Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns
The paper aims at presentation of a methodology where the classical 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 ascri...
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| Format: | Article |
| Language: | English |
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Nicolaus Copernicus University in Toruń
2021-09-01
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| Series: | Bulletin of Geography. Socio-Economic Series |
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| Online Access: | https://doi.org/10.2478/bog-2021-0028 |
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| author | Sokołowski Dariusz Jażdżewska Iwona |
| author_facet | Sokołowski Dariusz Jażdżewska Iwona |
| author_sort | Sokołowski Dariusz |
| collection | DOAJ |
| description | The paper aims at presentation of a methodology where the classical 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 |
| format | Article |
| id | doaj-art-7ce7d75a0dae423faad1b64ef180bdfe |
| institution | DOAJ |
| issn | 2083-8298 |
| language | English |
| publishDate | 2021-09-01 |
| publisher | Nicolaus Copernicus University in Toruń |
| record_format | Article |
| series | Bulletin of Geography. Socio-Economic Series |
| spelling | doaj-art-7ce7d75a0dae423faad1b64ef180bdfe2025-08-20T02:52:26ZengNicolaus Copernicus University in ToruńBulletin of Geography. Socio-Economic Series2083-82982021-09-01535314715610.2478/bog-2021-0028Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish townsSokołowski Dariusz0Jażdżewska Iwona1Nicolaus Copernicus University in Toruń, Faculty of Earth Sciences and Spatial Managment, Department of Spatial Management and Tourism, Lwowska 1, 87-100Toruń, PolandUniversity of Łódź, Faculty of Geographical Sciences, Institute of Urban Geography, Tourism and Geoinformation, Kopcinskiego 31, 90-142, Łódź, PolandThe paper aims at presentation of a methodology where the classical 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 Polandhttps://doi.org/10.2478/bog-2021-0028city size distributionweight of citieszipf's lawrank-size ruleweighted regressionusapoland |
| spellingShingle | Sokołowski Dariusz Jażdżewska Iwona Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns Bulletin of Geography. Socio-Economic Series city size distribution weight of cities zipf's law rank-size rule weighted regression usa poland |
| title | Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns |
| title_full | Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns |
| title_fullStr | Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns |
| title_full_unstemmed | Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns |
| title_short | Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns |
| title_sort | zipf s law for cities estimation of regression function parameters based on the weight of american urban areas and polish towns |
| topic | city size distribution weight of cities zipf's law rank-size rule weighted regression usa poland |
| url | https://doi.org/10.2478/bog-2021-0028 |
| work_keys_str_mv | AT sokołowskidariusz zipfslawforcitiesestimationofregressionfunctionparametersbasedontheweightofamericanurbanareasandpolishtowns AT jazdzewskaiwona zipfslawforcitiesestimationofregressionfunctionparametersbasedontheweightofamericanurbanareasandpolishtowns |