DEGREE PROJECT IN THE FIELD OF TECHNOLOGY CIVIL ENGINEERING AND URBAN MANAGEMENT AND THE MAIN FIELD OF STUDY THE BUILT ENVIRONMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019
Geographically Weighted Regression as a Predictive Tool for Station-Level Ridership
The Case of Stockholm
KARIM OUNSI
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT Abstract
English/ Engelska/ Anglais
This thesis studies a new regression method, Geographically Weighted Regression (GWR) to predict ridership at the station level for future stations. The case study of Stockholm’s blue line is used as new stations will be built by 2030. This paper is written in English.
Historically, linear regression methods, independent of the geographical location of the observations, was and is still used as the Ordinary Least Square regression method. With the rise of GIS-softwares these last decades, geographically dependent regression can be used and previous preliminary studies have shown a dependency between ridership and location of the station within the network.
GWR equations for new stations are determined and used to predict their respective ridership. GIS-data was collected using Geodata and Traffikverket (Traffic Authority) and ridership as well as socio-economic related material for the base year of 2016 was used in order to determine, first, significant variables from a group of candidate ones (Workers, number of bus lines and type of change were chosen) and, second the OLS and GWR equations. Significances of both models were compared and the OLS equation was used in order to determine the hypothetical ridership of the new stations if they were present in 2016. GWR equations were then determined using these calculated ridership of these new stations. Having all GWR equations (each station having its own equation), ridership was thus predicted for the new stations for 2030 using assumptions and planned, programmed development around the stations (population, apartment to be built…) and compared with the official predictions.
The results show that the GWR method, generally, overpredicts ridership when compared to the official predictions. Many reasons can explain this overprediction like the assumptions made with regards to the number of buses as well as the method followed to calculate the number of workers around each station.
Three main conclusions were drawn for this case study. One main conclusion, specific for this study and two other, more general, conclusions were deduced from this study. First, GWR is a good predicting tool for future stations that are close to most currently available stations. Second, GWR is a good predicting method for stations where limited changes in the future environment will occur.
1 Sammanfattning
Swedish/ Svenska/ Suédois
Denna avhandling studerar en ny regressionsmetod, Geografically Weighted Regression (GWR) för att förutsäga antal resenärer på stationsnivå för framtida stationer. Fallstudien av Stockholms blå linje används eftersom nya stationer kommer att byggas år 2030. Denna rapport skrivs på engelska.
Historiskt används linjära regressionsmetoder oberoende av observationens geografiska placering som den ordinarie Least Square-regressionsmetoden. Med ökningen av GIS- programvaror de senaste decennierna kan geografiskt beroende regression användas och tidigare preliminära studier har visat ett beroende mellan antal resenärer och plats för stationen i nätverket.
GWR-ekvationer för nya stationer bestäms och används för att förutsäga deras respektive antal resenärer. GIS-data samlades in med hjälp av Geodata och Traffikverket och antal resenärer samt socioekonomiskt relaterat material för basåret 2016 användes för att först fastställa betydande variabler från en grupp kandidater (Arbetare, antal busslinjer och typ av förändring valdes) och för det andra OLS- och GWR-ekvationerna. Betydelsen av båda modellerna jämfördes och OLS- ekvationen användes för att bestämma det hypotetiska antal resenärer för de nya stationerna om de var närvarande 2016. GWR-ekvationerna bestämdes sedan med hjälp av dessa beräknade antal resenärer för dessa nya stationer. Med alla GWR-ekvationer (varje station har sin egen ekvation) förutsades således antal resenärer för de nya stationerna för 2030 med antaganden och planerad, programmerad utveckling runt stationerna (befolkning, lägenhet som ska byggas ...) och jämförs med de officiella förutsägelserna.
Resultaten visar att GWR-metoden generellt sett förutsäger antalet resenärer jämfört med de officiella antalet resenärer. Många orsaker kan förklara denna överförutsägelse som antaganden om antalet bussar och metoden som följdes för att beräkna antalet arbetare runt varje station.
Tre huvudsakliga slutsatser drogs för denna fallstudie. En huvudsaklig slutsats, specifik för denna studie och två andra, mer generella, slutsatser härleddes från denna studie. För det första är GWR ett bra förutsägningsverktyg för framtida stationer som ligger nära de flesta tillgängliga stationer. För det andra är GWR en bra förutsägningsmetod för stationer där begränsade förändringar i den framtida miljön kommer att inträffa.
2 Résumé
French/ Franska/ Français
Cette thèse étudie une nouvelle méthode de régression, la régression géographiquement pondérée (GWR), pour prédire le nombre de voyageurs au niveau des stations pour de futures stations. L’étude de cas de la ligne bleue de Stockholm est prise vu que de nouvelles stations seront construites d’ici 2030. Cette thèse est rédigée en anglais.
Historiquement, les méthodes de régression linéaire, indépendantes de la localisation géographique de des observations, étaient et sont toujours utilisées comme méthode de régression des moindres carrés ordinaires (OLS). Avec le développement des logiciels SIG au cours des dernières décennies, l’utilisation de régression géographiquement dépendante devient plus accessible et des études préliminaires antérieures ont montré une dépendance entre le nombre de voyageurs et l'emplacement de la station dans le réseau.
Les équations GWR pour les nouvelles stations sont déterminées et utilisées pour prédire leurs nombres de voyageurs respectives. Les données SIG ont été collectées à l’aide de Geodata et de Traffikverket (Autorité des transports). Le nombre de passagers ainsi que les données socio- économiques pour l’année de référence de 2016 ont été utilisés afin de déterminer, en premier lieu, les variables significatives d’un groupe de candidats (travailleurs, nombre de lignes de bus type de changement ont été choisis) et, deuxièmement, les équations de OLS et de GWR. Les valeurs significatives des deux modèles ont été comparées et l'équation OLS a été utilisée afin de déterminer le nombre de voyageurs hypothétique des nouvelles stations si elles étaient présentes en 2016. Les équations GWR ont ensuite été déterminées à l'aide de ce nombre de voyageurs calculé de ces nouvelles stations. Disposant de toutes les équations GWR (chaque station ayant sa propre équation), le nombre de voyageurs des nouvelles stations pour 2030 a donc été prédite à l'aide d'hypothèses et de développements planifiés et programmés autour des stations (population, appartement à construire…) et comparés aux prévisions officielles.
Les résultats montrent que la méthode GWR surestime d’une façon générale le nombre de voyageurs par rapport aux prévisions officielles. Plusieurs raisons peuvent expliquer cette surestimation, telles que les hypothèses émises concernant le nombre d'autobus et la méthode suivie pour calculer le nombre de travailleurs autour de chaque station.
Trois principales conclusions ont été tirées pour cette étude de cas. Une conclusion principale, spécifique à cette étude et deux autres conclusions, plus générales, ont été déduites de cette étude. Premièrement, le GWR est un bon outil de prévision pour les futures stations proches de la plupart des stations actuellement présentes. Deuxièmement, le GWR est une bonne méthode de prévision pour les stations où des changements limités dans l’environnement futur auront lieu.
3 Stockholm is growing – and so is public transport
Stockholm County is growing rapidly, in recent years by about 40,000 inhabitants every year. By 2030 the (county’s) population is expected to have increased to about 2.6 million (from just under 2.1 million in 2010). This will increase pressure on public transport services. Roads and railways are already congested, particularly in the central parts of the city and during peak traffic. In-commuting from other counties will also increase and accessibility to public transport will need to be adapted to Introduction the changing needs. PUBLIC TRANSPORT should be perceived as the most attractive form of travel for every- one, including the elderly and travellers with disabilities. It is therefore crucial to Background the Stockholm region of the future that public transport develop at the same pace, at least, as the population increases and that the entire transport system be planned so as to facilitate public transport’s long-term expansion. According to the World Bank in 2018, more and more people are moving to cities leaving THE COUNTY COUNCIL invests billions in public transport every year. Over the coming behind rural areas. Inyears, fact, the countysince council 2007, will more be investing people more thanlive ever in to these meet the cities needs ofthan a in rural areas for the first time in history. growingEven population.if the rate The of biggest urbanization investments will is be decreasing, made in upgrading it thehas infra constantly- been positive structure but to an increasing degree also new construction and expansion. with a value always superior than 1,9% since 1960. More peopleMAJOR in cities INVESTMENTS means over the a next higher ten-year number period include: of people moving around during the day leading to an increase• extension to the ofnumber the metro of passengers within the public transportation network. SL, the region of Stockholm• the metro’s authority, Red Line quantifies this increase to more than 2 million passengers per • the Commuter Train programme day in 2013 from 1,6• millionextension of in the 20 Roslagen03, a Line. 20% increase in merely 10 years. 2500 Source: Facts about SL and the county 2014 Public transport’s positive development from 2003 to 2013
Thousands 2,017 2,000 2000 1,907 Public transport 1,900 1,848
1,800 1,785 1,742 1,700 Car 1,663 1,600 1500 Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Figure 1: Diagram illustratesThe diagram travelers illustrates per travel day per by day cars by car and ( ) andpublic public transportation transport ( ) in thousands. in thousands (Trafikförvaltningen, n.d.) Investing for a more efficient and demand-satisfying public transportation network is thus more important than ever. According to the American– 6 – Public Transportation Association, “every $1 invested in public4000 transportation generates $4 in economic returns” (American Public Transportation Association,3500 2019). Moreover, funding for public transportation is increasing from a bit over $40 billion to over $70 billion in 20 years in the United States of America. 3000 2500 2000 1500 1000 500 0
Figure 2: Total Funding in Public Transportation in the USA (in billions of 2017 dollars) This continuous increase is met with a growing concern within the transportation authorities, policymakers and even private firms demanding a more precise, detailed and accurate prediction of ridership in order to explain this never-reaching level of investment.
Today’s models, mainly lineal regression models, are used in order to predicted ridership or the transit share for a specific region. However, the assumptions previously made in order to ease their use and limit their cost are leading to errors in predictions, creating uncertainties and
4 risks that are increasingly higher to bear for investors. One of these assumptions is space independency between the observations. In 2000, Fotheringham et al. proved that global regression models estimate a limited number of parameters between the dependent and independent variables with estimated parameters independently determined with regards to spatial characteristics. This lead to a huge disadvantage of this models with regards to observations that are geographically dependent.
In fact, multiple studies like the one by Cordazo et al. in 2012, have proven a high correlation between transit use or ridership and geographic locations of the observation, with high spatial autocorrelation with closer observation having a higher influence than farther ones. This means that when using global, traditional regression models in order to predicted ridership, errors are generated due to the assumptions that observation are geographically independent while they are actually not.
As explained above, taking into consideration geographic location of the observation at the time was both time and cost consuming. Today, with the development of GIS, Geographical Information System models and softwares during the last decade, makes these excuses obsolete. These new softwares can acknowledge the geographic locations of the observations while developing a regression model. The Geographically Weighted Regression is one of these new methods that can be used in order to explain and (maybe) predicted ridership.
Objectives and Goals
The objective of this thesis is to determine if Geographically Weighted Regression method can be used in order to predict the station-level ridership at future metro stations.
Three kind of stations are to be compared, stations with different geographic locations compared to the rest of the network and built in different changing environment: Stations close to the existing metro stations of the network that will not experience major changes in their surrounding environment, stations built close to the existing metro station that will, however, experience considerable change to their surrounding environment and, finally, stations that will be built far away from the actual network that will experience big change to their surrounding environment.
The comparison between these three types of station will determine if and/or when is are predictions possible following the method use in this study. The case of Stockholm is studied here.
Thesis Structure and Flow
This paper is divided into seven parts. First, the literature review talks the way predictions were done until today, while introducing GWR, both theoretically and with regards to previous studies using it. Second, a methodology is presented in which detailed steps performed in this study are described in order to reach the results that are needed. Third, Stockholm as a city and its metro network is presented describing the extension of the metro network. This part also lists the candidate variables as well as the assumptions laid for this study. Fourth, results are presented (the models used, parameters, significance of the models and finally the ridership predictions). Fifth,
5 the analysis of these results is done extensively dividing the analysis into general, regional and station-specific. Sixth, the limitations of the studies are described mainly in order to present what should be avoided for future similar studies that are to be performed. Finally, the conclusions are presented both case study specific and generally.
6 ABSTRACT 1
English/ Engelska/ Anglais 1
SAMMANFATTNING 2
Swedish/ Svenska/ Suédois 2
RESUME 3
French/ Franska/ Français 3
INTRODUCTION 4
Background 4
Objectives and Goals 5
Thesis Structure and Flow 5
LITERATURE REVIEW 10
Old Forecasting Methods 10
Geographically Weighted Regression 11 Description 11 Difference between Spatial Autocorrelation and Spatial Non-Stationality: Accuracy of the model 14 Spatial Autocorrelation 15 Spatial Non-Stationality 16
Geographically Weighted Regression as Forecasting Method 17 Previous works and fields in use 17 Comparison between OLS and GWR 18 Predictions using GWR compared to other methods 18
METHODOLOGY 21
STOCKHOLM’S CASE STUDY AND DATA COLLECTION 24
Stockholm’s Metro System: Present Situation, Forecasting and Future Development 24 Stockholm today with ridership and population 24 Preliminary studies with Sampers for Stockholm’s new station 25 General idea with map of the planned extension 26 Transit-oriented development: Stockholm Case Study 28
Data and Candidate Variables 29 Line chosen 29 Candidate Variable 29 Prediction assumptions for the candidate variables 32
7 RESULTS 32
GWR Equations with Existing Conditions 32
Predictions Using the Determined GWR Equations 41
ANALYSIS 45
Division between the North and the South 45
The Model in Numbers 45
General Reasons 48
Bus Assumptions and Effect on Predictions 48
Special Case of Sofia 48
LIMITATIONS OF THE STUDY 49
CONCLUSION 51
REFERENCES 52
APPENDIX 56
Appendix I: Method and Tools in Determining Data in ArcGIS (ArcMap) 56 Income, Workers, Population and Age 56 Road density (m/m2) 56 Number of bus lines at a 200-meter buffer around the entrances of the metro 56 Terminal Station 56 Type of change 57 Commuting distance 57
Appendix II: Table of GWR Equations and Predictions for the 2016 Situation 58
Appendix III: Table of GWR Equations and Predictions for the 2016 Situation with New Stations 73
Appendix IV: GWR Prediction by ArcGIS (ArcMap) 89
8 FIGURE 1: DIAGRAM ILLUSTRATES TRAVELERS PER DAY BY CARS AND PUBLIC TRANSPORTATION IN THOUSANDS (TRAFIKFÖRVALTNINGEN, N.D.) 4 FIGURE 2: TOTAL FUNDING IN PUBLIC TRANSPORTATION IN THE USA (IN BILLIONS OF 2017 DOLLARS) 4 FIGURE 3:TRADITIONAL FOUR-STEP TRANSPORT MODEL (ADAPTED FROM WHITEHEAD & BUTTON, 1977, P.117) 10 FIGURE 4: DIFFERENT TYPES OF THE KERNEL FUNCTION (INSTITUT NATIONAL DE LA STATISTIQUE ET DES ETUDES ECONOMIQUES, 2018) 13 FIGURE 5:100-METER SQUARES IN RENNES, SAMPLED IN RED (FLOCH, 2015) 20 FIGURE 6: BOX-PLOT OF THE RCEQMR FOR THE HORWITZ-THOMPSON (1), REPRESSION (2) AND GWR (3) ESTIMATORS (FLOCH, 2016) 21 FIGURE 7: CATCHMENT AREA (SERVICE AREAS) FOR EACH STATION (OLD STATIONS IN BEIGE, NEW STATIONS IN PURPLE). 22 FIGURE 8: SERVICE AREA FOR THE BLUE LINE STATION TO BE PREDICTED FOR 2030 24 FIGURE 9: METRO NETWORK WITH THE ADDITIONAL STATIONS IN DASHED LINE. 26 FIGURE 10: PROJECTED RIDERSHIP ON THE BLUE LINE DURING THE MORNING PEAK HOUR WITH A FOUR-MINUTE HEADWAY (NYLÉN, 2017; HARDERS AND BJÖRKMAN, 2016) 27 FIGURE 11: PREDICTED RIDERSHIP ON THE YELLOW LINE DURING THE MORNING PEAK HOUR BY 2030. 28 FIGURE 12: RIDERSHIP VS. NUMBER OF WORKERS 36 FIGURE 13: OLS (UP) AND GWR (DOWN) STANDARD DEVIATIONS 37 FIGURE 14: GWR STANDARD DEVIATION WITH NEW STATIONS 40 FIGURE 15: THE DISTRIBUTION OF THE INTERCEPT OVER THE STUDIED AREA (FROM THE LOWEST IN BLUE TO THE HIGHEST IN RED; THIS APPLIES TO ALL DISTRIBUTIONS TO FOLLOW) 45 FIGURE 16: THE DISTRIBUTION OF THE WORKER’S COEFFICIENTS OVER THE STUDIED AREA 46 FIGURE 17: THE DISTRIBUTION OF THE BUS’S COEFFICIENTS OVER THE STUDIED AREA 47 FIGURE 18: THE DISTRIBUTION OF THE CHANGE’S COEFFICIENTS OVER THE STUDIED AREA 47
TABLE 1: EQUIVALENT PRESENT STATIONS FOR FUTURE STATIONS (WSP ANALYS & STRATEGI, 2013) ...... 26 TABLE 2: CANDIDATE VARIABLES EVALUATION AND SELECTION ...... 32 TABLE 3: SUMMARY OF MULTICOLLINEARITY ...... 33 TABLE 4: PERCENTAGE OF SEARCH CRITERIA PASSED ...... 34 TABLE 5: MORAN’S I TESTS ON THE DEPENDENT AND CANDIDATE VARIABLES ...... 34 TABLE 6: OLS EQUATION ...... 38 TABLE 7: GWR EQUATIONS ...... 38 TABLE 8: PREDICTED RIDERSHIP USING OLS EQUATION FOR NEW STATION IN 2016 ...... 39 TABLE 9: GWR EQUATIONS WITH THE NEW STATIONS ...... 40 TABLE 10: NUMBER OF ADDITIONAL POPULATION AND WORKERS BY 2030 ...... 41 TABLE 11: COEFFICIENTS AND GWR ESTIMATIONS FOR NEW STATIONS ...... 43 TABLE 12: NUMBER OF ADDITIONAL POPULATION AND WORKERS BY 2030 FOR BARKARBYSTADEN AND BARKARBY STATION ...... 44 TABLE 13: COEFFICIENTS AND GWR ESTIMATIONS FOR NEW STATIONS AFTER THE CHANGE IN WORKERS ...... 44
9 Literature Review
Having efficient and reliable ridership estimation is important for all stakeholders. Passengers can plan their trips by choosing confidently the time and route of their choice will be sure of their time of arrival to their destination. It can also create a routine when it comes to regular trips, mainly work-bound trips in the morning, increasing adequate planning and thus efficiency and productivity. Transit operators can plan efficiently for the needed capacities and frequencies by securing funds early on while spending them in the required areas and departments. Public authorities and operators can forecast resourcefully the funds needed for the future, the dispatching and evolution of jobs and population on the interested region as well as implementing policies and strategies in order to lead the region towards a more sustainable future.
Old Forecasting Methods
Transit ridership are usually estimated using comparison methods to equivalent situations, professional and elasticity analysis and travel demand models (Litman, 2004; Boyle, 2006). The first models are typically employed for route evaluation while the latter is used in assessing new amenities providing transit ridership only as a part of the prediction with no particular focus on transit ridership and public transportation travel that is treated as another mode (Zhang & Wang, 2014).
Transport forecasting and modelling took a serious turn in the fifties’ when the four-step model, a method that predicts traffic patterns at an aggregate level, was created (Horowitz, 1984). It has since been the dominant model for transport modelling and was adopted for transit ridership as well over the years (McNally, 2007). The four-step model is characteristic by its four step process by first generating the demand for travel in specific region, second distributing this demand by creating Origin-Destination region pairs, third assigning a mode of transport the travelers are going to use (public transport, car, walking, biking, etc.), and finally by assigning a specific route to each trip.
Figure 3:Traditional four-step transport model (adapted from Whitehead & Button, 1977, p.117)
10 Activity-based models are used for forecasting and prediction. This method focuses on predicting individual travel behavior at a disaggregated level (Hildebrand, 2003).
However, these overall travel demand forecasting methods require a huge number of surveys, data collection and processing. These are only a couple of reasons why this method is costly to implement and maintain (Marshall & Grady, 2006). They also fail to capture subtle land- use characteristics in specific areas that might influence ridership more or less than in the other region (Cervero, 2006).
For these reasons, other methods, such as regression models, were developed in order to have efficient and reliable forecasts and predictions of transit ridership. They are also faster and cheaper to develop. Creating a straight relationship between a couple of predefined factors (independent variables) with transit ridership (dependent variable), regression models are easy to use with less trouble in defining them providing a rapid alternative. According to consulted papers, these predefined factors are usually grouped in 4 categories: Demographic features, socio- economic indexes, land-use arrangement, geographic information.
Nevertheless, most current regression models accept spatial-independence in ridership estimation. The problem with this assumption is the fact that many (if not all) factors are spatially correlated (Zhang & Wang, 2014). New methods must then be utilized to acknowledge this spatial dependency between the different observations.
An Ordinary Least Squared regression (OLS) is a regression method that determines the parameters of the linear regression model by minimizing the square of the errors. The following equation summarizes this regression.
Geographically Weighted Regression
In the following section, the technical information of the geographically weighted regression is described as well as the different ways to evaluate its significance.
Description
Global calibrating models, using all the observations provided for a concerned region, predict global estimates for the whole interested region, while local models, using a handful of observation like GWR predict local models that for each interested observation. The main difference between the two methods is that the first emphasizes on the spatial similarities while the latter emphasizes on the spatial differences in the interested region. As a reminder, the OLS equation is presented below:
! = # + #1'( + #2'* +. . . +#,'- + ./
Where y is the dependent observed variable, xj is the j-th independent observations, variables or predictors (j = 1, ..., p), βj is the j-th model parameters to be estimated (j = 0, 1, ..., p) and epsilon y is the error at for observation y. An Ordinary Least Squared regression (OLS) is a
11 regression method that determines the parameters of the linear regression model by minimizing the square of the errors. The following equation summarizes this regression. It is important to note that OLS the βj are the same for all the studied region and do not change with space or dependent observation.
In fact, traditional global regression models, like OLS, assume that the whole studied region can be explained and predicted using one common equation with common parameters on the whole region. This rational is easily discredited by local regression models, like GWR (Fotheringham, Brunsdon & Charlton, 2002). This has been explained in section SOMETHING with case study examples from previous studies.
An advantage of GWR over other spatial methods, like multi-level modelling is that each calibration yields equations for each observation where each one of them is treated independently from the others, capturing geographic heterogeneity (Zhang et Wang, 2014).
The main idea behind the GWR method is the fact that each point i to be predicted is surrounded by an area of influence that decreases the farther the sampled observations are from point i, thus creating as many regression equations as there are observations to predicted. This is done by incorporating the geographical coordinates of each observation in its equation.
As stated before, GWR is inspired by OLS. OLS can be, actually, seen as an exception of GWR where all function is constant over space. Indeed, GWR uses a weighted least squares method to predict the parameters (Fotheringham and Charlton, 1998). The following function summarizes the GWR model:
!0 = #1(30, 50) + 7 #8(30, 50)'08 + .0 8
Where !0 is the dependent observed variable at location (ui,vi), #1(30, 50) is the intercept parameter at location (ui,vi), #8(30, 50) are the independent parameters for observation (ui,vi), '08 are the observation k at (ui,vi) and .0 is the error term for observation (ui,vi).
Beta best is thus equivalent to this equation:
9 < >( < #(:) = (; =(30, 50);) ; =(30, 50)?
Where Wi (uivi) is the weighting function.
This weighting function is spatially dependent providing a weight for the observation depending on its location from (and thus distance to) the observation that is to be predicted. It can be represented in a diagonal matrix where the primary diagonal line represents the weight function at location i (Fotheringham et al, 1998). Here is the weight matrix used:
12 A0( 0 … 0 0 A … 0 =(:) = @ 0* E 0 0 … 0 0 0 … A0D
Where A0F (G = 1, 2, … , H) is the weight given at location j
Coming back to the fact that OLS is an exception of GWR, it is clearer now that the weight function is introduced. In fact, one can assume that the weight function is equal to 1 for all points in the studied area.
These functions vary depending on the predicted information. There are several options from Gaussian, exponential, bi-square and kernel just to name the most used ones. One can differentiate between continuous weight functions where a weighting value is given to each observation in the studied area from weight function with compact support where the latter tends to a zero-value reached at the determined bandwidth value and assigned to observations having a distance greater than this bandwidth (Institut national de la statistique et des études économiques, 2018). However, according to Brunsdon, Fotheringham, and Charlton in 1998, there are the choice weight function has no significant effect on the results.
Figure 4: Different types of the kernel function (Institut national de la statistique et des études économiques, 2018) The following curves are written explicitly in the following equations, respectively uniform kernel, Gaussian kernel and Exponential kernel.
AIJ0FK = 1
( MNO > ( )Q AIJ0FK = L * P
( RMNOR > ( ) AIJ0FK = L * P
13 Another way to differentiate them is by classifying them in either a fixed or adaptive weight function. The main difference between the two is observation density and sample size and whether the bandwidth is constant or variable. The first kind determines the spread of the weight function according to a fixed distance (bandwidth) identical in the whole studied area to be used when one has high density of observation and sample points. The second determined the spread of the weight function according to the number of neighboring observations a point of interest has led to a greater spread when the density is low and varying the distance (bandwidth) (Fotheringham et al., 2002). The changing function can also determine the optimal bandwidth for highly dense observations.
In fact, this optimal value of bandwidth, that is a variable in the weight function equations with compact support, can be determined in other ways for a stated weighting function. The bandwidth value has the biggest influence on the results (Institut national de la statistique et des études économiques, 2018). Examples of these data-driven criteria are cross-validation (CV), generalized cross-validation (GCV), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The most in use are CV and AIC and are, thus, presented here (Fotheringham et al., 2002).
D * ST = 7 [!0 − !XY0(ℎ)] 0U(
Where !XY0(ℎ) is the value of y at i predicted where developing the model with all observation except !0. The optimum value of the bandwidth would be 0 if all the observations are used to estimate the model, meaning that the only available point in the model is !0, leading to !0 = !X. Generally, the bandwidth that minimizes CV is the one that maximizes the predictive capacity of the model.
H + (b) \]S(ℎ) = 2H ^H ^H (_X) + H ^H ^H (2`) + H a c H − 2 − (b)
Where n is the sample size, _X the estimate of the standard deviation of the error term, (b) the trace of the projection matrix of the observed variable y on the estimated variable !X.
When using one of these two statistical criteria, the bandwidth is determined when minimizing their values. The main difference between the two is that CV maximizes the predictive power of the model while AIC compromises between this predictive power and the model’s complexity. The weaker the bandwidth, the more the global model is complex. In general, AIC determines larger bandwidth than CV.
Difference between Spatial Autocorrelation and Spatial Non-Stationality: Accuracy of the model
The estimated GWR model needs to be evaluated and diagnosed passing by the same process of global models.
The estimated GWR can be evaluated thanks to coefficient of determination (R-Square), t- values and p-values.
14
∑ .* d* = 1 − 0 * ∑0 (!0 − !)
Where . is the residual between the observed value and the predicted one by the model, !0 is the observed value i (or at location i if dealing with GWR) and ! is the average of the observed values.
As stated before, the Akaike Information Criterion (AIC) can determine the optimal bandwidth for a given weighting function in the studied area. However, AIC can also evaluate the goodness-of-fit of the model. In general, an AIC value greater than 3 suggest a good fit of the model (Fotheringham et al, 2002).
In addition to these estimations and because local statistics are considered spatially disaggregated compared to global models, new evaluation statistics must also be performed to evaluate the model for local characteristics.
These characteristics can be classified into two categories: spatial autocorrelation and spatial non-stationality (Anselin, 1999). They have been challenging issues to deal with according to Fotheringham in 2002 and GWR permits to consider while considering the coordinates of the observation for spatial autocorrelation when calculating the intercept and spatial non-stationality when estimating the parameters. On one hand, spatial autocorrelation refers to an interaction in space, in other words the value of a certain variable compared to the value of its neighbours. On the other hand, spatial non-stationality refers to the structure in space (Anselin, 1999).
Spatial Autocorrelation
Spatial autocorrelation can be tested using the error of the GWR model created. In fact, GWR hypothesis that the error terms are identically distributed. Thus, a test for validating or not this independence of the distribution is the establishment of a hypothesis test (Leung, Mei and Zhang, 2000).
Ho: No spatial autocorrelation among the disturbance. H1: There exists either positive or negative spatial autocorrelation among the disturbances with respect to a specific spatial weight matrix W.
In order to accept or reject the null hypothesis, the test statistics Moran’s I is used. The values range between -1 and 1, where 0, theoretically, represent no spatial correlation (Rosenberg, 2010). However, for a defined sample size, the value representing no spatial correlation is -1/(N-1) where N is the number of spatial observations: it is the expected value. This value (or 0) is the expected value of the null hypothesis. Moran’s I is given as follows:
.̂ 15 Where W = a specific symmetric spatial weight matrix of order n; and N ;<[;<=(1);]>(;<=(1) ⎡ ( ⎤ <[ < ( ) ]>( < g = ] − h = ] − ⎢;* ; = 2 ; ; =(2)⎥ ⎢ … ⎥ < < >( < ⎣;D [; =(H);] ; =(H)⎦ A probability must be thus determined as well in order to accept or reject the null hypothesis. The equation given below calculates theoretically this probability when the Moran’s I value is less than a given value p (Leung, Mei and Zhang, 2000). 1 1 s t:H t:H [u(v)] o(]1 ≤ q) = − r Jv 2 ` 1 vw(v) Where u(v) = ( ∑D xqyvxH xqyvxH (z v) , w(v) = ∏D (1 + z*v*)1,*| and z = * 0U( 0 0U( 0 0 g<(= − q])g . This equation can be simplified after multiple assumption to the following expression (Leung, Mei and Zhang, 2000): } t:H t:H [u(v)] r Jv 1 vw(v) Spatial Non-Stationality For GWR, the dependent and a given independent variable are linked geographically. In other words, the hypothesis for GWR is that the variables are stationary in a given geographic area. In order to evaluate the efficiency of the model, it might be interesting to test the spatial non- stationality of the variables (Institut national de la statistique et des études économiques, 2018). Technically, the calculation of the variance of the variables for a given variable should be able to give a satisfying answer (Fotheringham et al, 2002): Txq~#9(:) = [(;<=(:);)>(;<=(:)][(;<=(:);)>(;<=(:)]<_* * Where _ = ∑0 (!0 − !X0)/(H − 25( + 5*) However, the theoretical distribution of each variable is unknown leading to a difficulty in using the above method. Thus, another method, the Monte Carlo Simulation, is used to help reject or accept the null hypothesis of the following hypothesis test: H0 : ∀k, βk(u1,v1) = βk(u2,v2) = ... = βk(un,vn) H1 : ∃k, all βk(ui,vi) are not equal. 16 In fact, if there is spatial non-stationality in the studied area, the locations (coordinates) of the observations are irrelevant and changing them will yield the same value of the variance. When dealing with the Monte Carlo Simulation, the geographical coordinates of the observations are permuted n times, finding n spatial variance estimations of the observations. The p-value of the spatial variability of the coefficients is then estimated. This p-value can determine if the null hypothesis should be accepted or rejected (Institut national de la statistique et des études économiques, 2018). Finally, the bandwidth can give an indication of the efficiency and reliability of the model. Its value is very important and when compared with the extent of the studied area can give, even if not precise, important information about the model nay if GWR should be even used in the first place. On one hand, if the bandwidth yields toward the maximum value possible (over the whole studied area), local autocorrelation and spatial stationality are weak and GWR should not be used. On the other hand, if the bandwidth is really small, it is important to check for randomness in the process (Gollini et al, 2015). Geographically Weighted Regression as Forecasting Method Geographically Weighted Regression or GWR, developed by Fotheringham and Charlton in 1998, is a new regression model inspired by the usual Ordinary Least Square (OLS) method regression that, however, takes into consideration spatial dependency when forecasting equations and its parameters. The authors refer to a family of “spatial adjusted” regression. Previous works and fields in use Since its introduction as a spatial data analysis in the late 1990’s, GWR has been used in a large number of areas. From health and healthcare (Zhang, Wong, So & Lin, 2012) and forestry (Pineda, Bosque-Sendra, Gómez-Delgado & Franco, 2010) to real estate (Dimopoulos & Moulas, 2016; Institut national de la statistique et des études économiques, 2018), passing by land and urban space use (Luo & Wei, 2009; Tu & Guo, 2008) and poverty rates (Floch, 2016), GWR has been more and more present in transport science, mainly as an explanatory method. The field of transportation was no exception. Determining the explanatory variables in order to identify potential causes and relations with transportation related issue is the main use today of this relatively new technique. Traffic accidents, average commute distances, transport-land use interaction and influence and public transport share (Chow et al, 2006) are only a couple of fields that were tackled by GWR over the years. In 2015, Qian and Ukkusuri evaluated after a comparison of the performances of the Ordinary Least Square (OLS) and GWR, the causes behind the taxi ridership in New-York city. Liu, Ji, Shi and Gao presented a research on the effect of the built environment on student’s metro commuting to their schools and back home in Nanjing, China. However, ridership forecasting on a station-based level is not developed enough when it comes to utilising the GWR method. A couple of preliminary studies in this field were, nevertheless, presented having mainly as the core subject the comparison of the level of efficiency and reliability between OLS and GWR. In 2015, Chiou, Jou and Yang determined the predictors 17 for ridership data for the state of Taiwan with the help of both OLS and GWR. Another study conducted by Blainey and Mulley in 2013 also determines the predictors for ridership data for railway stations in the Sydney region of New South Wales by also comparing both OLS and GWR methods. Studies in Madrid, Spain, Sydney, Australia and Adelaide, Australia conduct similar studies by examining the local characteristics of their respectable studied areas. They also predict some ridership data with the models that they created (Cardozo, García-Palomares, Javier Gutiérrez, 2012; Somenahalli, 2011; Blainey, Mulley, 2013). Comparison between OLS and GWR As stated above, global regression models, like OLS, assumes that the relationship between the dependent and independent variables are uniform over the study area, ignoring spatial characteristics such as distances to stations. OLS does not consider variations due to spatial autocorrelation (Fotheringham, Brunsdon and Charlton, 2000; Lloyd and Shuttleworth, 2005; Cardozo, 2012). In 2010, Harris et al. compared multiple methods, mainly variations of Kriging, multiple regression methods and GWR and concluded that GWR-based models out-performed MLR models. Previous studies that have focused on comparing OLS and GWR methods have frequently discovered that GWR provides more predictability than GWR due to this concern for spatial correlation. In fact, according to Hadayeghi, Shalaby and Persaud, estimation errors are smaller in a majority of cases when using GWR compared to OLS. They explain this result by claiming that the problem of spatial autocorrelation is reduced nay eliminated. This is the case for Cardozo, García-Palomares and Javier Gutiérrez when, in 2012 they compare station-level ridership forecasting between the OLS and GWR methods. Their analysis of the residuals proved better results with GWR than with OLS. In addition, when comparing Moran’s I values that were calculated, the one generated for GWR was closer to the expected value than the OLS one, concluding that spatial autocorrelation was reduced. In this same study, GWR performed better with p-values and z-values, describing less variance and greater likelihood for random distribution. Another study, already presented above, compares a global regression model with GWR in Taiwan and found an adjusted R-Squared for GWR more than 0,2 units higher than the traditional MLR model in addition to a better performance with regards to spatial autocorrelation for the GWR model (Chiou, Jou and Yang, 2015). Zhao et al. also, in 2005, found a better prediction performance with GWR with regards to OLS for the county of Broward, Florida. Predictions using GWR compared to other methods With the establishment of the formulas and equations for each observation, one can use the calculated coefficients to analyze how relationships vary across the studied area and study any possible patterns they might create. These coefficients can provide local understanding of the observed dependent variable (Fotheringham et al, 2002). In fact, these coefficients, seeing that they are localized, can provide information on the influence of changes in the station’s direct 18 environment will have on the dependent variable, in this case station-level ridership. Any evolution of population, jobs or even land use can provide detailed and specific information for the station. This leads to a more accurate and detailed forecast, compared to a generalized forecast with standardized coefficients for the whole studied region when dealing with global regression models (Lloyd, 2010). The model(s) can be evaluated over the whole studied area, determining the areas with better fits, variations of estimated coefficient and significance. Any future development, such as new residential buildings or workplaces can be thus evaluated independently for each station environment and area. In fact, for example, an increase in the number of jobs in one area can lead to an increase in ridership while in another it can have the opposite effect. This is where localized policies and plans, land-use for example, come in action and can be implemented, with more insurance and less risks with these more realistic predictions, in the area in order to improve ridership and/or the level of service of the station and/or public transport network. De Smith et al. (2009) call in “place-based” techniques. GWR can also be used in predicting models in areas where dependent variable observations are not available. The use of approaches based on the use of “Best Linear Unbiased Predictors (BLUP) estimators is more and more common nowadays (Chambers and Clark, 2012). This method is based on the replacement of non-observed dependent variables by predicted values thanks to a model where the parameters are estimated from observed dependent variables. Recent literature seems to prefer the use of GWR in estimation methods rather than methods originated from other methods. The fact that GWR considers spatial heterogeneity is regarded as theoretically improve the precision of the estimators. Floch presented in 2016 at the JMS (Journée de Méthodologie Statistique) a study of Rennes’ Iris zones where they wanted to predict the number of households with low incomes in areas of the city that was not observed. For that reason, and having the number of households beneficiation from free health care due to low incomes in all the studied area, they calculated first the GWR models for all the observed Iris zones determining the equations. 19 Figure 5:100-meter squares in Rennes, sampled in red (Floch, 2015) Each Iris zone is divided in 100-meter squares. Presenting the notation used, y represents the number of people with low income, x is the number of people having free health care. In U, all squares (N=2141) are assigned their coordinates, the number of low-income people, the number of people with free health care and the Iris it belongs to. A sample s of n/N=40% is selected. r is the complement of s in U where all yi’s are known in i ∈ s and xi are known for all squares in i ∈ U. In order to determine the predicted number of households with low incomes, three different estimation methods (Horvitz-Thompson, the classic regression one and the GWR one respectively) were calculated. Determining K=1000 estimators by Iris, the relative quadric average error of Monte Carlo estimation is calculated before calculating its square root (RCEQMR). ã >( 8 * ÑÖÜ ávà/(G)â = ä 7 (và/(G) − v/(G)) 8U( åÑÖÜ ávà/(G)â dSÑÖÜd ávà/(G)â = v/(G) 8 Where và/(G) is the estimator for the total of the variable y of the Iris j and the simulation k. 20 Figure 6: Box-Plot of the RCEQMR for the Horwitz-Thompson (1), repression (2) and GWR (3) estimators (Floch, 2016) One can realize that the best outcome was the GWR estimation. In fact, with a RCEQMR of 0.4, the Horwitz-Thompson estimator was the least performing of the three. The RCEQMR of both the “classic” regression and the GWR estimators are quite similar with 0,178 and 0,156 respectively. This is where the box-plot gives more information about these two RCEQMR showing a smaller spread regarding GWR. It can be thus safely said that the results showed the GWR estimator as the best compared to the other methods. Methodology A precise and extensive methodology was developed in order to determine the GWR equations for each station, for present as well as future conditions. The software used is ArcGIS (ArcMap). The first step is to choose a line to investigate thoroughly. In fact, even if evaluating the whole network would also yield interesting findings, limited time and resources constrained to selecting one specific line. The next step is to gather the data needed to produce the analysis, required by the candidate variable such as population, income, age, type of station and distance to the center of the network. Having gathered all the data needed to create both OLS and GWR equations, catchment areas (or service areas) around each metro station were defined. In fact, a catchment area is considered as the area around the station where the walking distance to the station is 800 meters or less, representing 10 minutes or less of walking time. This number was determined after previous literature and research review. It was evaluated that a station’s “neighborhood” or the 21 willingness distance to walk to and from a rail (and thus a metro) station is 800 meters (O’Neill et al., 1992; Hsiao et al., 1997; Murray, 2001; Zhao et al., 2003; Kuby et al., 2004; Sallis, 2008; Gutiérrez et al., 2011). In 2008, Gutiérrez et al. proved that network distance provides better estimates than Euclidean distances. Following this reasoning, determining the 800-meter catchment area following the road network around the respective stations was executed. It was also proven that riders are more willing to walk a larger distance at end stations. Figure 7: Catchment Area (Service areas) for each station (old stations in beige, new stations in purple). New station names are also presented on this map. T-Centralen is present here and on all following map by a black point for orientation. At some locations, mainly in the central area of the urbanized region and of the network, the dense metro network lead to stations being situated at less than 1600 meters, meaning that an overlap in catchment areas is unavoidable. Following the reasoning described above, possible riders have more than one station to choose from within walking distance in order to travel. In order to avoid double counting when determining the equations and forecasting the ridership and following the steps of various previous studies, Thiessen polygons as catchment areas were generated for these special cases, meaning that possible riders always choose the closest stations at walking distance (Cardozo et al., 2012; Zhang and Wang, 2014). This method is also reinforced by Wardman’s 2004 study in Manhattan that suggest that riders are more likely to choose the closest station due to a higher out-of-vehicle value a time compared with in-vehicle value of time. The next step is to determine the significant variables from the previously presented candidate variables as well as the best OLS equation. In fact, ArcGIS permits the evaluation candidate variables by creating OLS regression equation. The most significant equation is chosen in order to proceed with the analysis. The choice is made after comparing the significant indicators such as p-value, R-Squared, the variance inflation factor and the global Moran’s I p-value. Moran’s 22 I is also performed individually on each candidate variable determining the most significant variables with regards to spatial correlation. Using ArcGIS, the now determined OLS equation is used to forecast ridership for the whole network, at the future stations that are being built, as if they were existent today. Even if these ridership computations are completely hypothetical, they are necessary in determining GWR equations for these stations (and all station more generally). In order to formulate GWR equations, the weight function must be determined. Multiple functions are adequate for the job, however, according to Zhao et al. in 2005, adaptive kernel does not have a limited number of observations meaning an advantage for observation on the limits of the study area. Having the knowledge of all dependent and independent variables on the whole system for 2016 including the hypothetical ridership for the new stations on the blue line as well as the most adequate weighted function for the presented situation, GWR equations can be computed by ArcGIS for all stations on the blue line for current conditions. These different equations are then evaluated and compared with regards to significance and goodness-of-fit using R2, AIC, p-value and t-test methods with regards to the previously computed OLS equation. Having the GWR equations for the whole network, the chosen line with its new stations is isolated and updated with the predicted data for the time of prediction in question. Depending on the variables that were chosen, the data needed would be different. Some data might be lacking. Some assumptions can thus be made in order to remedy this. Population data, when detailed estimations are lacking, can be determined by multiplying the official number of apartments planned to be built by the average number of persons per household. When this is also lacking, the projected evolution of the population in the region can be used for the service areas. Regarding workers, they can be obtained by multiplying the population by a ratio Population to Workers determined by the stations’ equivalent stations (stations that are present today in the network with similar characteristics to a future stations). Regarding the median income, a trend line is determined from past statistics and interpolated into the time of prediction. The change in land use incorporated and updated to the state of the time of prediction should also be considered. Other information is assumed to remain unchanged from today. 23 Figure 8: Service Area for the Blue Line Station to be predicted for 2030 Having determined the ridership according to GWR models, ridership is compared to official forecasts and analyzed. Finally, each new station is evaluated with regards to its GWR model and the ridership it forecasted with regards to the official forecast. The determined parameters can help determine policies that can be proposed. For instance, the choice of building new apartments in specific areas can also be analyzed and other areas, not considered, can be proposed. Stockholm’s Case Study and Data Collection The following section presents the present metro situation in Stockholm as well as the plans for a future extension of this current network. It also presents the data collected through candidate variable that can explain the ridership for current and future states. Stockholm’s Metro System: Present Situation, Forecasting and Future Development Stockholm’s metro network developed over the years starting in the 1950’s to become a complex start network with T-Centralen in its core. Forecasting for the ridership has been done using a special model, Sampers, developed by Trafikverket, the transportation authority in Sweden. This model has been used in preliminary studies to forecast the ridership on stations and lines to be constructed by 2030. Stockholm today with ridership and population In the 1940s, Sweden decided to build a metro network in its capital, even if, at the time, the number of inhabitants of Stockholm did not technically require, this new form of public 24 transportation. The green line in the 50s, the red one in the 60s and the blue one in the 70s were constructed with gradual extensions over time. Today the system welcomes almost a million passengers every day (MTR, 2018). This number is expected to increase by 170 000 in 2030 (Stockholms läns landsting, 2016). In fact, Stockholm is expected to welcome between 30 000 to 35 000 new residents every year until 2030, making it the fastest-growing European capital. The last seven years saw a growth by 250 000 people in Stockholm county. The current capacity of the network would not sustain this influx of new residents. In addition, Stockholm is facing, with the rest of Sweden, a housing scarcity problem. The official rent-controlled queue has around 500 000 people waiting in line for an accommodation. The average waiting time is nine years with some neighborhoods having an average time up to 20 years. For this reason, Stockholm’s city council is backing the construction of 40 000 new permanent homes by 2020 and 100 000 more by 2030. Movable modular homes and a big co- living space for global entrepreneurs are also considered to be adopted to ease the housing problem (Savage, 2016). For these reasons, Stockholm has decided to expand and enlarge its public transportation network, namely its metro network, constructing new housing next to these new stations. Preliminary studies with Sampers for Stockholm’s new station Preliminary studies were done starting from 2007 and were updated continuously with the progression and direction the metro expansion project took. The forecasting part and projection of ridership for the new completed network by 2030, including these new stations were determined thanks to Sweden’s national model system, Sampers. According to Trafikverket’s website, updated in 2018, it uses a cross-sectional analysis for determining future passengers and traffic volumes for different scenarios. Its main variables are GDP, fuel prices, employment and population growth. In addition to forecasting new ridership or/traffic flows, Sampers provides impact assessments and investment calculations for land-use or transport changes such as new residential project or infrastructure project for possible transport policy measures. According to Prognos över resandeutveckling for both the extension of the blue line and the construction of the new yellow line, the traffic analysis for 2030 was executed using both PTV Visum and Sampers. Ridership was thus found using these methods. However, the report presenting the results for the yellow line presents limits for PTV Visum. In fact, “VISUM is a generalizing model that includes the whole Stockholm län and whose strength is, first, providing a general analysis”. It continues in warning that detailed analysis of the results should be done in caution. Equivalent present stations to potential stations during the preliminary analysis has been determined by WSP in its Effekter på värdet på handelsfastigheter vid etablering av nya 25 tunnelbanelinjer i Stockholmsregionen report. The following table presents the equivalent station of the selected stations of the blue line: Table 1: Equivalent Present Stations for Future Stations (WSP Analys & Strategi, 2013) Station Equivalent Station Equivalent Station Station Kungträdgårde Hötorget Järla Västra Skogen n (New) Sofia Mariatorget Nacka Solna Centrum Hammerby Alvik Barkerbystaden Farsta strand Kannal Sickla Järla Barkerby Farsta Strand Station General idea with map of the planned extension As explained above, the new stations will be built on two different lines: the blue line and a new yellow line. Figure 9: Metro network with the additional stations in dashed line. Notice that the current arm of the green line towards Hagsätra will be integrated to the blue line by 2030 (Stockholms läns landsting, 2016) On one hand, the blue line, already existent, is facing an extension from both sides. In the north, a small extension will see the line grow by two stations after Akalla, Barkarbystaden and Barkarby. It is in the south that the extension is going to be significant with the addition of five new stations: Sofia, Hammarby kanal, Sickla, Järla and Nacka. In addition, at Sofia, the blue line 26 is splitting in two different branches, one that goes until Nacka passing by all the named stations and another that is connecting to the present green branch to Hagsätra at Gullmarsplan, turning it blue. The new station, Slackhusetområdet, is replacing the present Globen and Enskede gård stations (Nylén, 2017). The below figure XX presents the forecasted ridership on the whole line, with an obvious emphasis on the new parts of the line. Figure 10: Projected ridership on the blue line during the morning peak hour with a four-minute headway (Nylén, 2017; Harders and Björkman, 2016) On the other hand, the yellow line is going to be built from scratch from Odenplan to Arenastaden, with two stations between them, Hagastaden and Södra Hagalund. After Odenplan the line is joining the green line continuing to either Farsta Strand or Snarpnäck. The figure below (Figure XX) present the ridership between Odenplan and Arenastaden. It is important to note however that the ridership presented here was determined with the assumption that Odenplan is the terminal station and with a line having only three stations instead of the current four (Harders and Björkman, 2016). In fact, the decision to change the initial assumptions was made in 2017. 27 Figure 11: Predicted ridership on the yellow line during the morning peak hour by 2030. The upper graph represents the ridership heading towards Odenplan and the lower one heading towards Arenastaden. Legend: Dark red: Boarding with a five-minute headway, Pink: Boarding with a 10-minute headway, Dark blue: Alighting with a five minute headway, Light blue: Alighting with a 10 minute headway, Bold line: Load for a 5 minute headway, Light line: Load for a 10 minute headway (Harders and Björkman, 2016) Transit-oriented development: Stockholm Case Study There have been multiple studies drawing a connection between transit use and Transit- Oriented Development (TOD). In Stockholm, the planned construction of multiple residences as well as workplaces around not only the new stations but current stations show the interest of Stockholm’s policy makers in TOD. By definition, TOS is the development of urbanized neighborhood where transit is easily accessible. Mixed land use as well as pedestrian oriented mobility in such regions is a core aspect in addition to a densely designed roads and buildings (Zhao et al., 2005). Even if no clear conclusion can be drawn, some studies, like the one done by Parker et al in 2002, show transit ridership can be increased by up to 40% at individual stations after TOD was implemented around them. A case study of Portland asserts this finding after a survey in 1994 concluded that transit share is higher and car ownership lower in TOD in comparison to traditionally developed neighborhoods (Lawton, 1997). 28 With regards to Stockholm län a goal of 140 000 new residences by 2030 is shared among the different municipalities, mainly Nacka, Järfalla and Solna as the latter will have the new stations built within their municipal boundaries. A total of 78 000 of these new residences will be built around these stations (Stockholms läns landsting, 2016). For example, around the future Hammerby Kannal station, around 2140 residences and a total of 73 000 square meters of new locals and offices will be built (Stockholm växer, 2018). However, in order to strengthen and increase the share of transit in the region, existing stations like Kista, Rinkeby and Kristineberg will also see a densification of their neighborhoods with additional residences and workplaces. As an example, the area around Kista will see the construction of a 1600 new residential building and a couple of new office buildings. These projects are intended to densify and diversify, if not already present TOD’s, potential one in order to increase the share of transit in the whole Stockholm region in general and more specifically, lead to relatively high transit use around future stations. This is where GWR comes in. In fact, according to Somenahalli, in 2011, GWR were better in developing the relationship between transit use and TOD’s. Data and Candidate Variables Line chosen The blue line was selected to be investigated in this case. There are mainly two reasons behind this bias. On one hand, the fact that the blue line is indeed expanding greatly, will thus allow the careful analysis and discussion over both old and new stations, discarding both green and red lines. On the other hand, even if one can consider the newly constructed yellow line as part of the green line, the preliminary studies were conducted as if the line would end at Odenplan with a missing station leaving behind problematic results for this study. The complexity and uncertainty of the newly constructed green line regarding, for example, headway, the number of stations and the number of branches were also additional reasons that favored the use of the blue line for this study. All stations, as explained in the methodology were assigned an 800-meter service area each, except for terminal stations, in this case, Nacka Barkarby Station and Hjulsta where they were assigned a 1000-meter service area each. Candidate Variable The choice of candidate variables was established thanks to studies while insuring the logic with the case in hand, i.e. Stockholm. The dependent variable will be the number of boarding passengers at each station during the morning peak hour, meaning between 7:30 and 8:30. This criterion was selected as a simple goal to be able to compare predicted data from the model developed here with official predictions. The present (2016) data was available in the yearly published report by SL, AB Storstockholms 29 Localtrafik: SL och ländet 2016. This data is the base for the OLS and GWR equations developed for forecasting and evaluation for 2030 situation. Multiple independent variables were chosen in order to explain the ridership starting with the socio-economic factors and ending with accessibility ones. Population, income, age distribution and workers for 2016 were all acquired from the Läntmateriet and GeoData Portal website, respectively the official Swedish authority in gathering statistical and infrastructural information and the website where this information is published. Both these websites make this data public for research purposes. This data sets were already divided into small area, called SAMS in the data. The road network was found on NVDB website. It provided the road network for the whole Stockholm Län. Finally, the metro network for 2030 was provided by Torbjörn Ekerot and Henrik Sarri, respectively an IT-manager from SLL and Metria. The shape file had also the network of the other mode of public transport for the county, such as the bus network and stops as well as the commuter rail (pendeltåg) network and stops. It also assigned each station, present and future, if it is to be considered a significant changing point, a regional one, or not at all. The latter information was taken as a base to determine the type of change that takes place at each station. Unfortunately, detailed land use was only available for current state and only for the municipality of Stockholm. It was thus disregarded as a candidate variable. The first explanatory variable is the density and size of the population living around the stations. According to Messenger and Ewing in 2007, the relationship between the public transport ridership and population density, even if not direct, exists and is regularly used a factor to justify transportation station expansion or upgrades. Multiple other authors have also asserted the existence of this relationship (Javier Gutiérrez et al, 2011; Sekhar Somenahalli, 2011). In 1996, Seskin et al. presented sufficient evidence to establish a positive relationship between the two. The second potential explanatory variable is the number of workers around a station. In fact, even if one can easily hypothesis and deduce it from what was explained with the population explanatory variable, Murray et al. (1998) discovered that the more workers live around a transit service the greater the probability of the latter will be used. The third potential significant variable is the income of the population respectively to where they live. In fact, it was used in Chow et al., in 2006 and proven to be a significant variable. In addition, an increase of income in specific areas leads to a decrease in transit use for the benefit of the car (Gómez-Ibáñez, 1996; Wachs, 1989; Kitamura, 1989). The fourth but last socio-economic variable considered is age. In fact, multiple previous studies (Cristaldi, 2005) consider it and even incorporate it in their respective models like in Bernetti et al, in 2008. Age groups can be created, with the first one between 0 and 19 years old, representing mainly the minor, non-active and unlicenced population, the second between 20 and 64, representing the active population and possibly licenced population and the last third group from 64 onwards representing the retired population. These groups were defined accordingly given the available data for Stockholm and the way the age groups are defined in previous literature. 30 The fifth candidate but first accessibility variable is road density. It was used in multiple previous studies such as Cardozo et al in 2012 and Zhao et al in 2005. In fact, road density can determine to a certain extent the accessibility of the metro station and consequently the number of alternatives to reach this station leading to a shorter and easier reach with high road density. The sixth one would define the number of bus lines in a 200-meter radius around each station. A study in 2004 by Kuby et al discovered a connection between feeder modes, for instance bus stops or bus lines accommodating a specific station and ridership at the station in question. The seventh candidate variable is the type of station itself one is dealing with, mainly with regards to terminal stations and change and transfer stations. The first type of stations tends to attract residents for larger areas than intermediate stations due to the fact that this station is the closest one to the network inclining riders to walk more than for other stations (O’Sullivan and Morral, 1996). The second type of stations attracts more riders than normal stations (Gutiérrez, Cardozo and García-Palomares, 2011). In fact, be it an interchange station or an intermodal one, they both usually have higher boarding than non-interchange non-intermodal stations. Dummy variables for both these kinds of stations can be used as it was done in Kuby et al, in 2004. The last accessibility and eighth candidate variable is the commuting distance to the central business district (CBD) or the central region of the network. In Stockholm case, T-centralen was assumed to be the central point of the network, being the start of the star network system of Stockholm and where all line meet. This was chosen after studying both the papers of Pushkarev and Zupan (1982) and Kuby et al (2004) where it was defined that passengers usually commute to the central part of the network, especially during the morning’s peak hour to reach their places of work. Finally, the last candidate variable is the land use around the station. According to multiple studies, such as the ones by Parsons Brinckerhoff in 1996, land use plays a role in transit ridership. In a study by Bhat and Gossen in 2004, an equation was developed in order to quantify the type of land use present in the area of interest, categorising land use in three different groups: residential, commercial/industrial/office and other types. 31 The value ranges between 0 and 1 with 0 being no land use diversity and 1 being perfect land use diversity. This equation was used in the study as multinomial logit model variable for the San Francisco area. Prediction assumptions for the candidate variables When the predictions are made, these assumptions are taken for the following independent variables. Regarding the population data, lacking detailed and precise number of inhabitants around the stations, except for Barkarbystaden and Barkarby Station where the exact number of inhabitants is known, the number of apartments planned to be built by 2030 are multiplied by the average number of persons per household. An increase in the population of 5% and this according to RUFS (Regional utvecklingsplan för Stockholmsregionen, 2010) is done on remaining stations where there is a lack of information with regards to specific population evolution and the number of apartments. Workers also lack detailed predictions. They are thus multiplied by a ratio Population to Workers determined by the stations’ equivalent stations, presented in an earlier part. Regarding the median income, a trend line is determined from past statistics and interpolated into 2030. Other information is assumed to remain unchanged from today. Results The main results are split into two parts, the first being for present conditions where the GWR equations were determined for the blue line and the second presenting the results and ridership by station for 2030. GWR Equations with Existing Conditions The presented candidate variables were analyzed on ArcMap using a tool called Explanatory variables. Table 2: Candidate variables evaluation and selection (AdjR2 is Adjusted R-Squared, AICc the Akaike's Information Criterion, p- value the Koenker Statistic p-value, VIF the Max Variance Inflation Factor and the variable’s significance at 0,01 is in yellow) Number Highest AICc p- VIF Model of AdjR2 value Variable s 1 of 11 0,33 1552,13 0,01 1,00 Bus 0,23 1565,55 0,10 1,00 Workers 0,22 1566,38 0,09 1,00 Age 2 2 of 11 0,47 1530,64 0,01 1,04 Workers Bus 32 0,46 1531,71 0,01 1,04 Age 2 Bus 0,45 1534,35 0,01 1,04 Pop Bus 3 of 11 0,52 1522,11 0,00 1,33 Workers Bus Change 0,51 1524,02 0,00 150,46 Pop Age 2 Bus 0,51 1524,07 0,00 1,32 Age 2 Bus Change 4 of 11 0,56 1515,00 0,00 150,49 Pop Age 2 Bus Change 0,54 1518,24 0,00 7,65 Age 1 Age 2 Bus Change 0,54 1518,46 0,00 38,62 Pop Workers Bus Change 5 of 11 0,56 1514,84 0,00 152,03 Pop Income Age 2 Bus Chang e 0,56 1514,89 0,00 162,54 Pop Age 2 Buses Change Dist 0,56 1516,48 0,00 308,66 Pop Workers Age 2 Bus Chang e Table 2 presents ArcGIS’s explanatory variable analysis in which the software analyses all giving variables, in this case all candidate variables. The analysis presents each possible equation for a specific number of variables in these equations in function of the three highest adjusted R- Squared. It also provides a multicollinearity table in which it presents each candidate variable’s covariates. The table goes even forward in explicitly stating that a combination of variables was not possible due to perfect multicollinearity. Table 3: Summary of Multicollinearity Variable VIF Violation Covariates s Pop 577,62 321 Workers (98,47), Age 1 (93,13), Age 2 (93,13), Age 3(93,13) Worker 222,84 309 Age 2 (98,47), Age 3(98,47), Pop (98,47), Age 1 (54,96) Inc 3,44 0 33 Age 1 46,83 201 Pop (93,13), Age 2 (77,10), Workers (54,96), Age 3 (38,93) Age 2 770,17 312 Workers (98,47), Age 3 (93,13), Pop (93,13), Age 1 (77,10) Age 3 31,80 279 Workers (98,47), Age 2 (93,13), Pop (93,13), Age 1 (38,93) Road 1,09 0 density Buses 1,55 0 Terminal 1,14 0 Change 1,40 0 Distance 3,35 0 The following table presents the number and percentage of equations generated and passed according the presented criteria. Table 4: Percentage of Search Criteria Passed Search Cutoff Trials # Passed % Passed Criterion Min Adjusted > 0,50 1015 115 11,33 R-Squared Max Coefficient < 0,05 1015 69 6,80 p-value Max VIF Value < 7,50 1015 417 41,08 Moran’s I test was also done in order to evaluate autocorrelation with regards to ridership. The following table presents the outcomes as well as the estimated Moran’s I value. Table 5: Moran’s I tests on the Dependent and Candidate Variables Variable Moran's Expecte Varianc z-score p-value Pattern Index d Index e Ridership 0,019397 - 0,00308 0,533356 0,593787 Clustered 0,010204 Population 0,513214 - 0,00463 7,69199 0 Clustered 0,010204 34 Age 1 0,375009 - 0,005029 5,435004 0 Clustered 0,010204 Age 2 0,548009 - 0,004924 7,957756 0 Clustered 0,010204 Age 3 0,675734 - 0,003933 10,929235 0 Clustered 0,010204 Workers 0,551187 - 0,004596 8,28109 0 Clustered 0,010204 Med Inc 0,659357 - 0,004869 9,5952 0 Clustered 0,010204 Road 0,268342 - 0,004724 4,052722 0,000051 Clustered Density 0,010204 Buses 0,149382 - 0,004242 2,450214 0,014277 Clustered 0,010204 Change -0,08105 - 0,004801 -1,022436 0,306575 Random 0,010204 Terminal 0,009537 - 0,004629 0,290162 0,771692 Mixed 0,010204 Distance 0,872311 - 0,005166 12,281491 0 Clustered 0,010204 The best fit was determined to include the number of workers in the station’s proximity, the type of station when it comes to changes and the number of bus lines in a 200-meter radius. However, the initial equation presented both the p-value and the t-value of the number of workers insignificant. Plotting the ridership as a function of the number of workers, it was shown that T-Centralen, Slussen and Gullmarsplan were in all of them huge outliers and when out of the data, the worker variable is significant with an R-Squared of 0,02166 before removing them and 0,23722 after removing them. It was thus decided not to include these three stations in future studies both for OLS and GWR. 35 16000 14000 12000 10000 8000 Ridership 6000 4000 2000 0 0 2000 4000 6000 8000 10000 12000 Workers Ridership with Outliers Ridership without outliers Linear (Ridership with Outliers) Linear (Ridership without outliers) y = 0,1758x + 1006,7 y = 0,2083x + 619,99 R² = 0,0283 R² = 0,236 Figure 12: Ridership vs. Number of Workers (R-Squared values show a better fit when T-centralen, Slussen and Gullmarsplan are taken out of the expression) After taking these outliers out, both OLS and GWR analysis were executed again leading to the following residual maps. 36 Figure 13: OLS (up) and GWR (down) Standard Deviations 37 The significance of the OLS parameters as well as for both equations are presented in the following tables. Table 6: OLS Equation Variables Coefficients Standard t-Statistic Probability VIF Error Intercept -552,050799 351,437275 -1,570837 0,119624 - Workers 0,311537 0,054621 5,703612 0,000000 1,044079 Buses 88,258312 18,137573 4,866049 0,000005 1,327416 Change 1038,326730 283,930296 3,656978 0,000429 1,277995 Number of 97 Observation Number of 4 Variables Adj R- 0,546342 Squared Residual 33224590,80 Square 8728 AICc 1631,798893 Table 7: GWR Equations Variables Minimum Maximum Mean Standard Deviation Intercept -2446,301797 657,6131415 -563,7553011 716,045689 Workers -0,004097741 0,258132412 0,149459243 0,050484 Buses -2,954762007 88,47400346 39,9531998 23,725989 Change -130,9206048 2793,393959 883,5952445 738,663661 Number of 4 Variables Number of 42 Neighbors 38 Adj R- 0,683548 Squared Residual 16766876,58 Square 66 AICc 1500,09803 Looking at the maps, one can see different cluster in the OLS residual map that were reduced nay sometimes corrected in the GWR residual map. Looking closely at the value, one can safely say that the GWR has a higher predictability with an overall adjusted R-Squared of 0,68 compared to 0,55 for the normal OLS model. In addition, the residual square is almost half for the GWR model compared with the OLS one. It is important to specify that when the OLS equation was determined, ArcGIS launched a warning stating that the model should be checked for spatial autocorrelation, hinting that a spatial independent model might not be the best fit. This was proven with both Moran’s I test as well as the comparison between the OLS equation and GWR ones. The OLS equation was thus used in order to predict the ridership at the new stations for current situation. The following table presents the predicted ridership. Table 8: Predicted Ridership using OLS Equation for New Station in 2016 Station Predicted Ridership Nacka 2940 Järla 1053 Sickla 1118 Hammarby Kannal 1854 Sofia 2026 Barkarbystaden 265 Barkarby Station 608 The following map show the overall standard deviation of residual when GWR equations are calibrated for the new stations with this OLS estimated ridership. 39 Figure 14: GWR Standard Deviation with New Stations The coefficients of the GWR equations as well as their significances are presented bellow. Table 9: GWR Equations with the New Stations Variables Minimum Maximum Mean Standard Deviation Intercept -2367,47257 625,462321 -570,298174 670,481597 Workers 0,009195 0,24977 0,151743 0,043329 Buses 7,585861 86,22674 42,060432 19,308832 Change -120,334075 2667,703535 873,7549 688,076229 40 Number of 4 Variables Number of 46 Neighbors Adj R- 0,69915 Squared Residual 17569889,26 Square 64 AICc 1600,959011 Predictions Using the Determined GWR Equations Having determined the GWR equations, future ridership can be thus determined. The future number of workers in the respective station’s service area should be thus determined. For the presented stations, the number of planned residences has been multiplied by the average number of persons per household. The average number of persons per household depends on the municipality and is respectively 2,12 and 2,47 for Stockholm and Nacka in 2018 (Statistiska centralbyrån (SCB), n.d.). Each new station’s equivalent station is also presented as well as the ratio Population to Workers. Finally, this ratio is multiplied to the number of people living in the area, leading to the additional number of workers living in the area. Adding these numbers to the current number of workers in the area gives the information needed to input into the equation. Table 10: Number of Additional Population and Workers by 2030 (*Note: For Barkarbystaden and Barkarby Station, the total population and the number of workers is presented) Station Number Househo Additional Equivalent Ratio Additional of ld Population Station Pop/Wor Workers residence s Nacka 6500 2,47 16055 Solna 0,540875 8684 Centrum Järla 950 2,47 2347 Västra Skogen 0,462653 1086 Sickla 2000 2,47 4940 Liljeholmen 0,555743 2746 Hammerb 2140 2,12 4537 Alvik 0,577865 2622 y Kannal Sofia 155 2,12 329 Mariatorget 0,580132 191 41 Kungträd- 0 2,12 0 Hötorget 0,563254 0 gården Fridhems- 134 2,12 285 - 0,612255 174 plan Stadshage 1975 2,12 4187 - 0,630363 2640 n Rinkeby 1100 2,12 2332 - 0,294039 686 Tensta 1030 2,12 2184 - 0,347523 759 Kista 1600 2,12 3392 - 0,467844 1587 Akalla 1000 2,12 2120 - 0,443841 941 Barkarby- - - 4946 Farsta Strand 0,462653 2288 Staden* Barkarby - - 1755 Farsta Strand 0,462653 811 Station* Regarding Barkarbystaden and Barkarby Station, the future number of residences is already known by SAM. Adding the population to each service area by proceeding in the same manner done for the current situation, one can proceed in multiplying this population data by the ratio Population to Workers and getting the number of workers in the service area. Remaining stations on the blue line where no significant information has been found saw an increase of 5% of its worker’s population and this according to RUFS’ estimated increase of the population by 2030. T-Centralen’s service area remained untouched, however. Using the GWR equations, the ridership of the chosen blue line stations is predicted. The following table presents the GWR equation for each station as well as the final determined ridership. Having all the needed data and statistics, a deep analysis and discussion of these results is discussed in the following section. 42 Table 11: Coefficients and GWR Estimations for New Stations Name Intercept Worker Bus Change Predicted by Predicted by Coeff. Coeff. Coeff. GWR SLL Nacka - 3000 587,71361 36,517037 949,625133 32 0,13881581 07 7 4200 Järla - 600 514,98852 0,14376295 38,812961 844,623781 84 6 65 4 1169 Sickla - 800 628,53274 0,15307304 36,370452 942,764456 11 8 15 8 1444 Hammarby - 1200 Kanal 1667,6785 0,17223955 21,962985 2007,36610 14 6 43 6 2298 Sofia - 1600 1487,5451 0,16621622 18,791536 1860,82295 22 7 61 4 1632 Barkarbyst - 2300 aden 6,7022540 0,12151317 52,664246 282,178624 07 6 18 6 554 Barkarby - 1200 station 28,110621 0,11704238 54,708347 306,278404 92 7 43 3 701 After looking at the results, one can see that the ridership predicted for Barkarbystaden and Barkarby Station were very much under predicted, less than a quarter of the official prediction for Barkarbystaden. For this reason, the way the workers were determined for these two stations was reevaluated and calculated the same way it was done for other stations with information about the number of planned residences to be built by 2030. The following table shows the newly calculated additional workers. 43 Table 12: Number of Additional Population and Workers by 2030 for Barkarbystaden and Barkarby Station Station Number Househo Additional Equivalent Ratio Additional of ld Population Station Pop/Wor Workers residence s Barkarby 16593 2,42 40156 Farsta Strand 0,46265 18578 staden Barkarby 5078 2,42 12289 Farsta Strand 0,46265 5686 Station Recalculating the ridership for these two stations, the final ridership predictions for all stations new stations are as presented below. Table 13: Coefficients and GWR Estimations for New Stations after the change in workers Name Intercept Worker Bus Change Predicted by Predicted by Coeff. Coeff. Coeff. GWR City Nacka - 3000 587,71361 36,517037 949,62513 32 0,13881581 07 37 4200 Järla - 600 514,98852 0,14376295 38,812961 844,62378 84 6 65 14 1169 Sickla - 800 628,53274 0,15307304 36,370452 942,76445 11 8 15 68 1444 Hammarby - 1200 Kanal 1667,6785 0,17223955 21,962985 2007,3661 14 6 43 06 2298 Sofia - 1600 1487,5451 0,16621622 18,791536 1860,8229 22 7 61 54 1632 Barkarbyst - 2300 aden 6,7022540 0,12151317 52,664246 282,17862 07 6 18 46 2566 Barkarby - 1200 station 28,110621 0,11704238 54,708347 306,27840 92 7 43 43 1342 44 Analysis Analyzing the predicted ridership for the new stations, one can see that they are, generally overestimated compared to official results, thus with regards to the Sampers model used in Vissum. This can be explained by multiple reasons both general, regional and station specific and the assumptions behind them. Division between the North and the South One can see a clear schism between the north stations (Barkarbystaden and Barkarby Station) and the south stations (Sofia, Hammerby Kannal, Sickla, Järla and Nacka). The first mentioned have ridership estimates that are close to the estimations made by SLL, even if slightly over estimated. However, it is important to stress that the models of the northern stations has been developed with only one ridership that was predicted by the OLS model while in the southern station’s models, this number is definitely higher, especially when moving further away from the center of the study area towards Nacka. The Model in Numbers The model’s coefficients are very broad and different. Looking into the intercepts, stations like Sofia and Hammerby Kannal have values well below the average of -570 with -1487,54 and -1667,67 while the stations in the north (Barkarbystaden and Barkarby Station). Figure 15: The distribution of the intercept over the studied area (from the lowest in blue to the highest in red; this applies to all distributions to follow) 45 Looking into the workers coefficients, these values seem to decrease the further one moves away from the city center towards the end of the lines. This means that, at least for the blue line, the further one goes from the city center, the less workers use the metro to get to their respective places of work. Figure 16: The distribution of the worker’s coefficients over the studied area Looking into the bus coefficient, south stations have values below the average of 42,06 with respectively from Sofia to Nacka, 18,79, 21,96, 36,37, 38,81 and 36,52. With regards to northern stations, they are slightly above average with respectively 52,66 and 54,70 for Barkarbystaden and Barkarby Station. The same pattern can be observed than the one observed for workers, yet inversely. In fact, the farther the station is compared to the central area the greater the bus coefficient influences the estimated ridership. This is quite common for metro network, especially star network like the one in Stockholm: in central area the dense metro stations presents does not present the need to use buses to get to a specific station while the further one goes from the center, the lower the density of metro stations, leading to the use of buses to reach these stations. 46 Figure 17: The distribution of the bus’s coefficients over the studied area Looking into the change coefficient, the station in the north have coefficients that are below average while the south stations have coefficient above the 873-mean value. The same pattern can also be deduced. The change coefficient in stations in the central part of Stockholm increase the number of passengers in each specific station compared to stations outside of the city center. Figure 18: The distribution of the change’s coefficients over the studied area 47 General Reasons In general, this might be due to the use of the average number of persons per household. In fact, even if these new station with the exception of Sofia and Hammerby Kannal are outside of municipal Stockholm, they are relatively close to it. This means that the average number of persons per household in this area might be closer and thus lower than their average municipal one, i.e. Nacka and Järfalla. The major change of the areas between 2016 and 2030 might affect the way the GWR equations are predicted leading to a change in the calibration of the variables that are geographically dependent. The GWR equations were estimated for a spatial area that is different in 2030 than it is today, like Sickla, Järla and Nacka. Sofia are predicted relatively accurately due to the fact that the environment has not changed much. Bus Assumptions and Effect on Predictions Looking closer into the difference between the north and south stations in the first place might explain the difference seen between GWR values and the one by SLL: this is mainly due to the assumption taken with regards to the number of bus lines. In fact, the number of buses in the areas of interests were left as is. Although, in 2030, with new development and metro stations built, the current state will definitely evolve. On one hand, the stations in the north of the blue line see a slight overprediction of respectively 11,6% and 11,8% for Bakarbystaden and Barkarby Station compared to SLL estimations. This is mainly due to the fact that a limited number of bus lines were found around the future stations, none for Barkarbystaden and six for Barkarby Station. An increase in the number of residence and two new metro stations will definitely lead to new lines stopping in the area, especially in Barkarbystaden. On the other hand, the stations in the south and in municipal Nacka are overwhelmingly overestimated. In fact, the predicted ridership at Järla by the GWR model is almost twice as the ridership predicted by SLL. Here, a huge number of bus lines that pass in the region that lead to Nacka and beyond east will be removed by 2030. Today, these lines mainly start at Slussen. In 2030, it is planned that the lines that lead to Nacka will drastically decrease and the ones that leads farther east moved to Nacka’s bus terminal. This means that a lot of the buses accounted for when doing the predictions will be gone in the future and thus should not be accounted for in order to get a closer projected ridership to the SLL one. Unfortunately, no data is available today on the number of bus lines that are planned to cover both areas. Special Case of Sofia Sofia is the only station that has an estimation that is almost identical to the one predicted by SLL. 48 A simple explanation might be the fact that the region barely changes with regards to the socio-economic dynamic as well as the transit characteristic with regards to 2016. In fact, hardly any residence will be built in the area, only 155, a thin increase of less than 200 workers. The area has already a high-service when it comes with bus stops and bus lines that pass through it. A change in the number of lines will thus be limited in the area. Limitations of the Study Multiple limitations can be drawn in this study dipping a toe into the multiple defects of the model and the study itself. First, land use variables are, according to preliminary studies an important component that can explain a part of ridership. However, accurate land use data was not available for the whole study area. Only municipal Stockholm had land use data with the required accuracy. For this reason, land use was disregarded when calculation both OLS and GWR equations. Lack of land use data and variable automatically puts limits for this study as it is a crucial information to incorporate in the study, especially when debating on a subject that has the change of land use for the future service areas of the new stations in its core. Second, when service areas were drawn on ArcGIS, three main critics can be said. First, when Thiessen polygons were used for close stations, the latter assumes, at least in the central part of Stockholm that people always choose the closest station independently of the type of station. Behavioral studies show that this is not always the case. Second, problems with generating the service area on ArcGIS led to having some stations with either service areas way bigger or way smaller than 800 meters road length wise and the fix was thus done manually and might not be precis. Third, the network layer used in order to create the service areas had missing pedestrian tracks for some regions, meaning that some service areas might have been created with flawed road and pedestrian network especially at the outskirts of the metro network where the problem was considerable. Manual fixes were thus undertaken in order to resolve the problem. Third, assumptions and hypotheses taken in order to be able to pursue the study can definitely be questioned. The way the GWR equations for the new stations were determined is completely problematic. Determining ridership for stations that do not yet exist in a year they definitely will never do can never be observed. This hypothetical situation has led to error being included and dragged in the study that can never be identified. The assumption about the population and workers being homogeneously distributed over the multiple SAMS is far from the situation on the ground and can lead to inaccuracy and misrepresentation, especially in relatively large zones (which are mainly clustered in the outskirts of the metro network) where irregularities can be more pronounced. As already discussed above, the unchanged bus network between 2016 and 2030 is a huge drawback for accurate prediction at the new stations. Finally, the choice of the number of persons per household and of the equivalent stations while calculating the number of workers in service areas is unrealistic. First, the exact number of persons per household cannot be known and the value that was used was for the current state of 2018. Second, to assume that the ratio of workers to population in new stations is identical to their 49 chosen current equivalent station cannot be proven yet and is totally hypothetical done for the purpose of easing the calculation of the potential number of workers in the service areas. The ridership predicted by SLL was assumed to be correct and unfaulty, However , this predictions cannot be observed yet. Comparing the GWR predictions with other predictions cannot prove for sure how GWR performs with regards to the situation on the ground. In future studies, these limits should be considered and tackled in order to improve the potential predictiveness of the model. 50 Conclusion After going through the analysis of these results, one case-specific conclusion and two main conclusions were deduced from this study. In this case, GWR equations overpredicted the ridership for future stations with regards to the official predictions. However, a generalization of this results cannot be drawn due, first, the many case-specific assumptions taken here and, second, the lack of other studies available today using the same process. The general conclusion are as follows. First, GWR is a good predicting tool for future stations that are closely located from most present stations. Second, GWR is a good predicting method for stations where limited changes in the future environment will occur. These conclusions help in realizing when to use GWR. In fact, according to these results the conclusion determined, Geographically Weighted Regression can be used as both an explanatory and predictive tool but in limited cases. With regards to its explanatory power, the model can help explaining in details and area specific the current situation or the possibility of building one or more stations for a given area which will not change drastically. This can also be taken further in determining the ridership using the GWR equation. GWR is thus performs good for a limited number of stations built next to an existing, stable environment. For example, densely populated cities with an existing but limited public transportation or metro network are ideal cases for the use of this method. In addition, developed countries with limited funds are good situation where an area/station-specific equation explains and predicts the ridership reassuring policymakers and investors. The determined parameters can also help determine area-specific and thus more accurate and precise policies that can be proposed. For instance, the choice of building new apartments in specific areas can also be analyzed and other areas, not considered, can be proposed. However, this study is still preliminary and experimental in the field of the predictive power of GWR with regards to new metro stations. 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Zhang, D. and Wang, X. (2014). Transit ridership estimation with network Kriging: a case study of Second Avenue Subway, NYC. Journal of Transport Geography, 41, pp.107-115. Zhang, P., Wong, D., So, B. and Lin, H. (2012). An exploratory spatial analysis of western medical services in Republican Beijing. Applied Geography, 32(2), pp.556-565. Zhao, F., Chow, L., Li, M. and Liu, X. (2005). A Transit Ridership Model Based on Geographically Weighted Regression and Service Quality Variables. Miami: Lehman Center for Transportation Research. Zhao, F., Chow, L., Li, M., Ubaka, I. and Gan, A. (2003). Forecasting Transit Walk Accessibility: Regression Model Alternative to Buffer Method. Transportation Research Record: Journal of the Transportation Research Board, 1835(1), pp.34-41. 55 Appendix Appendix I: Method and Tools in Determining Data in ArcGIS (ArcMap) Income, Workers, Population and Age All of the above was done by a method of intersect and dissolve like in NYC. The service area was divided on the given SAM’s areas. The proportional population (with the respective age groups) and workers were then added to each division that fell within each respective SAM’s area. It was assumed that the population and the number of workers were homogeneously distributed on the SAM’s area and thus on the division of the service area that fell in each SAM area. A step further was taken in calculating the median income. A weighted average in function of the number of workers was done. The following equation explains how the median income was determined for each service area. ∑ =çqéLqt_ê!_ë:5:t:çH ∗ ÜLJ]Hy ∑ =çqéLqt_ê!_ë:5:t:çH Where the Workers_by_Division was calculated as explained above. Road density (m/m2) The layer was intersected using the tool “Intersect” then the summation of the length of roads was done in the area, the all divided by the area of the service area. Number of bus lines at a 200-meter buffer around the entrances of the metro The number of buses located at a 200-meter radius was considered. The buffer tool was used. Some adjustments were done manually in order to correct any mistakes. The number of bus lines were finally divided by 2 in order to account for only the feeder type of the buses in the morning leading to the station. Terminal Station Terminal station were added regarding their respective years. In 2016, Akalla, Hjulsta and Kungsträdgården on the blue line, Hässelby Strand, Hagsätra, Farsta Strand and Skarpnäck on the green line and Mörby Centrum, Ropsten, Norsborg and Fruängen on the red line were assigned the dummy value of 2 while all other stations were assigned 1. In 2030, Kungsträdgården is replaced by Nacka and Akalla by Barkarby. All other stations remain the same. 56 Type of change The type of station was just translated to a dummy variable using the “bytespunkt” column from SLL of future stations. Commuting distance The point to distance tool was used to determine the distance from a station to T-centralen. Euclidian distances were used as the Stockholm metro network has a star shape and limited curves in its network. 57 Appendix II: Table of GWR Equations and Predictions for the 2016 Situation Bus R2 Error Err_Int Err Err Err Change StdResid Observed Bus Std Station Local Predicted Intercept Workers Change Residual Std Std Workers Std Std 50 381,00860604 8000020 81000 3999980 0,0824318699 92900 27,907992566 099999 - 319,18364583 0,4441783725 595,87442389 Ängbyplan 400,00000000 0000000 0,7458085427 32000 4999950 599999 0,0040977414 71,125968780 400001 60000 5000010 440,98145246 - 57,098757896 - 60700 514,80259472 - 195,87442389 6000010 0,0593645491 4000000 390,01528203 302,69122643 2000010 74700 - - 133,80545402 1000030 11,278708959 199999 229,47469086 4000000 Akalla 69000 800,00000000 0000000 0,6710868392 79000 933,80545402 4000030 44,963659706 500003 0,1150892652 56000 51,527385300 799999 249,97661361 1999990 0,3430774643 Fittja 600,00000000 0000000 0,0672741394 57500 913,86196874 6000000 595,27149881 8000050 14000 800003 - 37000 36,149360753 304,26764042 2999990 0,7356709750 426,63361665 0,1173638830 33000 21,495694744 400001 - 105,82480043 0000000 - 313,86196874 6000000 2000000 415,96984168 0999990 0,1390729690 000 28,419469743 200001 2,4345265595 350,35597889 1000010 60000 82000 2594,8676502 79999900 - 486,80516682 1999990 0,0969523992 54,652318977 100002 831,29695161 8999970 405,13234971 8000000 92300 Brommaplan 3000,0000 00000000 0,6896898033 166,41114393 4999990 16000 382,83798985 0,0612488680 5000010 999999 20000000 203,52635604 363,34765862 9000020 37,011163379 2642,3266001 444,09129042 4000020 0,0504749233 06900 27,175983193 600000 342,91849731 7000000 2,1819841865 20000 2000000 73000 Liljeholmen 4200,0000000 00000000 0,8292718698 3755,9087095 80000000 - 2279,9439401 49999900 0,1551619448 87000 58 00005 Örnsberg 900,00000000 0000000 0,7500061087 96000 804,33399002 2999960 - 1435,5252488 59999900 0,1721990080 17000 73,274249673 499995 1673,4824144 60000000 95,666009977 2 438,83802864 2999970 384,67439868 3999980 0,0582111461 48800 30,089817141 400001 319,91416888 8000010 0,2179984498 45000 Kärrtorp 900,00000000 0000000 0,4969109286 19000 652,07083272 2999970 - 78,980294095 800005 0,1510341920 61000 34,499126787 599998 396,49580479 9999970 247,92916727 7000000 450,83172477 8000020 367,23931636 8000000 0,0610710451 82900 26,322733271 000001 287,48614340 5000010 0,5499372684 99000 Stureby 500,00000000 0000000 0,4381768446 79000 0999970 241,95626093 500001 6000000 1000000 449,29461506 661,16417225 - 6000010 0,1445625482 57000 59,022435228 503,32315617 - 161,16417225 346,29712979 2000020 64400 - 26000 4000030 0,0652775087 28,539746966 275,96537884 3999990 0,3587048828 999999 000000 40,755052802 100003 - 69000 285,98799107 2999990 0,5462751965 5000020 359,45168974 458,29041066 0000010 1345,9215919 90000000 - 250,35268417 2000010 0,0624743132 50000 28,705381298 799999 Globen 300,00000000 0 0,6027237730 79000 550,35268417 1999950 - 1093,4946076 79999900 0,1565601973 76000 928,37317775 - 770,26162380 9999950 0,1936642139 89000 30,689816188 199998 0999960 4999980 448,48760379 328,12057522 - 326,23892662 9000000 7000020 06000 Huvudsta 600,00000000 0000000 0,6310111965 70000 926,23892662 4999980 0,0391747078 15100 20,981597599 499999 296,87398470 1999970 - 0,7274201647 97000 429,22363042 Universitetet 500,00000000 00000000 7000030 282,02006773 4000010 64000 200000 - - 322,45734143 6999990 0,0342228494 11,968639394 257,38762027 0000010 0,7512571968 0000000 822,45734143 754,89347965 200002 0,5979048678 44000 6999970 - 9000040 0,1456084126 84000 33,071257853 1061,7704260 3000020 - 72000 499998 460,33775929 - 88,644500890 1999990 369,98996917 0,0579747050 77500 26,736378512 000002 292,39790117 4000030 0,1925640447 den 988,64450089 Hammarbyhöj 900,00000000 0,5605228012 23000 - 558,03171047 1000010 0000000 32,349929759 299997 7999990 1000000 0,1588673267 67000 849,76154358 59 10000 Johannelund 200,00000000 0000000 0,6403986013 49000 499,50325141 2000000 67,535018443 400006 0,0621520527 41000 71,575835008 900000 254,32217367 9999990 - 299,50325141 2000000 431,62759706 0000030 372,75060285 0000010 0,0857700649 76000 25,259079793 700000 302,57129171 8000000 - 0,6938927294 Hagsätra 1200,0000000 00000000 0,3862280965 10000 676,46344108 4000010 - 112,01354510 6000000 0,2451297689 33000 66,796599924 800006 247,35680759 9000010 523,53655891 5999990 440,89909469 2000010 377,71317763 8999980 0,0879741185 96600 33,171547694 200001 301,26793064 8999990 1,1874294259 60000 3 Mälarhöjden 700,00000000 0000000 0,5916315791 40000 7000000 756,55706724 699997 2999990 7000000 450,1293626 842,25405869 - 0000040 0,2223802274 98000 61,505305715 975,18827678 - 142,25405869 398,53582521 2000020 56500 - 07000 0000000 0,0605608743 26,617553751 340,10519247 2000000 0,3160292807 500001 75,088329771 700003 0,3275982010 320,52446289 0999980 40000 8000010 380,76014560 452,24994158 4999990 430,01920041 5000000 148,15626728 3999990 0,0851525331 52700 27,465320656 300001 Islandstorget 800,00000000 0000000 0,7376696804 91000 651,84373271 5999980 - 9,3220040306 80001 0,0046977212 59070 626,46372559 - 451,58650102 1999990 0,1575504087 93000 46,272049757 799998 6000020 440,65876328 294,61031054 218,08936423 5999990 3999970 4000010 Bergshamra 1100,0000000 00000000 0,6004337239 83000 881,91063576 3999950 0,0350286091 22800 12,001772224 300000 244,65882296 1999990 0,4949166620 70000 5 391,82765560 Skanstull 2200,0000000 89999800 374,22222415 4000000 87000 999999 1,1087460379 434,43736072 7999990 6000010 0,0473706655 25,146691876 382,63244440 8000030 90000 00000000 1765,5626392 2446,3017970 50000 0,811436941 82000 70000100 - 00000100 0,1836337602 40000 7,9875016840 2793,3939585 0999990 - 67300 000001 390,86684041 - 29,237172903 1000000 343,44604783 0,0674992722 11300 30,265223379 100000 271,53745252 4999990 0,0748008525 1029,2371728 Hökarängen 1000,0000000 0,3892885835 02000 80,839664990 000003 99999900 00000000 40,749803809 299998 6999990 0,1636291690 78000 228,73964856 60 40000 Masmo 200,00000000 0000000 0,0834831172 46800 509,47622438 1000010 541,50961899 3000000 0,1531789930 87000 17,452718908 200001 - 70,907150568 099993 - 309,47622438 1000010 273,33938040 4999990 410,84565528 0000020 0,1332577566 62000 36,835203519 399997 299,15327122 1000010 - 1,1322050409 Fridhemsplan 5700,0000000 00000000 0,6663443348 85000 4208,8873744 90000200 - 1350,1606165 90000000 0,1947628960 83000 5,0839532507 60000 1677,0823235 80000100 1491,1126255 10000000 346,56200091 6999980 305,58991338 7000020 0,0366043898 30100 19,167419121 599998 271,90649835 3000020 4,3025854582 00000 24289 Västertorp 700,00000000 0000000 0,4913304378 23000 00000100 562,73787546 599994 9000040 1000000 452,74565654 1059,1249247 - 7999970 0,21549 50000 68,419025854 800,83592721 - 359,12492470 450,73080551 9999990 06200 - 76000 4999970 0,0798770576 32,155204800 371,06450334 4000000 0,7932156156 100002 7,0729239605 80000 1,4620703444 265,68073801 8999990 90000 9000030 294,84390198 388,09712830 0999990 1477,7908623 50000000 567,42530208 4000010 0,0351035264 65900 18,828421751 400001 S:t Eriksplan S:t 2500,0000000 00000000 0,6433285646 56000 1932,5746979 20000100 - 1157,4306630 79999900 0,1908414393 36000 2264,7457926 - 1853,5308792 59999900 0,1802904562 63000 0,5665473646 73000 79999800 6000010 417,54477483 329,73098872 - 114,61706477 4000010 sen 8999990 33000 Medborgarplat 1400,0000000 00000000 0,7339589552 72000 1514,6170647 80000000 0,0407938139 21300 22,230361368 000001 348,40857413 3000000 - 0,2745024526 90000 456,27606521 Tallkrogen 400,00000000 9000020 0999990 349,30923568 9999980 48100 899999 - - 252,34097455 8999970 0,0661716362 28,862977895 274,48627283 5000020 0,5530445135 0000000 652,34097455 2,4700656332 300000 0,4299810130 63000 1000040 - 30000 0,1511864304 60000 43,373486362 301,82476341 7032 9999990 0,0235955067 446,78622877 10,542147495 400000 3999990 325,11069338 0,0376265960 04900 20,781332843 300000 325,51492999 3000010 91500 789,45785250 Gamla stan Gamla 800,00000000 0,6826818835 05000 - 1539,9371961 5000010 0000000 50000 - 1,192669 70000000 80000000 0,1731170632 97000 1991,2016753 61 Karlaplan 900,00000000 0000000 0,6422924919 56000 883,79949507 7999950 - 1317,6440465 70000000 0,1330945795 60000 - 2,9547620066 00000 1929,6116710 70000100 16,200504922 000000 455,63658628 7000000 329,90584159 3999980 0,0357189578 38800 20,836729038 300000 341,78424538 5000020 0,0355557595 89100 Enskede Gård Enskede 300,00000000 0000000 0,5566283665 90000 491,52387650 6000020 - 831,98030349 8000010 0,1485065467 88000 48,542547944 100001 1078,9520831 49999900 - 191,52387650 5999990 456,17669256 8000020 355,42911624 0999970 0,0635603447 01200 29,016081353 97000 299999 283,48263484 4000020 - 0,4198458176 Solna strand Solna 300,00000000 0000000 0,6064906666 59000 3000010 517,27831381 500001 5999970 3000010 444,03191135 646,57691808 - 3999940 0,1643945012 22000 45,994079434 675,62107330 - 346,57691808 331,67481975 4000000 74700 - 87000 4999980 0,0413602214 19,916800459 281,84539531 7999990 0,7805225462 099999 55,355567651 199998 0,2707956378 280,59434123 9000020 09000 8000020 355,09900310 429,34149354 1999980 264,21663197 9999990 116,26380358 3000000 0,0753732544 27800 31,200002376 200000 Rågsved 800,00000000 0000000 0,3727204580 14000 683,73619641 6999970 - 55,356295264 700002 0,2141600231 84000 816 357,60119063 - 155,18420301 0000000 0,1421576634 94000 50,761209 300003 1000010 444,64480720 287,11151102 94,941523850 799996 1999980 0000020 Hallonbergen 1000,0000000 00000000 0,6191678597 42000 905,05847614 8999940 0,0417882422 71300 10,892999018 299999 225,39093778 3000000 0,2135221694 10000 445,59182501 Skärmarbrink 1200,0000000 70000100 347,34743104 0000000 50800 600001 1,5978875157 712,00561432 2000040 8000010 0,0572486610 26,743109434 272,96925251 4999990 60000 00000000 487,99438567 1022,4117719 699998 0,6064199718 57000 8000010 - 00000000 0,1624172861 80000 35,213232194 1283,7029449 527580357 0999990 - 83000 2000010 451,06247093 - 384,64714673 7999990 312,28354249 0,0654011438 88400 12,431906158 600000 233,83227095 9999990 0,8 684,64714673 Hjulsta 300,00000000 0,6279081661 02000 14,031083532 800000 2000010 0000000 53,960249604 900000 3000000 0,1045030145 49000 293,49021923 62 44000 Zinkensdamm 800,00000000 0000000 0,7338928462 32000 1245,3346312 90000100 - 1897,0913488 30000000 0,1742320324 90000 6,0213496488 80000 2313,2497527 59999900 - 445,33463129 0000000 461,17148034 5000020 328,62510933 9999990 0,0403066239 29200 20,934872961 400000 327,98844469 1999970 - 0,9656595220 Husby 1100,0000000 00000000 0,6711258954 14000 810,36578627 6999980 46,244686972 499998 0,1130873431 73000 51,399713712 500002 248,37565708 1000010 289,63421372 3000020 448,08291871 5999990 298,63886994 9000020 0,0576977857 25000 11,203795838 400000 226,97601918 0000010 0,6463853042 04000 Telefonplan 2400,0000000 00000000 0,6730759017 97000 50000100 1190,6584335 300004 89999900 448,48377470 1195,4488602 - 80000100 0,1418587724 06000 88,474003462 1459,5732862 1204,5511397 49999900 392,90706886 2000020 31500 2,6858299178 4999970 0,0720334157 40,170400242 336,37809314 3999990 00000 600003 55,187351483 699999 0,0931945913 270,70248338 5999980 48800 2000010 341,52047364 458,85939131 9999990 391,20280211 4000010 42,763213459 900001 0,0657773722 14500 28,765395526 999999 Bandhagen 900,00000000 0000000 0,4079457669 25000 857,23678654 0000030 - 128,73260497 0000010 0,1605223963 35000 265,46036385 36,851426511 299998 0,1586870135 75000 42,687281261 400003 1000010 9000000 462,14148677 344,14226395 - 125,69111562 8000000 9999980 97000 Gubbängen 600,00000000 0000000 0,4034401567 73000 725,69111562 9000020 0,0663464045 07600 29,401003738 400000 271,24442126 6000020 - 0,2719753997 436,01717102 Thorildsplan 800,00000000 40000100 308,48968736 4000020 69100 099998 0,4766207737 207,81484139 8000000 1000020 0,0379275520 19,995153365 278,38520544 3000020 00000 0000000 592,18515860 1405,7364264 300000 0,6818980270 80000 2000000 - 00000000 0,1981377222 20000 10,531239780 1704,0234619 99990 3000010 0,9775785939 403,65037259 394,59996368 89 3999980 365,50561171 0,0822380394 95700 25,263438310 200002 300,01888901 7999980 53000 1505,4000363 Vällingby 1900,0000000 0,6503008701 63000 59,790046312 100003 09999900 00000000 71,987519605 000003 4000000 0,0511202562 70600 280,37976409 63 Skarpnäck 1000,0000000 00000000 0,4417763933 81000 941,19418006 5999940 109,13495601 1000000 0,1542342235 93000 32,898103524 699998 231,49615976 1000000 58,805819933 800002 347,47409708 4999980 357,32672319 3000020 0,0658547420 75700 28,999874585 899999 281,07034063 4999980 0,1692379962 34000 Kista 1200,0000000 00000000 0,6755585432 80000 1519,2457378 39999900 50,124270961 000001 0,1113019075 93000 51,241878409 999998 241,51733168 1999990 - 319,24573783 8000030 423,79887683 7000020 296,78839275 0000010 0,0558776784 96600 11,146102359 06000 200000 225,26348324 0000000 - 0,7532953844 0000 Abrahamsberg 1000,000 00000000 0,6830421384 19000 1000030 788,46196097 599997 90000000 452,50359347 729,26302882 - 4000020 0,1577395583 84000 46,116584656 1046,7025071 270,73697117 9000020 365,54076469 7999980 63700 0,5983089970 5000000 0,0503562000 27,431309206 350,25594082 9000000 62000 600002 363478291 - 1,4214722853 - 43000 324,61363843 7000020 0,2418563666 7999980 325,29120876 80000 384,75875872 1000010 1919,1210260 60000100 - 93,056355420 100004 0,0 40100 20,684998709 399999 Kungsträdgård en 500,00000000 0000000 0,6630348197 65000 593,05635542 0000050 - 1424,3352154 70000100 0,1616116609 71000 497,01373529 - 169,06134449 1000000 0,1558535815 28000 28,876005512 199999 7999970 500001 457,18141953 390,43891385 - 21,144402209 4999970 7999980 47800 Björkhagen 700,00000000 0000000 0,5243468813 47000 721,14440220 9999950 0,0584424835 20500 26,094851827 500001 311,88310269 0999980 - 0,0462494784 396,96507086 Hornstull 2100,0000000 99999800 342,88346423 3999970 75000 100000 1,1277317908 447,67013028 3999980 2000000 0,0435635202 22,323448124 322,68697127 7999990 90000 00000000 1652,3298697 2046,3163212 600000 0,7693398034 91000 20000000 - 30000100 0,1602957035 95000 21,587092880 2436,9496359 4999970 - 22000 3999980 449,48295913 - 277,30975424 4999990 396,95690904 0,1223425389 34000 31,523241987 300000 292,74530692 8999980 0,6169527645 777,30975424 Vårby gård 500,00000000 0,1203379638 22000 414,48259116 4999970 4000030 0000000 34,211071513 500002 32,086999973 700003 0,1624519633 42000 - 64 Rådmansgatan 1500,0000000 00000000 0,6354459114 03000 1406,8053608 49999900 - 1226,2318875 20000100 0,1610288144 23000 4,6481924869 00000 1679,8115963 80000100 93,194639153 699995 433,70247994 2000020 305,85005130 2000000 0,0346250278 70000 18,897916822 100001 281,55180899 4999990 0,2148814993 31000 Mörby centrum 2000,0000000 00000000 0,6247918185 10000 1859,2113170 00000000 - 215,56826809 6000000 0,1516023847 48000 51,592296040 800001 381,27332690 3999990 140,78868299 7000000 332,88054745 0999980 317,19912598 8999980 0,0356157179 66700 11,848147422 500000 233,74300795 9000010 0,4229405535 26000 Axelsberg 500,00000000 0000000 0,7006211144 20000 3000020 1194,2276313 199995 10000100 2999990 445,87626471 735,47860175 - 29999900 0,2003479839 35000 66,752439163 1408,6917933 - 235,47860175 392,60471810 7000000 13200 - 20000 5999980 0,0563382976 26,915109966 328,60979066 4999990 0,5281254473 399999 49,111352470 500002 - 95000 249,69306873 2999990 0,4191338386 3000020 319,38153943 277,59457805 6000030 500,05004856 5000000 - 116,34928110 0000000 0,0360884421 85600 12,351643550 000000 Danderyds sjukhus 2800,0000000 00000000 0,6056529928 24000 2916,3492811 00000100 - 314,10011182 0999980 0,1489461552 25000 - 657,61314151 2999960 0,0976812289 82100 18,129039532 299998 130,92060482 2000000 342,65356449 424,24931929 160,08939669 0000000 1000000 2000000 Alby 1000,0000000 00000000 0,0558814600 74800 839,91060331 0000060 0,1460302133 08000 37,634599602 199998 308,70951645 7000010 0,4672048193 27000 8340 65000 419,41360731 Näckrosen 1100,0000000 2000000 5000010 303,66442080 7999990 52900 100000 - - 143,32575384 3999990 0,036456 11,051474868 236,95201489 3000010 0,3417289075 00000000 1243,3257538 366,68905311 299999 0,6177424309 75000 50000000 - 1000020 0,1724281204 35000 48,200349746 483,24980355 8999980 0,0542374372 406,45820152 22,045251186 100000 5999980 287,14821424 0,0535523290 12600 11,326527368 300001 221,97144196 4000010 15700 977,95474881 Rinkeby 1000,0000000 0,6331667795 28000 - 23,215401972 4000030 00000000 52,190582368 900003 0000000 799999 0,1175971897 36000 305,72415809 65 75000 Rissne 900,00000000 0000000 0,6056410105 23000 1221,9827341 70000000 - 59,406762512 900002 0,1085031384 10000 53,086970374 700002 346,91526146 5000010 - 321,98273416 9000030 416,42026566 0999970 287,97491711 7000020 0,0533139746 60000 12,267477916 200001 225,81278756 8999990 - 0,7732158127 38 Gärdet 1100,0000000 00000000 0,6349106473 25000 729,82019431 1000020 - 1265,3113791 59999900 0,12375681 77000 - 2,4288567278 60000 1907,1716765 19999900 370,17980568 8999980 391,58962541 1999980 333,99165367 1999980 0,0357334392 22400 19,436709193 999999 348,07172221 7999990 0,9453258760 35000 Hässelby gård 900,00000000 0000000 0,6520568142 39000 1000010 100000 899994 2000030 433,18784009 685,47512740 57,456172853 0,0654623910 76800 73,518112400 258,34129047 214,52487259 8999990 377,93643674 7000020 49600 0,4952236714 9000030 0,0880884263 25,628992580 306,68421721 9999990 45000 100000 2,6348354931 30000 - 34000 291,72354606 0999980 0,4554844949 7000020 319,09209515 462,59348034 6000030 1881,3683457 40000000 - 210,70415775 6000000 0,0373823262 00400 19,561521195 200001 Rådhuset 1000,0000000 00000000 0,6754334042 66000 1210,7041577 60000000 - 1484,5440776 09999900 0,1813139904 06000 1608,4208443 - 1351,5686061 70000100 0,1990617186 05000 20,894368063 900000 69999900 2000010 406,54842431 327,76848696 - 254,25815570 9999980 8999980 41000 Kristineberg 1100,0000000 00000000 0,6982005554 01000 1354,2581557 00000100 0,0406941304 04200 22,430753923 499999 304,82374224 4000020 - 0,6254068162 80000 351,37208787 Högdalen 1000,0000000 4000010 4000010 349,67174465 6999980 25400 800000 - - 357,86389383 7000010 0,0699774109 30,309527561 276,84706065 5000010 1,0184755880 00000000 1357,8638938 54,161556708 199999 0,3827158180 95000 30000100 - 799999 0,1823587167 36000 53,477798853 299,87209499 8000020 0,1166545764 235,08014513 27,423174761 399999 0000010 354,86429502 0,0447527382 26100 25,579907615 700002 341,94532430 8000010 48000 2072,5768252 Alvik 2100,0000000 0,7071381751 10000 - 1233,4970572 39999800 00000000 29,841175688 500002 79999900 00000000 0,1960799048 68000 1463,8438126 66 75000 Blåsut 600,00000000 0000000 0,5320927067 64000 673,42575910 6999980 - 397,08228912 5999980 0,1463876090 63000 41,017743950 200000 680,53177823 6000040 - 73,425759107 100006 454,62663597 8000020 364,02248547 2000030 0,0619235150 70500 27,574719208 499999 283,41173300 7000010 - 0,1615078248 Hötorget 500,00000000 0000000 0,6479849880 90000 750,25293119 2000010 - 1321,2742271 40000000 0,1630427052 07000 1,6552460669 50000 1790,2181634 20000100 - 250,25293119 2000010 452,21414569 9000030 313,84121889 5000000 0,0353084772 55500 19,553830174 57000 400002 293,33102328 0000010 - 0,5533947435 Bagarmossen 1100,0000000 00000000 0,4612843516 09000 7999950 100003 700000 1000000 449,37236498 702,89041280 56,347773490 0,1531085533 05000 32,325533317 280,26772267 397,10958719 1999990 359,92351707 1999980 52700 0,8836982826 9000000 0,0624262369 27,206412238 282,23133316 3999980 08000 100000 00020 44,544529705 800002 0,6589497545 277,02695276 1000020 88000 7000020 355,97565532 447,58507703 3000010 526,23461640 0000050 294,93607667 10 0,0622751254 37800 26,966539413 200000 Sandsborg 700,00000000 0000000 0,4963690024 10000 405,06392332 8999980 - 240,82009523 2000000 0,1428053399 55000 220,48662224 - 22,957684563 499999 0,2581324116 32000 58,716835610 899999 8000000 419,14269541 441,10525263 192,19445813 1999990 8000020 4000010 Sätra 800,00000000 0000000 0,3350859182 83000 607,80554186 7999980 0,1096187322 25000 26,932583491 100001 321,03332196 3999980 0,4585418289 12000 309,31959797 Farsta 1200,0000000 6000000 345,62276719 8000020 44900 299999 0,5671099270 175,41821462 6000010 2000000 0,0697813410 31,574652989 274,76017769 7000020 01000 00000000 1024,5817853 3999990 200002 0,3754177308 92000 70000000 138,03074343 0,1676284348 15000 38,161076433 183,60355974 0000000 3999980 - 01000 3000000 279,99353354 - 105,78452647 5999980 448,96281957 0,0920257868 34000 36,669931046 199999 373,01569326 9000000 0,3778106056 1905,7845264 Fruängen 1800,0000000 0,3924615092 90000 - 306,27441593 69999900 0 61,260444889 500000 2999950 8999990 0,2349097993 87000 548,44020356 67 2500 46000 Duvbo 600,00000000 0000000 0,5960776887 91000 996,11859556 8000050 - 199,28154588 4000000 0,1354826380 00000 50,927888303 899998 419,81637323 7999980 - 396,11859556 7999990 426,21398529 7000020 291,19779820 7000010 0,0433678445 2 11,841148610 499999 231,83158314 7000000 - 0,9293890140 Solna centrum Solna 1600,0000000 00000000 0,6258536968 92000 1954,1718613 90000000 - 534,39487806 1999980 0,1905230065 55000 40,781591501 100003 634,63249951 7000040 - 354,17186139 0999990 399,29830639 1999970 311,53358747 3000010 0,0359952077 67700 12,322395185 50000 100000 258,90639898 4000020 - 0,8869856338 Odenplan 2100,0000000 00000000 0,6294153624 18000 10000100 1127,0790447 20000 40000100 10000100 376,61291069 3753,5960217 - 40000000 0,1708922608 42000 9,2039323801 1506,5441289 - 1653,5960217 296,94312837 6999990 94900 - 50000 9999990 0,0341661561 17,678724996 269,58477746 6999980 4,3907045529 100001 4,0068409 - 0,1382845794 - 50000 308,47460624 2999980 1,3212021476 7999980 316,37382294 52000 440,49125054 0000030 1860,6103508 39999900 - 581,97798624 6000000 0,0352040507 58500 19,915928182 900000 Östermalmstor g 800,00000000 0000000 0,6470697122 98000 1381,9779862 50000000 - 133 40000100 0,1513576683 75000 1522,1341220 - 1273,8599671 50000100 0,2134502916 95000 6,9067485433 70000 80000000 8999980 440,69459321 313,10089751 - 343,60550911 8000020 1000030 42000 Stadshagen 700,00000000 0000000 0,6735189274 05000 1043,6055091 20000100 0,0379370926 54100 20,354541575 599999 282,45016036 5999980 - 0,7796907754 30000 369,11895173 Tekniska Tekniska högskolan 2000,0000000 09999900 0000010 310,01421823 5999980 53600 900002 - - 785,39694779 9000010 0,0342203902 16,724380856 293,93274260 7000020 2,1277611027 00000000 2785,3969477 1162,2734856 90000 0,6242532855 95000 90000000 - 80000000 0,1442804765 50000 6,6639854240 1662,4279655 9000000 - 10000 4000000 400,89637748 - 613,68419356 0000010 311,91657746 0,0401064207 86100 13,199099764 100000 247,36856996 7000010 1,5307800919 2113,6841935 Sundbyberg 1500,0000000 0,5935546214 26000 - 349,83660420 60000000 00000000 48,809561265 799999 2000040 0000010 0,1540608162 99000 520,08096552 68 52000 Åkeshov 500,00000000 0000000 0,7106111012 36000 581,86018136 2000050 - 175,30121011 8000000 0,0287973364 72600 64,840857528 300006 600,84214018 6000050 - 81,860181362 000006 436,08459174 2999980 377,22962683 9999980 0,0728100863 32300 27,776724418 200001 321,78933116 2000000 - 0,1877162892 Svedmyra 400,00000000 0000000 0,4517906354 89000 641,67246573 9000020 - 209,28156952 2000010 0,1408800305 24000 54,157337540 299999 479,29724570 5000020 - 241,67246573 8999990 438,79350462 0000020 349,88671455 8999980 0,0645772159 17000 28,063311678 92000 300000 276,26573817 6000010 - 0,5507658230 70303 Farsta strand Farsta 700,00000000 0000000 0,3699125191 56000 70000000 3999990 799998 6000000 0999980 345,17070337 1020,8731618 155,16994445 0,1693788682 89000 37,454062656 170,02765378 - 320,87316187 346,27622300 8999980 09800 - 14000 1000000 0,0706191229 32,0232 275,93453968 5000000 0,9296071733 499999 55,809578995 800003 - 39000 282,03050348 1999970 0,1756482284 8000000 357,08859251 461,96414607 8999970 636,80185336 8000020 - 81,143183860 700006 0,0659570629 17100 29,079576532 600001 Sockenplan 500,00000000 0000000 0,4914688287 92000 581,14318386 1000010 - 374,94929115 1000010 0,1335636628 47000 432,65317313 - 223,70419624 7999990 0,2357902069 64000 67,453374499 600002 8000000 445,43061250 429,61126843 23,020394736 800000 0999980 5000000 Bredäng 1100,0000000 00000000 0,4419973898 28000 1076,9796052 60000000 0,0863324378 20300 27,336048784 799999 341,91251735 6000020 0,0516812138 42700 199617 12000 460,52181984 Skogskyrkogår den 400,00000000 7000020 9000020 351,17665679 7000020 14100 200001 - - 341,62580585 9999990 0,0618473911 26,582594784 273,82461389 5000030 0,7418232777 0000000 741,62580585 101,95 999998 0,4665551576 85000 9000020 - 1000000 0,1476519894 17000 41,736115818 400,47472135 7999980 0,0363476684 374,57660104 13,614986100 199999 1999990 382,68484910 0,0662164951 01400 36,614411365 999999 331,39296771 5999990 40500 ansen 886,38501389 Midsommarkr 900,00000000 0,7637727983 75000 - 1795,8953483 9999990 0000000 65,085972513 200005 90000000 80000100 0,1528556614 70000 2095,0394501 69 Tensta 900,00000000 0000000 0,6303027641 05000 708,47144594 5000030 13,064506556 700000 0,1057194319 90000 53,149011678 999997 292,43805827 0999990 191,52855405 5000000 455,05665826 6999990 304,24191955 9000000 0,0622074865 16100 11,953781053 300000 229,54967751 8000010 0,4208894663 45000 Stora mossen Stora 500,00000000 0000000 0,6895764162 78000 599,83414603 9999950 - 1011,6690456 60000100 0,1817060148 73000 37,727444562 999999 1242,0010775 50000000 - 99,834146039 499998 442,64447279 6000000 356,90967013 5000000 0,0461698214 79900 26,446998268 23000 900000 346,24583352 0000020 - 0,2255402522 Stadion 700,00000000 0000000 0,6350286707 60000 20000100 1261,1701128 81000 40000000 8000030 462,30623559 1110,8265621 - 89999900 0,1396847130 89000 0,8381125463 1824,2928808 - 410,82656211 317,96462515 7999990 18400 - 98000 6000020 0,0348127206 18,876142701 312,78470257 3999990 0,8886459460 999999 45,939076799 699997 - 60000 288,28300686 7999970 1,3047168825 2000000 398,75620164 349,02995413 1000020 96,406729401 899995 - 455,38527367 6000000 0,1105391637 34000 27,585711070 399999 Skärholmen 800,00000000 0000000 0,2223482304 93000 1255,3852736 80000000 169,47830307 9999990 0,2268245455 85000 000 1,7512912867 326,60848999 9000030 0,1768356165 46000 44,198556607 800001 40000 398,11104286 395,08725776 573,95869447 4000030 6999980 4000010 Vårberg 1100,0000000 00000000 0,1686001246 14000 526,04130552 5999970 0,1178548832 88 28,577239505 400001 290,43688358 8999990 1,4417050337 00000 03900 451,99860165 Hässelby strand 700,00000000 8999980 499999 388,99095735 6000020 51500 300001 - - 16,333303725 5000020 0,0940889903 26,098088366 315,10622524 6000010 0,0361357395 0000000 716,33330372 900001 999997 0,6740474395 15000 6000050 46,333768692 0,0672506155 45600 76,854735540 262,17542385 6999990 0,4633456668 440,01335171 203,87827989 6000010 6999980 410,36452112 0,0686753140 11400 35,527566082 699998 347,60521554 7999990 99000 n 796,12172010 Hägerstensåse 1000,0000000 0,5972299785 78000 - 897,01507556 4000020 00000000 80,180266424 300001 90000100 7000050 0,1782189563 62000 1135,5262090 70 6751157 Västra skogen Västra 1300,0000000 00000000 0,6459022286 46000 600,72151355 9999950 - 897,55247891 0999980 0,213 99000 16,091194506 200001 1079,2085222 20000100 699,27848644 0000050 443,06701547 7999970 315,35397270 9000000 0,0377025212 15000 19,955991354 500000 293,37952632 8999990 1,5782679865 80000 Mariatorget 1900,0000000 00000000 0,7393519157 49000 1756,5097653 60000100 - 1924,5982559 50000100 0,1787615085 15000 2,1592202092 90000 2334,9352874 40000100 143,49023464 1000000 402,72268152 4000000 335,93910367 1999990 0,0410278934 64900 21,984742328 500001 349,72277308 8999990 0,3563003556 15000 7014995 Blackeberg 500,00000000 0000000 0,7235179132 06000 5999950 50000 999999 7999980 199995 449,98407158 565,56335401 9,5658479735 0,0176699300 73000 76,242395389 382,98025651 - 65,563354016 380,32581686 9999980 58000 - 78000 7000020 0,0864103242 27,032418951 320,18946008 5000010 0,145 899999 73,023146362 299997 1,0290389573 302,55918535 0000010 50000 6000010 364,04159810 456,74658555 4000000 325,56480541 2000000 470,01003017 3000020 0,0814552956 04100 25,601223515 899999 Råcksta 1100,0000000 00000000 0,6749234807 57000 629,98996982 6999980 42,180934125 599997 0,0343748337 60400 716 1950,4510688 - 1678,9018766 80000000 0,1489942297 81000 73,704318704 399995 00000000 600001 453,08815845 374,24047 - 53,380779053 2000020 7999980 63000 Aspudden 1000,0000000 00000000 0,7768777124 88000 1053,3807790 50000000 0,0637769112 85000 35,170165539 999999 312,97203639 1000020 - 0,1178154362 342,73967771 Ropsten 3800,0000000 60000000 320,10419335 6000000 34900 700001 3,3143470111 1135,9582264 20000100 1000010 0,0352883579 14,155821723 319,30521740 0000000 50000 00000000 2664,0417735 1106,7039743 899999 0,6216445925 48000 80000200 - 40000100 0,1127855568 86000 10,618891362 1697,7613127 5000030 - 70000 0999990 259,95915393 - 375,04543923 0000010 414,78591884 0,1469852282 52000 34,235985079 199999 310,83126617 6999970 1,4427091085 775,04543923 Norsborg 400,00000000 0,0654994193 82900 623,28719278 9999950 1000050 0000000 31,251740709 600000 129,72981167 3000000 0,0634957719 62700 - 71 000040 80000 Hallunda 300,00000000 0000000 0,0616137368 91300 892,98058965 3 625,46565047 0000010 0,0790252262 69800 27,563822097 300001 - 127,94150668 6000000 - 592,98058965 3000040 418,08447536 5000000 417,09607203 7000000 0,1451259733 43000 35,000069144 900003 309,27460142 6999990 - 1,4183272151 72 Appendix III: Table of GWR Equations and Predictions for the 2016 Situation with New Stations Change Std Resid Observed Bus Std Error Station LocalR2 Predicted Intercept Workers Change Residual Int Std Err Std Err Workers Bus Std Err Std Err 361,26086556 0000015 90000 0000013 0,0762711518 78100 26,936741799 899998 - 306,74643005 0,4325695989 587,38832157 Ängbyplan 400,00000000 0000000 0,7273692341 98000 1999995 599994 87000 70,067816737 800001 5999960 1999995 433,19808421 - 81,939355236 0,0139878123 515,26018219 - 187,38832157 5999984 0,0536537832 5000006 388,83988268 282,96159374 1000002 24400 - - 127,32970867 3999974 10,882691585 900000 221,95127054 4000010 Akalla 28000 800,00000000 0000000 0,6994017182 61000 927,32970867 5000006 0,2248969523 87000 0,1263363590 15000 51,782345814 499998 266,83799153 1000000 0,3274605161 Fittja 600,00000000 0000000 0,0785728103 43900 938,01186611 9000047 537,23930733 8000003 68000 400002 - 01000 33,485119017 292,55978943 2000002 0,8061511913 419,29090940 0,1244741043 69000 27,401682787 199999 - 86,184702012 900004 - 338,01186611 8999990 6000026 393,99437839 0000008 0,1288622512 26,135761125 599998 2,3196723755 308,45700201 6999979 90000 30000 2576,6265592 20000217 - 536,56577393 2999946 0,1334934147 55,510245585 400000 816,51786778 8999979 423,37344077 6999985 38000 Brommaplan 3000,0000000 00000000 0,6674926375 182,51432626 2000026 71400 338,20880207 0,0516433753 1000008 100002 19999791 228,21580217 332,31455162 4999979 37,578364813 2494,1946226 593,34462070 4000022 0,0427654370 26700 21,870096287 500001 308,87482818 0999998 2,5999278536 20000 1999997 94000 Liljeholmen 4200,0000000 00000000 0,8032606714 3606,6553792 99999822 - 2139,2665141 39999799 0,1549228248 79000 73 Örnsberg 900,00000000 0000000 0,7495121592 56000 792,47996849 3999991 - 1449,2440949 10000058 0,1745089244 53000 66,788312197 400003 1697,6251515 10000023 107,52003150 5999995 432,95932172 4000006 360,37753392 0000019 0,0528078802 51800 27,269103664 300001 303,75430607 0999974 0,2483374906 39000 Kärrtorp 900,00000000 0000000 0,6960400775 35000 666,97284612 9999994 - 111,08088199 3999995 0,1487894129 24000 46,348127726 599998 386,66204942 2999985 233,02715387 0000006 452,29959469 8000021 337,67618939 5999984 0,0428848066 71300 11,763344964 600000 270,82439173 7999974 0,5152053121 46000 Stureby 500,00000000 0000000 0,4770689437 08000 5999983 258,76905198 699998 5000032 6000012 444,41632152 671,22768727 - 4999976 0,1539513800 13000 54,385346745 521,17480612 - 171,22768727 329,91898468 6999977 12900 - 94000 1999976 0,0486508983 21,008310046 259,29295392 5000006 0,3852866759 500000 1 43,526030974 000001 - 88000 268,18189616 0000008 0,5572369863 6999996 342,66247206 448,79413339 7000010 1328,7236629 79999972 - 250,08469040 2999996 0,0459334254 17100 19,689068365 200001 Globen 300,00000000 0000000 0,6548472756 87000 550,08469040 2999968 - 1089,6559051 10000049 0,160818930 38000 934,52622374 - 775,79649492 8000016 0,1920047285 08000 31,639192601 200001 2999946 9999975 441,66761863 308,26462831 - 328,76158636 6999975 2000013 25000 Huvudsta 600,00000000 0000000 0,6304804599 79000 928,76158637 0000032 0,0369039022 52900 18,756150327 099999 277,19938343 5000016 - 0,7443642515 10871 64000 422,25952196 Universitetet 500,00000000 39999951 0999973 270,94419499 9999979 81700 700000 - - 322,85836370 6000023 0,0325310409 11,317991634 240,618 2000009 0,7645969999 0000000 822,85836370 759,45981533 599998 0,5977222575 82000 1000030 - 6000020 0,1476036246 06000 33,618384413 1058,2635271 1999997 - 97000 9999999 456,47993781 - 114,15534347 7999996 342,43628395 0,0415643799 04300 12,305382806 700001 282,21696698 4000010 0,2500774601 den 1014,1553434 Hammarbyhöj 900,00000000 0,7002099496 97000 - 524,90393527 80000056 0000000 40,572264056 900003 1000012 2000012 0,1569430801 48000 798,90084574 74 76000 Johannelund 200,00000000 0000000 0,6548735241 93000 477,50403948 8999979 14,734677179 100000 0,0739266746 40900 69,728909161 900006 282,28223956 0999983 - 277,50403948 8999979 432,40021045 3999989 341,54170550 9999986 0,0798697916 83400 24,115505963 400000 289,10451924 0000002 - 0,6417759121 457 Hagsätra 1200,0000000 00000000 0,3854953697 61000 681,73091320 1000021 - 104,73575369 3999996 0,2197707 28000 62,773434395 800003 292,66502714 6999989 518,26908679 8999979 434,81266327 2999998 353,61762780 3000005 0,0724939481 29700 30,502979870 099999 284,75393565 6000010 1,1919365064 00000 Mälarhöjden 700,00000000 0000000 0,5950770418 73000 4000021 765,91738356 300000 1000019 3999993 440,90523656 840,11527838 - 7999991 0,2221542120 42000 60,938481498 985,06088391 - 140,11527838 384,87153210 7000007 32700 - 88000 2000027 0,0578623862 25,904552236 329,96354571 5000009 0,3177900073 600001 73,774569299 400000 0,3418220877 308,36014110 2000000 46000 0999994 361,70951728 443,21946377 5999993 439,04915825 5000009 151,50220243 6000005 0,0810061914 71800 26,545528942 600001 Islandstorget 800,00000000 0000000 0,7311862311 25000 648,49779756 4000052 - 23,387822373 399999 0,0091954902 42980 662,30236367 - 490,76045894 1000024 0,1597596330 38000 45,663919796 999998 4000048 436,16280118 275,58473363 225,33711877 1000007 8999993 3999974 Bergshamra 1100,0000000 00000000 0,5974502952 91000 874,66288122 9000050 0,0327850067 94300 11,296922815 900000 224,53181224 7999994 0,5166353438 59000 3 412,50734397 Skanstull 2200,0000000 99999964 357,19671504 7999987 83000 800001 0,7454459447 307,50192672 7000011 2000001 0,0393996040 19,473844616 354,61829509 4000018 11000 00000000 1892,4980732 2367,4725695 900000 0,8125039533 61000 70000077 - 00000191 0,1685813330 65000 26,670661328 2667,703535 2000008 - 10900 500001 384,58555419 - 22,036545929 7000022 324,45901551 0,0464780325 33700 17,445280901 299999 252,95705582 2999990 0,0572994635 1022,0365459 Hökarängen 1000,0000000 0,4821840080 04000 76,951907471 900000 29999988 00000000 44,425465951 800000 0000008 0,1617559036 34000 219,53784891 75 00000 Masmo 200,00000000 0000000 0,0940189376 56500 522,00158605 1000004 480,57541551 2999996 0,1577263987 70000 24,396004845 299998 - 51,869817153 699998 - 322,00158605 1000004 273,80219410 2999977 388,47530541 2000012 0,1233351168 40000 33,910649342 399999 287,05228039 0000021 - 1,1760372743 0000 Fridhemsplan 5700,000 00000000 0,6615649775 84000 4200,3040806 70000076 - 1315,1569503 79999898 0,1925422047 65000 8,7217466694 40000 1634,5970635 50000030 1499,6959193 29999924 341,31009839 0000007 292,66963877 6999989 0,0349666724 26100 17,485681158 700000 255,51511500 3999995 4,3939394890 50000 Västertorp 700,00000000 0000000 0,5287747229 25000 89999890 640,74755218 799999 7999946 2999972 446,57279785 1036,1633642 - 2000049 0,2139299791 09000 61,947031042 885,74064536 - 336,16336429 385,15809348 4999995 49100 - 69000 4999976 0,0602832782 27,833236612 329,57485083 3000028 0,7527627430 000000 2616028 10,553154711 800000 1,3999265465 247,11680155 6000013 80000 2000004 280,78560278 389,39625912 8999995 1454,3657629 19999952 545,1 5999958 0,0334704442 87400 17,043714639 200001 S:t Eriksplan S:t 2500,0000000 00000000 0,6381491303 43000 1954,8738397 10000084 - 1137,1129063 90000035 0,1874459785 24000 2107,1905180 - 1755,6835218 10000002 0,1693834632 95000 18,868789803 700000 30000021 2000026 428,40643908 308,72700230 - 263,20461586 2000020 sen 1000027 52000 Medborgarplat 1400,0000000 00000000 0,7306626135 94000 1663,2046158 60000104 0,0354382162 78200 18,129537039 999999 318,46520699 0000013 - 0,6143806251 87000 450,48848574 Tallkrogen 400,00000000 6999988 4999994 329,04232123 2000006 19900 700001 - - 249,72546669 8000016 0,0451296256 16,391043941 255,44995500 9999996 0,5543437281 0000000 649,72546669 14,515359292 799999 0,5267112725 91000 5000023 - 499999 0,1561664003 00000 45,255423535 298,72094798 2000007 0,0210560672 437,54198416 9,2129134544 20001 2999995 304,73470322 0,0335832474 99600 17,563884704 199999 297,36058746 6000027 75600 790,78708654 Gamla stan Gamla 800,00000000 0,6736631135 77000 - 1431,9944267 5999955 0000000 12,492229268 299999 49999935 79999912 0,1692912379 94000 1823,7693858 76 74300 Karlaplan 900,00000000 0000000 0,6338489631 52000 924,83630135 8000014 - 1162,3761763 69999939 0,1339464871 94000 11,939447243 400000 1694,3356982 00000024 - 24,836301357 699998 445,79311463 9000009 312,81765391 5999983 0,0321007715 12300 15,657005000 500000 318,37272273 0000021 - 0,0557126176 Enskede Gård Enskede 300,00000000 0000000 0,6055787463 77000 489,28846984 0000005 - 844,02886660 5999951 0,1587033170 77000 46,845003187 899998 1082,0349362 10000069 - 189,28846984 0000005 446,72322401 8999986 338,01868531 0000023 0,0462931777 79000 19,878068332 11000 100000 265,17345975 6000000 - 0,4237265037 Solna strand Solna 300,00000000 0000000 0,6123931628 03000 5000028 529,72643521 100001 1999965 5000028 437,90861352 648,81799525 - 7000017 0,1694968736 37000 45,294740153 685,79114122 - 348,81799525 306,82429952 6000004 53100 - 38000 1000007 0,0379283675 16,899936519 258,25141005 7999976 0,7965543140 899999 gsved 54,229778928 999998 0,2532337730 266,29086046 3000001 11000 2000007 335,08286672 424,93411587 4999974 289,73446014 2999978 107,60766944 3000006 0,0608020519 08100 28,119595953 699999 Rå 800,00000000 0000000 0,3855907901 40000 692,39233055 7000037 - 50,546373763 100000 0,1968165940 89000 4622 366,86546588 - 171,83516389 1999997 0,1468205453 07000 50,659081326 200003 5999981 436,83112499 274,83235282 95,185243233 600005 8000007 7000022 Hallonbergen 1000,0000000 00000000 0,6232179256 70000 904,81475676 5999959 0,039335 86500 10,560066075 200000 217,68056353 3999987 0,2178994073 15000 442,62176064 Skärmarbrink 1200,0000000 89999894 322,66491669 9999992 09400 500000 1,6021637852 709,15255547 4999986 9999999 0,0414860674 14,252481303 259,33755047 3000022 50000 00000000 490,84744452 952,20830909 099998 0,6824996160 55000 5000014 - 5000004 0,1651308622 97000 38,217009078 1210,1494578 2000026 - 74000 4000007 449,12694977 - 368,82186248 5000014 289,19511787 0,0596814218 97600 11,961213823 600000 225,75232887 6999997 0,8211973533 668,82186248 Hjulsta 300,00000000 0,6565827686 12000 - 28,399410085 4000007 0000000 53,941596927 699997 9999993 600000 0,1153824742 18000 309,01548690 77 56262 80000 Zinkensdamm 800,00000000 0000000 0,7274318228 75000 1278,6977855 40000041 - 1824,93 59999935 0,1692940615 39000 15,748873325 900000 2208,8735661 30000199 - 478,69778553 7000016 453,41419544 7999987 311,93206068 2999975 0,0360170064 03100 17,803729140 600002 304,47026332 3999973 - 1,0557626786 Husby 1100,0000000 00000000 0,6960326789 10000 800,39329409 2000019 1,2468838238 90000 0,1247255712 79000 51,643556555 200000 265,64495158 6999980 299,60670590 7999981 445,93465890 9000007 277,22021380 1999989 0,0516673017 29500 10,781867010 299999 219,15298430 6999997 0,6718623455 75000 998681 Telefonplan 2400,0000000 00000000 0,6738910870 19000 00000043 1201,2071384 200004 40000061 439,48033830 1192,5257036 - 50000002 0,1448894850 43000 86,226740010 1468,0913295 1207,4742963 99999957 378,18542587 6000011 75700 2,7475047030 6000021 0,0687598856 38,340 324,13522367 1000006 70000 999999 52,760460378 200001 0,0945077758 253,83007679 2000000 11700 3000015 324,43773982 451,89052517 2000026 406,09319941 5000015 42,707168444 499999 0,0500143938 66300 22,226115533 700000 Bandhagen 900,00000000 0000000 0,4431310108 70000 857,29283155 5000021 - 138,05523836 5000008 0,1623231884 08000 262,80984586 28,440260994 999999 0,1600722403 60000 44,814572764 899999 0999985 7000007 453,96080624 324,69038653 - 127,09854467 6000004 6999995 44000 Gubbängen 600,00000000 0000000 0,4892106577 85000 727,09854467 6999950 0,0458736990 26200 17,517159540 500000 252,17332318 6000005 - 0,2799769119 8522368 430,20041330 Thorildsplan 800,00000000 19999989 291,30710110 0000011 24800 300001 0,4659625824 200,45729557 6999996 8999998 0,0358230731 18,073399054 262,06292407 4000023 98000 0000000 599,54270442 1358,2880357 400000 0,6722722915 12000 3000032 - 99999989 0,196 61000 10,595808876 1665,5735923 5999997 0,9885653750 395,49613839 390,97378839 9999989 5999992 336,61143934 0,0764168117 84500 24,190686346 700002 287,36842470 9000010 90000 1509,0262115 Vällingby 1900,0000000 0,6598228543 02000 11,796173895 600001 99999897 00000000 70,525344618 399998 0999983 0,0622647117 20000 304,09586814 78 Skarpnäck 1000,0000000 00000000 0,6776347211 43000 908,05639971 0000051 61,157961356 199998 0,1482373656 16000 48,310111283 500000 221,05400128 9000013 91,943600290 000006 351,34684881 4999987 328,17959825 6000020 0,0434647924 83900 11,801470020 800000 261,07369359 6999988 0,2616889851 16000 Kista 1200,0000000 00000000 0,6953151924 01000 1525,3559628 90000001 8,3630044949 00000 0,1222310578 58000 51,474154048 999999 257,83382839 5000012 - 325,35596288 5999986 416,27382693 3999999 273,42621036 2999996 0,0499832896 76600 10,704502726 21000 099999 217,28067727 4999988 - 0,7815912071 8932 Abrahamsberg 1000,0000000 00000000 0,6648484566 24000 3999964 761,20609257 699998 00000044 447,00564344 737,59711067 - 0999999 0,1639698540 68000 47,040363172 1011,8696915 262,4028 5999979 323,81568922 5000028 22600 0,5870236610 7000011 0,0454189370 25,181640023 305,48706536 7000014 51000 600000 12,450334995 100000 - 89000 296,06244896 9000002 0,5811289816 7000006 304,60574513 397,40239272 3000028 1727,9117481 90000026 - 230,94204780 6000005 0,0325536102 84600 17,307508349 399999 Kungsträdgård en 500,00000000 0000000 0,6535361448 73000 730,94204780 6000005 - 1302,5447850 40000079 0,1605676482 78000 520,33266072 - 241,57386299 1999988 0,1488345797 05000 44,626542553 000000 3000004 90000 453,86040639 350,48503023 - 5,3960436691 8999999 0999996 77600 Björkhagen 700,00000000 0000000 0,7296044155 87000 705,39604366 9000051 0,0418414658 41900 11,675420836 200001 290,40630701 8000007 - 0,0118892143 stull 408,96406381 Horn 2100,0000000 10000142 313,82066483 1999977 40100 700001 1,0430359352 426,56421478 9000005 0000027 0,0378761332 18,419095481 292,80837979 9000022 70000 00000000 1673,4357852 1885,8361629 800001 0,7439384833 00000 09999949 - 00000090 0,1629631455 84000 22,274114819 2271,6628610 2999983 - 16000 4999987 440,75945204 - 278,88050953 9000004 379,54804559 0,1146278034 86000 29,751977422 900001 282,51184026 8000014 0,6327272353 778,88050953 Vårby gård 500,00000000 0,1311470483 29000 381,79852645 9000016 4999987 0000000 37,931379458 000002 18,521291410 000000 0,1639668920 14000 - 79 78572 Rådmansgatan 1500,0000000 00000000 0,6310626579 70000 1396,5279079 10000067 - 1172,9566825 39999974 0,1627218904 16000 11,366648792 700000 1586,22 69999959 103,47209209 0000004 426,04375611 6999987 294,25414106 1999974 0,0327071739 58000 16,964115463 900001 262,03603917 8000010 0,2428672891 08000 Mörby centrum 2000,0000000 00000000 0,6172171970 39000 1841,6009785 10000004 - 256,02490742 2000013 0,1558241897 00000 51,183494466 200003 414,17073567 1999978 158,39902149 4000010 331,65498462 6999976 293,47477165 3000005 0,0335934349 74600 11,311879601 599999 220,19784099 8000004 0,4776018116 31000 Axelsberg 500,00000000 0000000 0,7018241319 69000 4999987 1203,4991826 300004 79999928 4999987 437,12788204 732,52193206 - 99999892 0,2013548960 44000 64,868833775 1419,0454248 - 232,52193206 378,50448239 9999972 03200 - 22000 8999993 0,0538102228 25,972370137 318,04632140 2999979 0,5319311387 500000 48,774560385 599997 - 93000 228,62273321 6999990 0,4362862847 2999996 292,57983684 282,19616954 9999992 530,04095977 4000044 - 123,11831839 2999996 0,0336223588 50300 11,584156723 600000 Danderyds sjukhus 2800,0000000 00000000 0,6002941236 82000 2923,1183183 89999786 - 357,32243371 3999999 0,1545888642 97000 - 625,46232127 3000043 0,1020402304 86000 21,318027407 300001 120,33407483 0999995 337,72390126 408,00797675 141,49658356 0999994 5999984 6999994 Alby 1000,0000000 00000000 0,0596453187 32500 858,50341643 9000034 0,1391344737 25000 35,731454396 600000 299,41300102 5000028 0,4189711863 16000 19000 411,45238792 Näckrosen 1100,0000000 6000007 4999987 294,74663992 7999979 89600 199999 - - 146,36497134 9999986 0,0354112557 10,775162766 230,57302291 4000006 0,3557276021 00000000 1246,3649713 369,19641265 600000 0,6190929308 87000 40000011 - 2999982 0,1731048681 14000 48,177228011 485,43553643 06995438 4999984 0,06 399,09552615 24,224916382 899998 6999995 270,29008565 0,0510446817 28800 10,980726414 699999 215,93099165 6999993 31400 975,77508361 Rinkeby 1000,0000000 0,6547512808 71000 - 39,060558956 6999950 00000000 52,328983378 899999 4999973 599998 0,1204938562 63000 310,62497653 80 14000 Rissne 900,00000000 0000000 0,6207875226 87000 1230,2952136 90000082 - 97,200228937 299997 0,1204578467 51000 52,790413781 900000 362,18245220 0000000 - 330,29521369 1000015 409,81209936 2000026 266,75952809 5000007 0,0474791043 57100 11,566912494 700000 216,31026427 8000005 - 0,8059674524 9 Gärdet 1100,0000000 00000000 0,6301501579 18000 678,32315674 3000027 - 1139,8630316 39999917 0,1285058547 36000 10,647908095 400000 1700,5109811 40000013 421,67684325 6999973 390,47926335 6999979 311,1458762 4999994 0,0322760306 02900 14,907589906 900000 316,95433983 8000010 1,0798956124 60000 Hässelby gård 900,00000000 0000000 0,6623818285 06000 8999972 90000 100003 2999983 425,31263580 682,63597734 4,8295251838 0,0772356246 32700 71,181742356 288,31847218 217,36402265 0999999 345,14533107 9000016 23100 0,5110688099 4000024 0,0814509734 24,555641516 292,67930908 3000021 83000 900000 10,201795834 200000 - 49000 265,58609049 0999993 0,5317898022 9000026 298,34381622 454,97445425 0000008 1788,2938423 09999945 - 241,95077505 8999994 0,0340932500 19500 16,950577349 000000 Rådhuset 1000,0000000 00000000 0,6669063091 02000 1241,9507750 60000069 - 1411,7804847 69999930 0,1775174977 06000 4177 1587,2066713 - 1301,2909655 70000026 0,1965100912 46000 16,198419246 299999 19999941 9000010 414,83689597 297,61828500 - 255,97041778 9000019 6000008 65000 Kristineberg 1100,0000000 00000000 0,6756627711 94000 1355,970 90000056 0,0363672052 87800 19,293994695 300000 279,75768536 2000018 - 0,6170386970 90000 353,51939480 Högdalen 1000,0000000 8000004 1999985 326,75890495 9000006 18400 500001 - - 387,21125695 9999994 0,0532904622 24,619645691 256,64244240 9000012 1,0953041406 00000000 1387,2112569 73,290611903 200002 0,4150686395 27000 50000006 - 599995 0,1731886560 08000 52,311097876 337,68228865 0 4999987 0,1691301683 254,55958017 43,053704661 499999 8000004 324,32264839 0,040997169 56400 23,351205706 599998 313,91639659 6000027 93000 2056,9462953 Alvik 2100,0000000 0,6873752963 42000 - 1187,3372612 39999779 00000000 28,322714704 999999 29999943 20000073 0,1912920336 76000 1439,1479606 81 04000 Blåsut 600,00000000 0000000 0,6584868410 69000 679,64836761 2000015 - 377,39586004 0999992 0,1541831638 84000 43,515600402 099999 644,73288965 6999987 - 79,648367612 000001 453,78424634 4999985 337,57998313 6000010 0,0431154372 15400 13,329440757 900000 267,06674002 1999976 - 0,1755203453 Hötorget 500,00000000 0000000 0,6418203934 38000 783,05945611 4999989 - 1249,3912455 40000000 0,1638265666 16000 10,698413294 000000 1668,4723721 49999956 - 283,05945611 4999989 443,49124580 5000005 299,69397204 6999988 0,0328228658 58200 17,213311276 31000 999999 271,15517183 9999980 - 0,6382526347 59599 Bagarmossen 1100,0000000 00000000 0,7028201121 34000 1000018 000000 499999 2999985 451,06714117 665,06147206 10,9301 0,1471291288 18000 48,083558778 268,11981113 434,93852793 8999982 331,12677394 9999972 12800 0,9642434312 2999982 0,0430453165 11,653807366 264,21451037 3999985 74000 600001 45,410238499 000002 0,6986128740 259,10335211 4000018 67000 7000018 331,37248385 442,46500803 3999995 518,77444517 4999983 309,11175093 8999990 0,0430231609 01200 13,634447756 200000 Sandsborg 700,00000000 0000000 0,6106646847 78000 390,88824906 1000010 - 251,46798259 6000013 0,1530902312 37000 255,87758189 - 59,292208088 199999 0,2497702768 70000 60,323996948 599998 7999988 415,58006751 402,84693567 195,90099422 2999998 4000007 8000023 Sätra 800,00000000 0000000 0,3481798779 37000 604,09900577 7000002 0,0949673032 39200 25,009211601 800001 299,47751532 2999977 0,4713916993 06000 365,28512274 Farsta 1200,0000000 8999987 327,56363649 8999983 78000 200002 0,3296004137 120,39812758 0999997 7999992 0,0478218799 16,984835573 257,39801734 6000017 14000 00000000 1079,6018724 3000011 200003 0,4901389148 33000 20000063 139,43849213 0,1622184279 19000 44,444458194 162,20788370 000053 3000028 - 17000 9999994 288,00242557 - 120,73117071 2999982 411,67135729 0,0785334554 43200 32,844208568 600003 344,59259945 5000027 0,4192019233 1920,7311707 Fruängen 1800,0000000 0,4133189230 33000 - 334,73136527 19999909 00000000 61,102972580 399999 5 7000009 0,2301467312 75000 577,10915171 82 84000 Duvbo 600,00000000 0000000 0,6003295026 82000 1006,5088167 40000043 - 212,40353140 9000010 0,1397229591 95000 50,779137119 900000 426,02518890 9000008 - 406,50881674 2000022 418,86996225 0000015 280,50730219 1999997 0,0411238865 31500 11,407792552 600000 224,16514790 9000012 - 0,9704893006 Solna centrum Solna 1600,0000000 00000000 0,6265329339 03000 1975,1753278 59999925 - 550,60689590 2000019 0,1897832836 19000 41,436288596 600001 649,50950167 5000024 - 375,17532785 8000003 396,73549110 6999973 295,27049632 6999989 0,0344097145 88600 11,598472767 22000 600001 243,64847028 7999999 - 0,9456560763 denplan O 2100,0000000 00000000 0,6266719988 70000 30000055 1101,5739589 000001 09999888 30000055 370,38549191 3762,5556837 - 29999890 0,1709936327 46000 13,334959185 1460,5873944 - 1662,5556837 284,42836826 4000028 23000 - 90000 3999999 0,0324965276 15,806638362 249,83548468 6000001 4,4887170799 199999 11,594010006 000000 - 80000 286,63662668 2999974 1,3153927024 1999973 301,30964610 433,81934177 5000013 1688,5623137 09999898 - 570,64279636 3000002 0,0320827613 56000 16,801855007 000000 Östermalmstor g 800,00000000 0000000 0,6386030016 78000 1370,6427963 59999920 - 1226,2155189 80000070 0,1524173230 07000 4 1509,662764 - 1242,9252897 70000063 0,2079891349 13000 7,5858607325 20000 20000030 9000013 435,57959326 293,14090029 - 344,28762744 0000024 2000026 36000 Stadshagen 700,00000000 0000000 0,6636626874 17000 1044,2876274 49999945 0,0356873840 59600 18,536153513 199999 265,82078539 0000026 - 0,7904126657 50000 363,01729560 Tekniska Tekniska högskolan 2000,0000000 50000010 1000034 297,49734795 5000009 83300 600000 - - 807,53364709 2999980 0,0323809619 15,270688535 274,10654226 7999998 2,2245046086 00000000 2807,5336470 1105,0813424 300000 0,6197854413 20000 90000159 - 49999966 0,1480489260 99000 12,596605684 1564,7845715 1000025 - 30000 3000003 398,81740388 - 633,15230639 1000018 293,35053199 0,0373416437 71500 12,172300903 300000 234,52358726 8000000 1,5875744143 2133,1523063 Sundbyberg 1500,0000000 0,6033447494 51000 - 364,34154992 89999922 00000000 48,470103599 900000 1000024 7000017 0,1601158013 19000 528,28795632 83 71000 Åkeshov 500,00000000 0000000 0,6805432531 04000 546,91733348 0000025 - 254,89814002 2000007 0,0753705857 46400 64,285124321 400005 603,52743304 3999963 - 46,917333480 200000 431,42559145 0000013 346,47321697 0000010 0,0621475152 36500 26,395454578 900001 302,59301886 2999998 - 0,1087495373 Svedmyra 400,00000000 0000000 0,5095453465 71000 624,60913728 3999985 - 227,69278975 2000010 0,1536867037 29000 49,907446041 900002 492,72501695 6999980 - 224,60913728 4000013 441,44444196 1999985 332,86321556 6000008 0,0468507758 07400 19,596286044 51000 599999 258,80506545 8999991 - 0,5088049954 Farsta strand Farsta 700,00000000 0000000 0,4909126413 89000 20000110 5999998 599997 5999997 7000028 359,52754827 1042,8164839 162,03579170 0,1628155093 19000 44,386051240 141,64246090 - 342,81648391 329,47417068 4999990 04500 - 11000 0000011 0,0489040916 17,182635284 259,70774174 1000007 0,9535193772 300002 49,898249109 799998 - 75000 264,67295335 0000000 0,1694739220 4000010 339,94839584 452,27059992 2000025 654,21084713 4999995 - 76,648072408 399997 0,0470668948 84200 19,695931158 899999 Sockenplan 500,00000000 0000000 0,5511031912 04000 576,64807240 7999962 - 399,78983713 6000017 0,1517434609 33000 466,97986317 - 266,68609402 8000014 0,2368828114 07000 67,228632306 500003 5999981 438,51818342 399,58014991 30,339860840 699998 6999997 3000014 Bredäng 1100,0000000 00000000 0,4591974624 87000 1069,6601391 59999972 0,0760439270 60100 26,149066425 499999 323,58032616 3999985 0,0691872355 29400 91000 455,98353483 Skogskyrkogår den 400,00000000 8000018 8000026 325,35479777 5999998 01500 100001 - - 340,58660755 5000000 0,0425006293 12,695652083 254,67504404 4999993 0,7469274250 0000000 740,58660755 122,19261039 099997 0,5979881817 53000 7999969 - 9000003 0,1525182304 61000 46,017881942 396,35382194 52152716 5999974 0,0122252972 378,33151742 4,62 20000 1999990 350,10569179 0,0576026871 37600 31,282595881 999999 301,67251084 2999998 81900 ansen 895,37478472 Midsommarkr 900,00000000 0,7594690408 36000 - 1792,3502953 8000009 0000000 60,030849048 400000 69999912 49999897 0,1617641929 61000 2075,1077478 84 Tensta 900,00000000 0000000 0,6570874295 71000 696,91546435 0999969 - 23,631872528 900001 0,1147781626 36000 53,244885924 300000 305,34085215 6999972 203,08453564 9000003 450,84606403 9999987 282,94895691 4000007 0,0572559493 72600 11,527764913 100000 222,11571054 8999999 0,4504520541 43000 Stora mossen Stora 500,00000000 0000000 0,6753414092 00000 608,23182772 7999985 - 974,06803158 8000053 0,1795799200 97000 38,180745238 999997 1213,5422344 79999934 - 108,23182772 7999999 437,46294410 2999984 328,36542597 3000015 0,0432441571 40900 24,801762267 65000 099999 317,41142095 8999997 - 0,2474079900 5 Stadion 700,00000000 0000000 0,627413356 80000 29999980 1159,7587190 300000 19999919 3999995 453,14824992 1143,1247020 - 59999976 0,1422908369 72000 11,151972760 1662,5752274 - 443,12470203 303,65948926 9000005 52900 - 93000 6000005 0,0321845946 16,154121335 292,66076637 9999984 0,9778802016 500001 79 48,276752720 399998 - 10000 277,88198156 9999994 1,3904726635 0000015 381,48633879 346,77936683 3000016 106,44902996 8999994 - 482,18722984 5999980 0,1037914431 27000 26,2867727 700001 Skärholmen 800,00000000 0000000 0,2279015211 08000 1282,1872298 49999994 155,38128857 8000010 0,2220217974 02000 24,535462130 286,69424470 4000027 0,1762104362 11000 48,338947639 300002 399999 394,46073119 373,45993431 583,19434830 9000020 2000026 3000019 Vårberg 1100,0000000 00000000 0,1838510667 37000 516,80565169 0999980 0,1079460204 06000 26,806582163 800002 277,78717704 3999975 1,4784598369 20000 58710 446,49904573 Hässelby strand 700,00000000 8000017 30000 347,37326271 2999974 25500 200001 - - 1,9426543285 2000013 0,0832020862 24,716384634 294,69882559 2999981 0,0043508588 0000000 701,94265432 0,7379250120 100007 0,6708419894 44000 8999993 - 73000 0,0767311265 06100 72,859261317 296,68396219 6210420 9000023 0,4626255195 433,81659471 200,69462752 0000012 9000022 374,89486639 0,0594294892 24800 31,179304113 499999 320,55799966 0999997 47000 n 799,30537247 Hägerstensåse 1000,0000000 0,6049430850 29000 - 938,16014636 9999960 00000000 70,817647676 500002 99999895 6000049 0,187 78000 1177,6229206 85 Västra skogen Västra 1300,0000000 00000000 0,6381195223 40000 607,10118954 5000011 - 903,63590501 0999977 0,2033082860 62000 20,182389066 999999 1092,5157834 30000056 692,89881045 4999989 438,57355603 2999988 290,24621521 0999992 0,0347091295 10000 17,071846838 599999 268,55830539 4999991 1,5798919039 30000 Mariatorget 1900,0000000 00000000 0,7298418124 48000 1749,9520005 39999972 - 1820,1846036 30000083 0,1711433191 61000 16,000855138 399999 2183,7974637 19999996 150,04799946 2999996 412,39824164 8000010 314,97782482 9999975 0,0357099262 13600 18,194305198 799999 320,59552903 7999995 0,3638424811 49000 Blackeberg 500,00000000 0000000 0,7132179592 61000 1999987 15,741575804 299996 5000016 600001 441,74527032 560,16909992 - 100000 0,0259417345 32300 73,978720022 397,80894015 - 60,169099921 352,32970375 0000022 89900 - 96000 3000000 0,0798215852 25,816367670 303,00235412 4000021 0,1362076833 799998 993 71,173540639 699 1,0755460401 287,84031976 5000004 60000 4999982 334,70306251 448,83370145 4999999 347,65245800 9999975 482,74131028 9000012 0,0739598713 56400 24,443315555 600002 Råcksta 1100,0000000 00000000 0,6730229295 19000 617,25868971 0999988 - 5,9436555245 40000 0,0493863577 28300 1950,5514229 - 1674,4915477 39999987 0,1565717567 31000 64,980585227 500001 09999928 000002 445,77146309 344,29911187 - 35,292854472 3000023 5999984 59000 Aspudden 1000,0000000 00000000 0,7684579264 44000 1035,2928544 70000066 0,0553648607 79700 29,795652472 099999 290,85830545 2000025 - 0,0791725298 3 334,50903584 Ropsten 3800,0000000 39999919 307,06685340 4000028 88100 500000 3,4635079764 1158,5747138 30000064 3999982 0,0331757082 12,788107905 309,57973247 799998 40000 00000000 2641,4252861 1040,0086576 200001 0,6224508046 88000 70000163 - 70000048 0,1166982336 83000 14,575308976 1612,5105949 0000007 - 00000 4000019 263,68666031 - 421,09583899 3000004 394,99093525 0,1369343356 15000 32,174427328 999997 299,54662494 8999977 1,5969554110 821,09583899 Norsborg 400,00000000 0,0762036912 42500 575,93870872 8000051 4000019 0000000 35,160788169 299998 111,22638545 4999999 0,0730730399 18000 - 86 70000 Hallunda 300,00000000 0000000 0,0715362799 18300 916,50333005 7999960 578,17787193 9000056 0,0872488768 47000 31,755720135 000001 - 110,19517841 5000001 - 616,50333005 7999960 410,24948911 4000028 397,34599165 9999981 0,1355486215 57000 32,854770852 500003 298,28151896 9999979 - 1,5027522188 8347429 Barkarby Barkarby station 608,00000000 0000000 0,6599545689 20000 676,52625679 5999984 - 28,110621921 400000 0,1170423870 51000 54,70 900002 306,27840429 3999984 - 68,526256795 699993 436,13322700 1000023 300,30221471 3000012 0,0645542047 35900 12,552252030 37000 500000 232,08929116 1000006 - 0,1571223024 Järla 1053,0000000 00000000 0,7460741795 00000 40000052 514,98852838 699997 7000040 421,24276465 1012,6105466 - 3000016 0,1437629561 83000 38,812961652 844,62378142 40,389453364 600001 351,60872346 1000011 76400 0,0958816548 1000016 0,0375619116 12,036004544 309,51442590 8000021 41100 400001 ,0207927076 21,962985426 900001 0 330,34337656 5000028 19200 1000001 327,43227936 367,18089463 6999978 2007,3661062 79999940 7,6346849854 40000 0,0364171310 75800 14,654703902 900000 Hammarby Hammarby Kanal 1854,0000000 00000000 0,7529168747 97000 1846,3653150 09999904 - 1667,6785139 30000008 0,1722395555 53000 949,62513373 - 587,71361317 6999957 0,1388158096 81000 36,517037068 000000 7000056 400003 172,93816401 349,17584807 - 54,765317301 0000008 Centrum 1000019 53000 Nacka Nacka 2940,0000000 00000000 0,7403972393 13000 2994,7653172 99999879 0,0366397965 42300 12,230079545 800001 308,26496292 8999978 - 0,3166757182 87000 417,66619061 Barkarbystade n 265,00000000 1999990 900002 294,23124343 6999989 60000 199999 - - 43,163415043 9000020 0,0606978555 11,352949671 227,11339146 5999996 0,1033442878 0000000 308,16341504 6,7022540068 300001 0,6827158947 71000 3999976 - 00000 0,1215131764 99000 52,664246183 282,17862457 5000004 1,0763970817 395,18391242 425,37481007 9999975 8999975 296,15361077 0,0328097010 47400 15,133087232 599999 310,92034662 6000025 20000 1600,6251899 Sofia 2026,0000000 0,7129185205 32000 - 1487,5451218 19999912 00000000 18,791536613 500000 30000029 70000003 0,1662162266 04000 1860,8229536 87 Sickla 1118,0000000 00000000 0,7408260235 16000 1024,1889513 70000041 - 628,53274110 8999971 0,1530730478 33000 36,370452151 599999 942,76445682 8999982 93,811048633 200002 417,53389997 9000012 355,58283736 5999978 0,0380078605 74700 12,145567547 000001 319,67035616 9000002 0,2246788790 99000 88 Appendix IV: GWR Prediction by ArcGIS (ArcMap) ArcMap proposes an option while calculating the GWR model to predict dependent variables at given location as well as their respective GWR equations. The tool is very useful and the results for 2016 are presented in the table below with each respective prediction done with the OLS equation. The way these predictions were executed and calculated by ArcMap are unclear. It was for this reason that the GWR equations for the new stations were finally determined using the prediction from the OLS equation. 89 TRITA TRITA-ABE-MBT-19647 www.kth.se