Zipf's Law for of American urban areas and Polish towns

What is it about?

The paper aims at the presentation of a methodology where the classical the linear regression model is modified to guarantee more realistic estimations and lower parameter oscillations for a specific urban system. That can be achieved by means of the weighted regression model which is based on weights ascribed to individual cities. The major shortcoming of the methods used so far – especially the classical simple linear regression – is the treatment of individual cities as points carrying the same weight, in consequence of which the linear regression poorly matches the empirical distribution of cities. The aim is reached in a several stage process: demonstration of the drawbacks of the linear parameter estimation methods traditionally used for the purposes of urban system analyses; introduction of the weighted regression which to a large extent diminishes specific drawbacks; and empirical verification of the method with the use of the input data for the USA and Poland

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Photo by Paulo Silva on Unsplash

Photo by Paulo Silva on Unsplash

Why is it important?

Among the practical problems connected to the application of the rank-size rule to human settlement systems, one can mention such estimation of approximating line parameters which would optimally correspond to the empirical urban distribution by size. The paper presents the originally modified regression model which significantly reduces the inconveniences related to the use of the classical regression. The merits of the suggested method were demonstrated on the basis of the USA and Poland.

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