The modifiable areal unit problem - analysis of correlation and regression

The paper focuses on the issue of the modifiable areal unit problem, which means a possibility of obtaining various results for spatial economic analyses depending on the assumed composition of territorial units. The major research objective of the work is to examine the scale problem that constitutes one of the aspects of the modifiable areal unit problem. Analysis of the scale problem will be conducted for two research problems, namely, for the problem of the causal relationships between the level of investment outlays in enterprises per capita and the number of entities of the national economy per capita, and the issue of the dependence between the registered unemployment rate and the level of investment outlays per capita. The calculations based on the empirical values of those variables showed that moving to a higher level of aggregation resulted in the change in the estimates of the parameters. The results obtained were the justification for undertaking the realisation of the objective. The scale problem was considered by means of a simulation analysis with a special emphasis laid on differentiating the variables expressed in absolute quantities and ones expressed in relative quantities. The study conducted allowed the identification of changes in basic properties as well as in correlation of the researched variables expressed in absolute and relative quantities. Based on the findings, it was stated that a correlation analysis and a regression analysis may lead to different conclusions depending on the assumed level of aggregation. The realisation of the research objective set in the paper also showed the need to consider the adequate character of variables in both spatial economic analyses and during the examination of the scale problem.