i
Mas e Deg ee P og am in
Da a Science and Ad anced Analy ics
Lisbon’s Real Es a e Analysis based on P oximi y Calcula ions
Ma ia Madalena Jo ge Do Nascimen o Valé io
P ojec Wo k submi ed o In e na ional Jou nal o Scien i ic and Resea ch
Publica ions
p esen ed as pa ial equi emen o ob aining he Mas e Deg ee P og am in Da a Science and Ad anced Analy ics
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
MDSAA
i
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
LISBON’S REAL ESTATE ANLYSIS BASED ON PROXIMITY
CALCULATIONS
by
Ma ia Madalena Jo ge do Nascimen o Valé io
P ojec Wo k p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in Ad anced
Analy ics, wi h a Specializa ion in Business Analy ics
Supe iso / Co Supe iso : Miguel Cas o
Co Supe iso : B uno Ja dim
ii
02 2023
STATEMENT OF INTEGRITY
I he eby decla e ha ing conduc ed his academic wo k wi h in eg i y. I con i m ha I ha e no used
plagia ism o any o m o undue use o in o ma ion o alsi ica ion o esul s along he p ocess leading
o i s elabo a ion. I u he decla e ha I ha e ully acknowledge he Rules o Conduc and Code o
Hono om he NOVA In o ma ion Managemen School.
Lisbon, Feb ua y 2023
iii
ABSTRACT
The eal es a e ma ke is always changing and e ol ing and wi h sus ainabili y becoming an
inc easingly impo an opic, he way he p ice o a p ope y is de e mined, and he ac o s aken in
conside a ion, should e ol e as well. Inspi ed by he popula concep o Sma Ci ies, mo e speci ically
he 15-minu e ci y app oach, which is a concep highly ocused on accessibili y and walkabili y in ci ies,
di e en a iables we e calcula ed o assess each p ope y’s accessibili y and di e si y o ameni ies.
Bo h hese ac o s a e di e en o each p ope y, depending on hei loca ion. This wo k p esen s an
analysis o he eal es a e ma ke in Lisbon whe e, aside om he physical a ibu es o a habi a ion,
he di e si y and accessibili y o di e ence se ices in each loca ion will be e alua ed and in eg a ed
in he machine lea ning p ocess. The goal is o know he impac o each calcula ed measu e when
p edic ing he p ice pe me e alue o each house, in o de o help unde s and why simila houses
ac oss Lisbon ha e such dis inc i e p ices. Bo h he Euclidean Dis ance and he Ne wo k Dis ance we e
used in he calcula ions. The dis ance o Tejo Ri e and he numbe o comme cial es ablishmen s
wi hin a 15-minu e walk adius we e wo o he mos impo an ea u es in he p edic i e models
es ed. Th ee di e en me hods we e es ed and imp o ed, elec ing he Random Fo es Reg esso as
he bes he one and he one o be used in he inal model. The inal model had hal o he a iance in
he a ge explained by he all he calcula ed ea u es, which makes his analysis a po en ial good ool
o help ill he gap o a p edic i e model ha only ac o s in he physical cha ac e is ics o a house.
KEYWORDS
Lisbon; Sma Ci y; Real Es a e; Accessibili y; Mobili y
Sus ainable De elopmen Goals (SGD): This Mas e ’s Thesis con ibu es o he
Sus ainable De elopmen Goal o Sus ainable Ci ies and Communi ies.
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INDEX
1. In oduc ion ................................................................................................................... 1
2. Li e a u e e iew ........................................................................................................... 3
2.1 The 15-Minu e Ci y App oach ............................................................................... 3
2.2 Real Es a e ............................................................................................................. 4
2.3 E alua ing Real es a e’s p ices h ough 15-minu e Ci y ea u es ......................... 5
3. Me hodology ................................................................................................................ 8
3.1 Dis ance Calcula ions ............................................................................................. 8
3.2 Me hods o unco e ela ionships ........................................................................ 9
3.2.1 Linea Reg ession ............................................................................................ 9
3.2.2 Decision T ee Reg esso ............................................................................... 10
3.2.4 Random Fo es Reg esso ............................................................................. 10
3.2.5 Lasso .………………………………………………………………………………………………………11
3.2.6 Spea man co ela ion ................................................................................... 11
3.3 E alua ion Me hods ............................................................................................ 11
3.3.1 R2 Sco e ......................................................................................................... 11
3.3.2 R2 Adjus ed Sco e .......................................................................................... 12
3.3.3 Mean Squa ed E o ..................................................................................... 12
3.3.4 Mean Absolu e Pe cen age E o ................................................................. 12
3.4 So wa e Used ..................................................................................................... 12
4. Resul s and discussion ................................................................................................ 14
4.1 Fea u e Analysis ................................................................................................... 14
4.2 Linea Reg ession Analysis ................................................................................... 16
4.3 Random Fo es Reg esso Analysis ...................................................................... 18
4.4 Resul s Compa ison ............................................................................................. 19
4.5 Discussion ............................................................................................................ 20
5. Conclusion .................................................................................................................. 24
6. Limi a ions and ecommenda ions o u u e wo ks ................................................. 25
Re e ences ....................................................................................................................... 26
Appendix.......................................................................................................................... 28

LIST OF FIGURES
Figu e 1.1 - Lisbon’s pa ishes mos p essu ed by local accommoda ion ......................... 2
Figu e 2.1 - Dis ance co e ed by each way o commu ing ............................................... 4
Figu e 2.2 - F amewo k p oposed by Pozoukidou & Cha ziyiannaki ................................ 6
Figu e 2.3 - Pa is F amewo k Resul p esen ed by Pozoukidou & Cha ziyiannaki ........... 7
Figu e 3.1 - Euclidean dis ance and Ne wo k dis ance ..................................................... 8
Figu e 3.2 - Decision T ee Reg esso ............................................................................... 10
Figu e 3.3 - Random Fo es Reg esso ............................................................................ 11
Figu e 4.1 - Linea Reg ession be ween P ice/me e and Comme ce Coun ................. 17
Figu e 4.2 - Random Fo es Reg esso Fea u e Impo ance ........................................... 18
Figu e 4.3 - Final model's mos impo an ea u es ........................................................ 20
Figu e 4.5 - Linea Reg ession be ween P ice/me e and Wa e dis ance ..................... 21
Figu e 4.5 - Linea Reg ession be ween P ice/me e and Shannon Di e si y Index ....... 21
Figu e 4.6 - Rada cha o he ea u es in A enidas No as and San a Cla a ................. 21
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LIST OF TABLES
Table 3.1 - Calcula ed Fea u es, Desc ip ion and Fo mula ............................................... 9
Table 4.1 - Lasso's Top 10 Impo ance ............................................................................ 14
Table 4.2 - Spea man's Co ela ion be ween some o he a iables .............................. 15
Table 4.3 - Linea Reg ession Coe icien s ...................................................................... 16
Table 4.4 - Linea Reg ession ea u es wi h VIF below en ............................................. 17
Table 4.5 - Linea Reg ession Model sco es .................................................................... 18
Table 4.6 - Random Fo es Reg esso sco es .................................................................. 19
Table 4.7 - Final model sco es ......................................................................................... 20
Table 4.8 - Random Fo es Reg esso sco es .................................................................. 23
ii
LIST OF ABBREVIATIONS AND ACRONYMS
MAPE Mean Absolu e Pe cen age E o .
MSE Mean Squa ed E o .
R2 R-Squa ed.
SUSHI Sus ainable His o ic Ci y Dis ic s.
VIF Va iance In la ion Fac o .
1
1. INTRODUCTION
O e he yea s ci ies ha e become as a eas, e y o en wi h ca -o ien ed de elopmen s,
cha ac e ized by a less appealing aes he ics o landscapes and an e e -g owing popula ion, so much
so, ha i is expec ed ha hund eds o people will mig a e o ci ies in he nex decade (Lusche , 2021).
Faced wi h his u u e scena io, he ecen heal h c isis o Co id-19 and he p olonga ed clima e
b eakdown, mo e ci ies a e shi ing hei ocus o becoming mo e sus ainable, inclusi e and wi h
quicke ways o commu ing (Pozoukidou & Cha ziyiannaki, 2021). These c ises ended up exposing he
ue p oblems and agili ies wi hin ci ies and hei need o a esponse. One o he mos s iking
ealiza ions was he ime sa ed by wo king emo ely Be o e he global Co id-19 pandemic people
would spend an ex ensi e pe iod o ime commu ing o wo k e e y day, which no only is e y ime
consuming bu also e y ha m ul o he en i onmen and public heal h (Johansson, 2017). This shi
om he adi ional o ice wo k and igid wo kspaces o di e en wo k s yles, aking in conside a ion
wha people enjoy and need o do (Taylo , 2021), has helped 15-minu e ci ies alloca e wo kspaces o
speci ic a eas, allowing companies o ha e o he small o ices ac oss own whe e hei employees
could go. No only i p omo es a be e li e-wo k balance, lea ing mo e ime o people o do wha
b ings hem joy, while no commu ing o wo k e e y day, bu also i helps o educe emissions and
diminishes he ans e abili y o COVID-19 (Mo eno, Allam, Chabaud, Gall, & P a long, 2021).
Acco ding o an in e na ional coali ion o mayo s ocused on clima e change and sus ainabili y called
C40 Ci ies, implemen ing he idea o a 15-minu e ci y could help he u ban a eas eco e om he
inancial and economic de as a ion o he pandemic (C40 Ci ies Clima e Leade ship G oup, 2021). As
he 15-minu e ci y concep g ows s onge , neighbo hoods wi hin ci ies will be ully ocused on
ul illing needs like accessibili y, walkabili y, esidence densi y and land mix use, es o ing he u ban
concep o p oximi y. Making he mos ou o he close loca ion be ween se ices, ac i i ies and
enabling people o access di e en oppo uni ies wi hin hei u ban en i onmen (Sma Ci y, 2022).
This p oximi y-based s a egies o e s people local access o a wide scope o ameni ies, like schools
and p eschools, heal hca e se ices, social se ices, es au an s, en e ainmen and cul u al e en s,
pa ks e c., e e y hing ha is c ucial o quali y o li e (Bouche , 2020). This ans o ma ion, howe e ,
migh be a double-edged swo d. As neighbo hoods p og ess in o small walkable a eas, he eal es a e
alue o he p op ie ies wi hin hose neighbo hoods may e y likely inc ease, gi en he ac ha one
o he mos impo an aspec s o a p op ie y is i s loca ion and i s p oximi y o poin s o in e es .
Lisbon has become one o Eu ope’s sma es ci ies, ha ing ecei ed he Eu opean G een Capi al Awa d
in 2020 (Sma Ci y Lisbon, 2018) and, o e he las decade, ampli ied he a ailable ways o commu ing
in he ci y by building mo e bike pa hs, ea anging key loca ions like squa es, oundabou s and s ee s.
One o he bigges pu poses o he s a egic plan o Lisbon o 2020 was o inc ease i s popula ion by
p omo ing housing, aking sma -ci y ini ia i es ega ding daily li e and ageing (POR Lisboa 2014-2020).
In 2019, be o e he Co id-19 pandemic, Po ugal had one o he mos dynamic eal es a e ma ke s
wi hin he Wes e n Eu ope, mos ly due o i s ax incen i es g an ed o o eign buye s and hei gold
isas (Almeida, 2019). In hese las ew yea s, Lisbon has become a ou ism magne wi h many o eign
eal es a e in es o s ha eno a e p ope ies in o sho - e m lease p ope ies like Ai bnb (Wa en &
Almeida, 2020). These ans o ma ions ha e caused an inc ease on Po ugal’s eal es a e p ices gi en
ha now hey a e di ec ed o ou is s, who ha e g ea e pu chasing powe . Acco ding o he Eu os a ,
back in 2019, Po ugal had an inc ease o almos 10% in hei eal es a e p ices, he bigges wi hin
Eu ope (Idealis a, 2021). As Lisbon and i s neighbo hoods con inue o change and become mo e
sus ainable, inclusi e and wi h ameni ies close p oximi y, i is na u al o assume ha he eal es a e
p ices in he capi al will ollow hese imp o emen s and, ul ima ely, inc ease.
8
3. METHODOLOGY
As p e iously seen, he 15-minu e ci y concep has ou p inciples ha assess di e en aspec s o a
ci y. This esea ch ocuses on he p inciple o p oximi y and i s impac on eal es a es, h ough a ious
p edic i e models cons uc ed, based on calcula ed a iables like he numbe o ameni ies in a 15-
minu e walk adius and bo h he Euclidean and Ne wo k dis ance be ween an ameni y and a p ope y,
excluding all he in o ma ion ega ding he physical aspec s o he la e . These calcula ed a iables y
o cha ac e ize and sco e each p ope y based on he 15-minu e ci y’s p inciple o p oximi y. This was
he selec ed p inciple o he analysis gi en i highly ocuses on accessibili y and mobili y in a ci y.
3.1 DISTANCE CALCULATIONS
Bo h he Euclidean dis ance and he Ne wo k dis ance we e used o calcula e he dis ance be ween
ameni ies and each p ope y, bo h calcula ed in e y dis inc ways. The Euclidean dis ance calcula es
he dis ance be ween wo poin s by using he Py hago as heo em (Equa ion 1), as o he Ne wo k
Dis ance, i uses Lisbon’s pedes ian ne wo k o ind and calcula e he bes ou e om one poin o
ano he , using nodes and a sea ch adius. The e is no speci ic o mula o ne wo k dis ance as i
depends on he opology and con igu a ion o he ne wo k being used.
To be mo e p ecise, he me hods behind hese dis ance alues a e he ollowing:
d(x,y) = √∑
n
i=1 (1)
Figu e 3.1 - Euclidean dis ance (le ) Ne wo k dis ance ( igh )
Re ie ed om - h ps:// inyu l.com/medium-AxU-pla o m
The sco es o each p ope y a e di ided in ype o ameni y, calcula ion me hod and scale, making i a
o al o 47 ea u es. Fo example, he e is a ea u e ha calcula es he ne wo k dis ance o eme gency
es ablishmen s and disca ds he 5 minu es o he ip, one ea u e ha calcula es he Euclidean
dis ance o he wa e , which in his case is he Tejo Ri e , and many o he s.
These calcula ed a iables con empla e se e al scena ios o y o cha ac e ize he loca ion o each
p ope y as bes as possible. Table 1 con ains he de ails and calcula ion me hods o some o he
ea u es. The ea u es ha a e missing a e calcula ed he same way and hey can be analyzed in Annex
1.

9
Name
Desc ip ion
Calcula ion
Name
Desc ip ion
Calcula ion
T anspo
Coun
Numbe o
Public
T anspo a ion
op ion in a 15-
minu e walk
adius
g oupby(['IMOVEL_ID',
' anspo _dis ']).agg(
{'geome y': ' i s ',
' anspo _coun ' : 'coun '})
Comme ce
Coun
Numbe o
comme cial
es ablishmen s in
a 15-minu e walk
adius
g oupby(['IMOVEL_ID',
'come ce_dis ']).agg(
{'geome y':' i s ',
'come ce_coun ':'coun '})
Shannon
Di e si y Index
Measu es he
di e si y o
ameni ies in a
15-minu e walk
adius
𝑯′=−∑𝒑𝒊 𝒍𝒏 𝒑𝒊
𝑺
𝒊=𝟏
S – N o he ameni ies
pi – N o es ablishmen s by ype
o ameni y
A e age
Ne wo k
Dis ance
A e age o he
ime o all he
di e en
ameni ies wi hin
a 15-minu e walk
adius
A g Ne wo k Dis ance =
dis ances.g oupby(
“index_o”,
g oup_keys=False)['dis ance'].mean()
T anspo
Dis ance
Euclidean
dis ance o he
closes public
anspo a ion
op ion
ckd_ ee= cKDT ee(B)
dis ,idx= ckd_ ee.que y(A, k = 1)
idx = i emge e ( * idx) (B_ix)
Wa e Dis ance
Euclidean
dis ance o he
Tejo Ri e
Wa e Dis ance = house_node.geome y
.dis ance(
i e _node.geome y)
Go e nmen
Sco e
Sum o he
dis ances, in
minu es, o all
go e nmen al
buildings in a
15-minu e walk
adius
Sco e = sum([1/(1+dis ) o dis
in a['dis ance']])
Go e nmen
Sco e 2.5
Sum o he
dis ances o
go e nmen al
buildings,
disca ding 2.5
minu es
Sco e_2.5 = sum([1/(1+dis +2.5) o dis
in a['dis ance']])
Go e nmen
Sco e 5
Sum o he
dis ances o
go e nmen al
buildings,
disca ding 5
minu es
Sco e_5 = sum([1/(1+dis +5)
o dis in a['dis ance']])
Go e nmen
Sco e 10
Sum o he
dis ances o
go e nmen al
buildings,
disca ding 10
minu es
Sco e_10 = sum([1/(1+dis +10) o
dis in a['dis ance']])
Table 3.1 – The calcula ed ea u es, i s desc ip ion and o mula.
3.2 METHODS TO UNCOVER RELATIONSHIPS
Wi h he emaining independen a iables, di e en ea u e impo ance echniques we e calcula ed
o u he mo e imp o e he p edic i e powe o he inal model. Each echnique calcula es a sco e o
he inpu a iables in ha gi en model. The me hods es ed in each model we e he Linea Reg ession,
Decision T ee Reg esso , and he Random Fo es Reg esso . Lasso and Spea man co ela ion we e also
analyzed.
3.2.1 Linea Reg ession
The linea eg ession uses he alue o an independen a iable o p edic he alue o he dependen
a iable, h ough a linea app oach. This analysis allows he use o assess he quali y o he a iables
in p edic ing he ou come along wi h which o hese a iables a e mo e signi ican and how each o
hem impac s he dependen a iable. In his phase o he esea ch he Linea model c ea ed o es
he ea u e impo ance is simply an ins ance, wi h no pa ame e s associa ed. The linea eg ession
o mula ep esen ed below (Equa ion 2).
10
Y = β0+β1X (2)
Whe e:
• Y – Dependen Va iable
• 𝜷𝟎– Cons an / In e cep
• 𝜷𝟏 – Slope / Coe icien
• X – Value o he independen a iables
A common phenomenon in a eg ession analysis is he Mul icollinea i y, i exis s when mul iple
independen a iables a e co ela ed in a model. The Va iance In la ion Fac o (VIF) iden i ies
mul icollinea i y by es ima ing how much he a iance o a eg ession coe icien is ampli ied due o
mul icollinea i y in he model. VIF anges om 1 upwa ds, whe e 1 is conside ed no co ela ed and
alues g ea e han 5 is conside ed highly co ela ed. The h eshold used in his case was o e ain he
a iable wi h a VIF alue below o equal o 10.
3.2.2 Decision T ee Reg esso
This me hod uses a s uc u e lowcha -like whe e all he possible anges o esul s a e con empla ed.
In a decision ee he e’s nodes and b anches, which con ain he condi ion and he esul , espec i ely.
Each obse a ion goes h ough his lowcha -like ee based on he alue o i s a iables and a model
is ained o p edic u u e obse a ions. Simila ly o he Linea Reg ession, only an ins ance o he
model was c ea ed o his pa .
Figu e 3.2 - Decision T ee Reg esso . Re ie ed om h ps:// inyu l.com/geeks- o -geeks
3.3.3 Random Fo es Reg esso
The Random Fo es Reg esso is an ensemble me hod composed o mul iple decision ees. The inal
p edic ion o each obse a ion is he a e age esul o all he ou comes p edic ed by each ee.
Gene ally, e u ns be e esul s han Decision T ee Reg esso me hod. Like he wo p e ious
Reg ession models, only an ins ance o he Random Fo es Reg esso is c ea ed o check he ea u e
impo ance based on his me hod.
11
Figu e 3.3 - Random Fo es Reg esso . Re ie ed om h ps:// inyu l.com/analy ics- idhya
Besides his ea u e impo ance me hod wo o he ea u e selec ion echniques we e es ed, Lasso
and he Spea man’s co ela ion.
3.3.4 Lasso
The Leas Absolu e Sh inkage and Selec ion Ope a o is based on a eg ession analysis ha ocuses on
enhancing he p edic ion accu acy o he models. This me hod is di ided in wo s eps, he
egula iza ion o model pa ame e s by sh inking he eg ession coe icien s, and he ea u e selec ion,
whe e e e y non-ze o alue is used in he p edic i e model.
3.3.5 Spea man co ela ion
E en hough Spea man’s co ela ion is no exac ly a ea u e impo ance me hod, i is an impo an
echnique ha measu es he s eng h o associa ion be ween wo anked ea u es by assessing hei
mono onic ela ionships, whe he linea o no . Spea man’s co ela ion is, simply, he Pea son’s
co ela ion be ween he ank alues o wo ea u es (Equa ion 3).
ρ=1 − 6∑di2
n(n2−1) (3)
ρ- Spea man’s ank co ela ion coe icien
di- Di e ence be ween he wo anks o each obse a ion
n – Numbe o Obse a ions
6 – Cons an Value
3.3 EVALUATION METHODS
To accesses each model’s p edic i e powe , R2 Sco e, R2 Adjus ed Sco e, Mean Squa ed E o (MSE)
and Mean Absolu e Pe cen age E o (MAPE) we e calcula ed. These sco es combined ansmi all he
in o ma ion needed o unde s and i he selec ed a iables a e helping he models in p edic ing he
a ge mo e accu a ely o no .
3.3.1 R2 Sco e
R-Squa ed anges be ween 0 and 1 which indica es he amoun o a iance in he ou pu o he
dependen a iable ha is p edic able om he independen a iable. A high alue would mean ha
12
mos o he changeabili y in he dependen a iable’s ou pu can be explained by he model. R-Squa ed
indica es he p opo ion o poin s ha lie wi hin he line c ea ed by he eg ession equa ion (Equa ion
4), he e o e, a highe alue indica es be e esul s.
R2= 1 − ∑(Yi−Yi)2
𝑛1=1
∑(Yi−Y)2
𝑛1=1 (4)
3.3.2 R2 Adjus ed Sco e
As we add new ea u es o a mul iple eg ession model, R-squa ed will ei he con inue o inc ease o
s op, ega dless o hei quali y. R-squa ed Adjus ed elimina es his issue by aking in conside a ion
he numbe o samples in he da ase , and he numbe o ea u es in he model, inc easing he sco e
only when he newly added ea u es imp o e he model’s accu acy (Equa ion 5). Jus like he R-
Squa ed, a highe alue indica ed be e esul s.
Adjus ed R2= 1 − (1−𝑅2)(𝑁−1)
𝑁−𝑝−1 (5)
3.3.3 Mean Squa ed E o
The MSE (Mean Squa ed E o ) measu es he o al e o in a model by calcula ing he a e age squa ed
di e ence be ween he obse ed alues and he p edic ed ones. This calcula ion epea s i sel o all
he obse a ions and a e wa d, all hose alues a e summed and di ided by he o al numbe o
obse a ions (Equa ion 6). This me hod highligh s he la ge e o s, making i use ul when wo king wi h
models whe e hese e o s mus be minimized.
MSE = 1n ∑(Yi−Yi)2
n
i=1 (6)
In a eg ession, as he da a poin s ge close o he eg ession line, he e o in he model dec eases,
p oducing mo e p ecise p edic ions.
3.3.4 Mean Absolu e Pe cen age E o
Mean Absolu e Pe cen age E o , o MAPE, measu es he accu acy o a p edic i e model by calcula ing
he a e age pe cen age e o s o he p edic ions. The e o is he di e ence be ween he ac ual and
o ecas ed alue, so a smalle alue would mean a smalle MAPE and he e o e, be e esul s.
3.4 SOFTWARE USED
To de elop his s udy, P ojec Jupy e and py hon lib a ies we e used. Jupy e no ebook was he
selec ed ool o de elop and un he code o his analysis, due o i s as accessibili y o py hon
lib a ies. The OSMnx (Boeing, 2022) is one o he py hon lib a ies ha was used, and i ca ied ou one
o he mos impo an pa s o he p ocess which was collec ing all he a ailable da a ega ding all
ypes o ameni ies (go e nmen , heal h, educa ion, inance, public anspo , leisu e, ood and i e ).
“OSM” means “Open S ee Map” and i allows he use o download geospa ial da a, model and
analyze eal-wo ld s ee ne wo ks. I allows use s o model walkable u ban ne wo ks wi h he use o
py hon, whe e hese models can be isualized and analyzed. The GeoPandas lib a y was also e y
help ul in o de o wo k wi h he coo dina es ha we e gi en, and use hem o calcula e he di e ence
dis ances, and he e o e, hei sco es ega ding he a ious ameni ies.
13
The ollowing Gi Hub link con ains wo o he no ebooks c ea ed o calcula e he di e en ea u es
used in his hesis: Gi Hub - Thesis eposi o y

14
4. RESULTS AND DISCUSSION
In his ollowing chap e he esul s and indings o he analysis will be exposed and discussed, o a
clea e in e p e a ion o he ou comes, his chap e will be o ganized in ou sub-chap e s, 1.Fea u e
Analysis 2. Linea Reg ession Analysis, 3. Random Fo es Reg esso Analysis and 4.Discussion
4.1 FEATURE ANALYSIS
Acco ding o he Lasso me hod, nine ea u es we e elimina ed and hi y- i e we e selec ed, mos o
which also selec ed in he p e ious me hods. E en hough hi y- i e we e selec ed, only he bes
wen y ea u es we e aken in o conside a ion. Some o he bes ea u es we e he “Shannon Di e si y
Index” , “go e nmen sco e”, and “educa ion sco e 2.5”. Lasso also allows o unde s and he impac
o each ea u e, o example he ea u e “Shannon Di e si y Index” has an impo ance alue o -
1423.94, which mean i is an impo an ea u e wi h an in e se co ela ion o he a ge . Some o he
ea u es selec ed by Lasso a e ep esen ed below, he comple e able is p esen in Annex 2.
Fea u e
Impo ance
Shannon Di e si y Index
1423.94
Go e nmen Sco e
1033.45
Educa ion Sco e 2.5
886.11
Go e nmen Sco e 2.5
847.97
Finance Sco e 2.5
526.85
Educa ion Sco e 10
433.22
Heal h Sco e 2.5
418.10
Finance Sco e 10
331.98
Leisu e Sco e 2.5
231.93
Food Sco e
207.02
Table 4.1 – Lasso’s Top 10 Impo ance
The Spea man’s co ela ion also o e ed some insigh s, no as conc e e as he p e ious me hods bu
ne e heless impo an . The mos in e es ing insigh was he co ela ion be ween he di e en sco es
which indica e ha some es ablishmen s in luence he p esence o o he s. Fo example, he numbe
o public anspo a ions wi hin a 15-minu e walk adius o a house is highly co ela ed wi h he ood
es ablishmen s sco e nea ha same house, meaning ha in a eas whe e he e a e mo e es au an s,
ma ke s e c., he public anspo a ion ne wo k o e s mo e op ions o a pe son o commu e. The
same happens wi h he numbe o educa ional buildings, like high schools o uni e si ies, in a 15-
minu e walk adius and he dis ance o heal h es ablishmen s, meaning ha schools o en ha e hea h
and eme gency se ices nea by.
Fea u es ha ha e a co ela ion highe han 0.8 should be disca ded, a leas one o hem, since his
means ha bo h a iables con ey he same in o ma ion. Ha ing wo e y simila ea u es, ansmi ing
he same in o ma ion, is no e y e ec i e.
15
The g aphic below shows he Spea man’s co ela ion be ween some o he a iables.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
1.Comme ce
Coun
1
0.7
0.6
0.9
0.8
-0.8
0.4
0.5
0.6
0.3
0.3
0.7
0.4
0.2
0.6
0.004
2.Public
T anspo
Sco e
0.7
1
0.7
0.7
0.6
-0.5
0.6
0.6
0.8
0.2
0.02
0.8
0.3
0.5
0.8
0.06
3.Finance
Sco e 10
0.6
0.7
1
0.7
0.5
-0.4
0.6
0.7
0.9
0.2
0.1
0.9
0.4
0.4
0.8
-0.2
4.Public
Building
Coun
0.9
0.7
0.7
1
0.7
-0.6
0.5
0.6
0.7
0.4
0.3
0.7
0.5
0.3
0.6
-0.1
5.T anspo
Coun
0.8
0.6
0.5
0.7
1
-0.5
0.3
0.4
0.5
0.3
0.03
0.6
0.4
0.1
0.5
-
0.007
6.Shannon
Di e si y
Index
-0.8
-0.5
-0.4
-0.6
-0.5
1
-0.1
-0.4
-0.4
0.08
-0.3
-0.5
0.06
0.00
8
-0.3
-
0.008
7.Leisu e
Sco e 2.5
0.4
0.6
0.6
0.5
0.3
-0.1
1
0.6
0.6
0.1
0.08
-0.3
-0.5
0.06
0.00
8
-0.04
8.En e ainm
en Sco e
0.5
0.6
0.7
0.6
0.4
-0.4
0.6
1
0.7
-
0.03
0.09
0.8
0.4
0.1
0.5
-0.3
9.Go e nme
n Sco e 5
0.6
0.8
0.9
0.7
0.5
-0.4
0.6
0.7
1
0.1
0.2
0.8
0.4
0.3
0.8
-0.2
10.Educa ion
Coun
0.3
0.2
0.2
0.4
0.3
0.08
0.1
-
0.03
0.1
1
0.07
0.2
0.4
0.7
0.5
0.4
11.A e age
Ne wo k
Dis ance
0.3
0.02
0.1
0.3
0.03
-0.3
0.08
0.09
0.2
0.07
1
0.02
0.2
-
0.06
-
0.03
0.2
12.Food
Sco e 2.5
0.7
0.8
0.9
0.7
0.6
-0.5
0.6
0.8
0.8
0.2
0.02
1
0.3
0.4
0.8
-0.2
13.G eenspa
ces Coun
0.4
0.3
0.4
0.5
0.4
0.06
0.7
0.4
0.4
0.4
0.2
0.3
1
0.2
0.4
0 .03
14.Educa ion
Sco e 10
0.2
0.5
0.4
0.3
0.1
0.00
8
0.3
0.1
0.3
0.7
-
0.06
0.4
0.2
1
0.7
0.4
15.Heal h
Sco e 2.5
0.6
0.8
0.8
0.6
0.5
-0.3
0.6
0.5
0.8
0.5
-
0.03
0.8
0.4
0.7
1
0.1
16.Wa e
Dis ance
0.004
0.06
-0.2
-0.1
-
0.007
-
0.00
8
-0.04
-0.3
-0.2
0.4
0.2
-0.2
0.03
0.4
0.1
1
Table 4.2 - Spea man’s Co ela ion be ween some o he a iables
Each ameni y has a se o sco es, bu only one sco e o each se will be kep . Despi e he ac ha
highly co ela ed ea u es should be emo ed, in his case and since each a iable e e s a di e en
ameni y, some highly co ela ed ea u es will be kep .
In he ollowing sec ions o he ea u e analysis echniques we e deployed in o de o be e
unde s and hese calcula ed ea u es.
16
4.2 LINEAR REGRESSION ANALYSIS
The Linea Reg ession ep esen a ion be ween a a ge a iable and an independen a iable is one o
he bes ways o isualize hei co ela ion and impac . Thei coe icien s ansmi some o he mos
impo an in o ma ion o unde s and hei beha io , he cons an and he slope. Table 4 con ains he
linea eg ession o each o he ea u es selec ed o he inal model.
Table 4.3 – Linea Reg ession coe icien s
Wi h he alues o 𝛽0 and 𝛽1 i is easy o unde s and each a iable’s beha io . The slope indica es i
he ea u e has a di ec o in e se o ela ionship h ough is sign, i he slope is nega i e hen a lowe
alue o he ea u e in ques ion, will gene a e a highe Ta ge alue. Fo example, he ela ionship
be ween he p ice pe me e and he numbe o comme ce es ablishmen s in a 15-minu e walk adius,
“comme ce coun ”, has a endency o lowe p ices ha ing a lowe numbe o comme ce
es ablishmen s nea by. These a iables ha e a posi i e linea ela ionship, and can be isualized below:
Fea u e
𝜷𝟎 /
In e cep
𝜷𝟏 / Slope
Fea u e
𝜷𝟎 /
In e cep
𝜷𝟏 / Slope
En e ainmen
Sco e 5
3426.65
246.07
Heal h Sco e
2.5
3610.76
65.60
Leisu e Sco e
2.5
3449.14
34.19
G eenspaces
Coun
3520.37
3.28
Shannon
Di e si y Index
5049.19
-1276.83
Public
Buildings
Coun
3274.14
19.84
Public
T anspo
Coun
3261.35
7.88
Public
T anspo
Sco e
3461.62
22.71
Educa ion
Coun
3923.01
-8.44
Educa ion
Sco e 10
3933.27
-35.19
Food Sco e 2.5
3571.87
12.46
Go e mmen
Sco e 5
3394.80
188.82
Comme ce
Coun
3376.03
0.63
Wa e
Dis ance
4519.41
-0.72
Finance Sco e
10
3404.08
106.01
A e age
Ne wo k
Dis ance
3040.67
80.37
17
Figu e 4.1 - Linea Reg ession be ween P ice/me e and Comme ce Coun
When accessing he Linea Reg ession’s ea u e impo ance esul s and excluding he a iables wi h a
VIF (Va iance In la ion Fac o ) highe han en, se en ea u es emained which a e also conside ed
impo an in he di e en ea u e impo ance models es ed. The selec ed a iables by he Linea
Reg ession’s ea u e impo ance a e he ollowing:
Fea u e
VIF
A e age Ne wo k Dis ance
1.7306
Wa e Dis ance
2.5302
Shannon Di e si y Index
4.3115
Educa ion Coun
5.0916
T anspo a ion Coun
5.1829
G eenspaces Coun
6.7085
Public Building Coun
8.3501
Table 4.4 – Linea Reg ession ea u es wi h a VIF below en
The ea u es abo e a e inside he h eshold, and he e is no su p ise in he ou come since all o hese
a iables a e ecu en ly labeled as impo an h oughou he di e en ea u e impo an analysis.
Gi en ha he Linea Reg ession is one o he simples p edic i e me hods, i is na u al ha he esul s
a e no op imal, howe e i is a e y good me hod o gain some insigh s ega ding each ea u e’s
co ela ion o he a ge .
24
5. CONCLUSION
O en, when app aising he alue o a p ope y, he le el o accessibili y and mobili y is no ac o ed
in, he physical aspec s such as he a ea and he numbe o ooms, a e much mo e impo an when
ying o p edic he p ice pe me e o a house, han he aspec s ega ding i s loca ion. Howe e , i
had o be unde s ood he impac hese o he aspec s could ha e on he inal p ice. Inspi ed by he 15-
minu e ci y concep and i s pilla o p oximi y, di e en a iables we e calcula ed in o de o
unde s and he accessibili y a ound each p ope y. A o al o o y-se en ea u es we e c ea ed using
Euclidean Dis ance, Ne wo k Dis ance, by coun ing he numbe o es ablishmen s by ameni y and a
ew o he me hods. No all he ea u es should be ac o ed in he inal model hus, in o de o selec
a se o a iables, di e en ea u e impo ance and ea u e selec ion me hods we e analyzed. Lasso,
Spea man’s co ela ion and he ea u e impo ance o h ee eg ession me hods we e deployed and
analyzed, lea ing only six een ea u es. These emaining ea u es we e used as inpu a iables in h ee
di e en models, he Decision T ee Reg ession, he Linea Reg ession and he Random Fo es
Reg esso . To e i y he quali y o each model ou di e en sco es we e calcula ed and, ou o he
h ee ins ances c ea ed, he Random Fo es Reg esso was he one ha pe o med be e . All sco es
had signi ican imp o emen s, specially he R2 sco e wi h a alue o 0.5, meaning ha hal o he
a iance in he a ge a iable is explained by he selec ed ea u es. Wi h he inal model ob ained, a
deepe analysis in o he mos impo an ea u es and hei impac on he a ge was made. Calcula ed
ea u es such as “wa e dis ance”, “comme ce coun ”, “public anspo dis ance sco e” and “g een
spaces dis ance sco e”, u ned ou o be qui e impo an o all he models, p o ing ha he
accessibili y and loca ion o a house do ha e an impac on i s selling p ice. When app aise s say ha a
p ope y’s loca ion is one o he mos impo an aspec s, i is ue. E en hough inding and unning
he p edic i e model was no he main ocus, he sco es o he inal mode we e conside ably good,
especially conside ing ha he inpu ed a iables we e idealized based on he concep o 15-minu e
ci ies, om which di e en sco es, dis ances and coun s o ameni ies we e calcula ed.
In conclusion, his analysis alone will no p edic he p ice pe me e o a house as accu a ely as wi h
i s physical a ibu es ac o ed in bu , i will help explain he di e ence in p icing when wo houses
wi h iden ical physical cha ac e is ics ha e highly dis inc i e p ices, as he e is a co ela ion be ween
hese calcula ed a ibu es and he a ge a iable ha p o es his heo y.

25
6. LIMITATIONS AND RECOMMENDATIONS FOR FUTURE WORKS
As s a ed p e iously, his analysis ocuses on unde s anding i he p oximi y p inciple o he 15-minu e
ci y app oach has any impac on he p ice pe me e alue o a houses. The a iables ha suppo his
analysis we e c ea ed based on wha he p inciple assess a he han wha migh be bes inpu s o
he p edic ions. No only his bu he e may be mo e a iables o cha ac e ize a p ope y’s loca ion
and accessibili y, ha we e no conside ed in his esea ch. The me hods used o he calcula ions o
said a iables we e highly ime consuming, which made any al e a ion o co ec ion, ha o ced a e-
calcula ion, a conside able se back. Besides he echnical limi a ions, he e we e also a ew opics ha
we e no discussed in his hesis, and i can be seen as limi a ions as well. Despi e he con i ma ion
ha he calcula ed ea u es impac he p edic i e models when es ima ing he p ice pe me e , he e
is no analysis ha con i ms ha he mos expensi e a eas in Lisbon a e in ac he ones ha ha e a
highe comme ce coun , o a lowe wa e dis ance. Ano he limi a ion is ha he impac o he
calcula ed ea u es is only es ed o he ci y o Lisbon hus i canno used as a ac wen es ing i in
o he ci ies. Las ly and p obably he bigges limi a ion is ha hese p edic ions and analysis is based
on he alues o oday and his is e y ola ile ma ke , whe e he p ices can easily change and a y
om ci y o ci y.
Fo u u es wo ks, i would be ad isable o de elop a be e p edic i e model, a deepe analysis
ega ding he machine lea ning pa o his p ocess, whe e a mo e complex p edic i e model, wi h he
ideal pa ame e s, would educe he MAPE and MSE o ou inal model, as well as inc ease i s R-squa ed
and R2 Adjus ed sco e. I may be in e es ing o es his analysis in di e en ci ies, whe e he 15-minu e
concep is g owing, and he eal es a e alues migh me shi ing, in o de o solidi y his co ela ion
be ween accessibili y ac o s and he alue o a p ope y. This analysis migh be a good ool o help ill
he gap o a p edic i e model ha only ac o s in he physical cha ac e is ics o a p ope y. Rega ding
he limi a ions p e iously p esen ed, he e is a good oppo uni y o u u e wo ks. A compa ison
be ween he p ice pe me e o a houses, pe pa ish and he alues o he calcula ed ea u es would
con i m i indeed he mos expensi e a eas ha e be e accessibili y ac o s o li e close o he i e .
To e i y ha his impac no only occu s in p ope ies in he ci y o Lisbon, o he ci ies can also be
analyzed, like Pa is, ha ollows he 15-minu e ci y concep , o o he ci ies ha don’ ha e hei
accessibili y ac o s as well de eloped, and check i he same impac is obse ed o i i is di e en , and
i i is ex emely di e en , why does i happen.
26
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28
APPENDIX
Name
Desc ip ion
Calcula ion
Name
Desc ip ion
Calcula ion
T anspo
Coun
Numbe o
Public
T anspo a ion
op ion in a 15-
minu e walk
adius
g oupby(['IMOVEL_ID',
' anspo _dis ']).agg(
{'geome y': ' i s ',
' anspo _coun ' : 'coun '})
Comme ce
Coun
Numbe o
comme cial
es ablishmen s
in a 15-minu e
walk adius
g oupby(['IMOVEL_ID',
'come ce_dis ']).agg(
{'geome y':' i s ',
'come ce_coun ':'coun '})
Educa ion
Coun
Numbe o
Educa ional
es ablishmen s
in a 15-minu e
walk adius
g oupby(['IMOVEL_ID',
'educa ion_dis ']).agg(
{'geome y':' i s ',
'educa ion_coun ':'coun '})
Public
Buildings
Coun
Numbe o
Public
T anspo a ion
op ion in a 15-
minu e walk
adius
g oupby(['IMOVEL_ID',
'PubBuilding_dis ']).agg(
{'geome y':' i s ',
'PubBuilding_coun ':'coun '})
Eme gency
Coun
Numbe o
Eme gency
es ablishmen s
in a 15-minu e
walk adius
g oupby(['IMOVEL_ID',
'eme gency_dis ']).agg(
{'geome y':' i s ',
'eme gency_coun ':'coun '})
G eenspaces
Coun
Numbe o
Public
T anspo a ion
op ion in a 15-
minu e walk
adius
g oupby(['IMOVEL_ID',
'g eenspaces_dis ']).agg(
{'geome y':' i s ',
'g eenspaces_coun ':'coun '})
Shannon
Di e si y
Index
Measu es he
di e si y o
ameni ies in a
15-minu e walk
adius
S – N o he ameni ies
pi – N o es ablishmen s by
ype o ameni y
A e age
Ne wo k
Dis ance
A e age o he
ime o all he
di e en
ameni ies
wi hin a 15-
minu e walk
adius
A g Ne wo k Dis ance =
dis ances.g oupby(
“index_o”,
g oup_keys=False)['dis ance'].mean()
T anspo
Dis ance
Euclidean
dis ance o he
closes public
anspo a ion
op ion
ckd_ ee= cKDT ee(B)
dis ,idx= ckd_ ee.que y(A,
k = 1)
idx = i emge e ( * idx)
(B_ix)
Go e nmen
Sco e
Sum o he
dis ances, in
minu es, o all
go e nmen al
buildings in a
15-minu e walk
adius
Sco e = sum([1/(1+dis ) o dis in
a['dis ance']])
Educa ion
Dis ance
Euclidean
dis ance o he
closes
educa ional
es ablishmen
Calcula ed he same way as
he T anspo Dis ance.
Go e nmen
Sco e 2.5
Sum o he
dis ances o
go e nmen al
buildings,
disca ding 2.5
minu es
Sco e_2.5 = sum([1/(1+dis +2.5) o
dis in a['dis ance']])
Eme gency
Dis ance
Euclidean
dis ance o he
closes
eme gency
building
Calcula ed he same way as
he T anspo Dis ance.
Go e nmen
Sco e 5
Sum o he
dis ances o
go e nmen al
buildings,
disca ding 5
minu es
Sco e_5 = sum([1/(1+dis +5) o dis
in a['dis ance']])
G eenspaces
Dis ance
Euclidean
dis ance o he
Calcula ed he same way as
he T anspo Dis ance.
Go e nmen
Sco e 10
Sum o he
dis ances o
go e nmen al
buildings,
Sco e_10 = sum([1/(1+dis +10) o
dis in a['dis ance']])
29
Name
Desc ip ion
Calcula ion
Name
Desc ip ion
Calcula ion
closes g een
a ea
disca ding 10
minu es
Comme ce
Dis ance
Euclidean
dis ance o he
closes
comme cial
es ablishmen
Calcula ed he same way as
he T anspo Dis ance.
Public
T anspo
Sco e
Sum o he
dis ances, in
minu es, o all
public
anspo a ions
in a 15-minu e
walk adius
Sco e = sum([1/(1+dis ) o dis in
a['dis ance']])
Public
Building
Dis ance
Euclidean
dis ance o he
closes public
Building
Calcula ed he same way as
he T anspo Dis ance.
Public
T anspo
Sco e 2.5
Sum o he
dis ances o
public
anspo a ions,
disca ding 2.5
minu es
Sco e_2.5 = sum([1/(1+dis +2.5) o
dis in a['dis ance']])
Food Sco e
Sum o he
dis ances, in
minu es, o all
es ablishmen s
ha sell ood in
a 15-minu e
walk
Sco e = sum([1/(1+dis ) o
dis in a['dis ance']])
Public
T anspo
Sco e 5
Sum o he
dis ances, in
minu es o
public
anspo a ions,
disca ding 5
minu es
Sco e_5 = sum([1/(1+dis +5) o dis
in a['dis ance']])
Food Sco e
2.5
Sum o he
dis ances o
es ablishmen s
ha sell ood,
disca ding 2.5
minu es
Sco e_2.5 =
sum([1/(1+dis +2.5) o dis
in a['dis ance']])
Public
T anspo
Sco e 10
Sum o he
dis ances, in
minu es o
public
anspo a ions,
disca ding 10
minu es
Sco e_10 = sum([1/(1+dis +10) o
dis in a['dis ance']])
Food Sco e 5
Sum o he
dis ances o
es ablishmen s
ha sell ood,
disca ding 5
minu es
Sco e_5 =
sum([1/(1+dis +5) o dis in
a['dis ance']])
Finance Sco e
Sum o he
dis ances, in
minu es, o all
inancial
es ablishmen s
in a 15-minu e
walk adius
Sco e calcula ed he same way as
he p e ious ameni ies
Food Sco e 10
Sum o he
dis ances o
es ablishmen s
ha sells ood,
disca ding 10
minu es
Sco e_10 =
sum([1/(1+dis +10) o dis
in a['dis ance']])
Finance Sco e
2.5
Sum o he
dis ances o
inancial
es ablishmen s,
disca ding 2.5
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 2.5
Leisu e Sco e
Sum o he
dis ances, in
minu es, o all
leisu e
es ablishmen s
in a 15-minu e
walk adius
Sco e calcula ed he same
way as he p e ious
ameni ies
Finance Sco e
5
Sum o he
dis ances o
inancial
es ablishmen s,
disca ding 5
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 5
Leisu e Sco e
2.5
Sum o he
dis ances o
leisu e
es ablishmen s,
disca ding 2.5
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 2.5
Finance Sco e
10
Sum o he
dis ances o
inancial
es ablishmen s,
disca ding 10
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 10

30
Annex 1 – Table wi h all he calcula ed ea u es, hei names, desc ip ion and o mula.
Name
Desc ip ion
Calcula ion
Name
Desc ip ion
Calcula ion
Leisu e Sco e
5
Sum o he
Dis ance o
leisu e
es ablishmen s,
disca ding 5
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 5
Educa ion
Sco e
Sum o he
dis ances, in
minu es, o all
educa ional
es ablishmen s
in a 15-minu e
walk adius
Sco e calcula ed he same way as
he p e ious ameni ies
Leisu e Sco e
10
Sum o he
dis ance o
leisu e
es ablishmen s,
disca ding 10
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 10
Educa ion
Sco e 2.5
Sum o he
dis ances o
educa ional
es ablishmen s,
disca ding 2.5
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 2.5
Heal h Sco e
Sum o he
dis ances, in
minu es, o all
heal h
es ablishmen s
in a 15-minu e
walk adius
Sco e calcula ed he same
way as he p e ious
ameni ies
Educa ion
Sco e 5
Sum o he
dis ances o
educa ional
es ablishmen s,
disca ding 5
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 5
Heal h Sco e
2.5
Sum o he
dis ances o
heal h
es ablishmen s,
disca ding 2.5
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 2.5
Educa ion
Sco e 10
Sum o he
dis ances o
educa ional
es ablishmen s,
disca ding 10
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 10
Heal h Sco e 5
Sum o he
dis ances o
heal h
es ablishmen s,
disca ding 5
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 5
En e ainmen
Sco e 5
Sum o he
dis ances o
en e ainmen
es ablishmen s,
disca ding 5
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 5
Heal h Sco e
10
Sum o he
dis ance o
heal h
es ablishmen s,
disca ding 10
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 10
En e ainmen
Sco e 10
Sum o he
dis ance o
en e ainmen
es ablishmen s,
disca ding 10
minu es
Calcula ed he same way as he
p e ious ameni ies o Sco e 10
En e ainmen
Sco e
Sum o he
dis ances, in
minu es, o all
en e ainmen
es ablishmen s
in a 15-minu e
walk adius
Sco e calcula ed he same
way as he p e ious
ameni ies
Wa e
Dis ance
Euclidean
dis ance o he
Tejo Ri e
Wa e Dis ance =
house_node.geome y.dis ance(
i e _node.geome y)
En e ainmen
Sco e 2.5
Sum o he
dis ances o
en e ainmen
es ablishmen s,
disca ding 2.5
minu es
Calcula ed he same way as
he p e ious ameni ies o
Sco e 2.5
31
Annex 2 – Lasso’s selec ed ea u es.
Fea u e
Impo ance
Shannon Di e si y Index
1423.94
Go e nmen Sco e
1033.45
Educa ion Sco e 2.5
886.11
Go e nmen Sco e 2.5
847.97
Finance Sco e 2.5
526.85
Educa ion Sco e 10
433.22
Heal h Sco e 2.5
418.10
Finance Sco e 10
331.98
Leisu e Sco e 2.5
231.93
Food Sco e
207.02
Heal h Sco e 10
183.32
Leisu e Sco e
131.63
Go e nmen Sco e 5
114.11
Food Sco e 2.5
111.49
Heal h Sco e
105.49
Leisu e Sco e 10
59.53
En e ainmen Sco e 5
52.59
Public T anspo Sco e 2.5
39.63
32
Annex 3- Rada cha o A enidas No as (blue) and San a Cla a ( ed) a iables alue.
17