is based are:

• Construction permits: Residential buildings
• Construction permits: Dwellings
• Construction permits: Construction costs
• Development structures
• Employees Industry
• Employees Furniture Industry
• Population density
• Total Purchasing power (TPP, Nuremberg)
• Housing Stock
• Dwelling size
• etc.

The RCR model does not function additively in the way that a simple multiple linear regression model would. Thus, the RCR takes into account purchasing power factors and sales in the form of limiting factors for the construction cost data, in relation to the number of construction permits, which in turn is standardised according to the structure of the dwellings.

What the RCR cannot do

Exceptions do not prove the rule, but rather they make us aware of the limitations of the model. The goodness of a rule is first of all dependent on the number of exceptions. If this is low, that is the probability of error is small, then the rule is good. As with all statistical models, the RCR has a probability of error (see Toolbox 3). However, the value a=0.09 (in the F-Test), is low for a socio-demographic model. With the type of complex systems which the RCR describes, there can be no 100 % proof explanation.

• Toolbox 3: Significance 

In order to be able to make decisions based on statistical assessment, the significance level is an important measure. It indicates the probability that the acceptance of the null hypothesis is an incorrect decision. If, for example, the significance level is 5%, then the level of accuracy of the analysis is 95%.

A further limitation of the RCR is related to the type of input data, which include those to do with construction permits and relative construction costs. This means that residential extensions and renovation work, which do not require construction permits, are not directly included. However, indirectly there is a link, because as a rule, a high level of construction activity for which permits are required correlates positively with construction activity for which a permit is not required.