Master Thesis ǀ Tesis de Maestría submitted within the UNIGIS MSc programme presentada para el Programa UNIGIS MSc at/en
Interfaculty Department of Geoinformatics- Z_GIS Departamento de Geomática – Z_GIS University of Salzburg ǀ Universidad de Salzburg
Inequidades socioeconómicas en relación a los espacios verdes y cobertura de copa: un enfoque espacial aplicado a la ciudad de Cali, Colombia Socioeconomic inequities in relation to access to green spaces and canopy cover: a spatial approach applied to the city of Cali, Colombia by/por
Juan Fernando Correa Caicedo 01522971 A thesis submitted in partial fulfilment of the requirements of the degree of Master of Science– MSc Advisor | Supervisor: Pablo Cabrera Barona PhD
Cali - Colombia, Enero de 2020
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SQ`+2Mi D2 /2 pBpB2M/ b /2bQ+mT / b
h`Qv 2i HX UkyydV
ล M/B+2 /2 /2HBM+m2M+B
h`Qv 2i HX UkyydV
SQ`+2Mi D2 /2 pBpB2M/ b [m2 bQM pBpB2M/ b
h`Qv 2i HX UkyydV
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G M/`v v *? F` #Q`iv UkyyNV
h K ฦขQ K2/BQ /2H HQi2 /2 pBpB2M/
a? M ? M 2i HX UkyR9V
.2MbB/ / /2 pBpB2M/ b
a2K2; 2i HX UkyRdVc. L1 Ukyy8V
:` /Qb 2b+QH `2b +m`b /Qb( ฦขQb)
. L1 Ukyy8V
SQ`+2Mi D2 /2 ? #Bi Mi2b +QM ;` /Q T`Q72bBQM H
L2b#Bii v J2BiM2` UkyReV
SQ`+2Mi D2 /2 ? #Bi Mi2b +QM K 2bi`ล
L2b#Bii v J2BiM2` UkyReV
1/ / K2/B /2 H b +QMbi`m++BQM2b
w?Qm v EBK UkyRjV
kd
kXjXRX
1M7Q[m2 2bi /Å&#x2018;biB+Q
1H BMbi`mK2MiQ K i2KÂ&#x20AC;iB+Q KÂ&#x20AC;b TQTmH ` T ` 2bi #H2+2` `2H +BQM2b /2 /2T2M/2M+B v bQ+B +BƦM 2Mi`2 /Qb p `B #H2b H2 iQ`B b bQM HQb Å&#x2018;M/B+2b /2 +Q``2H +BƦM- bBM [m2 H `2H +BƦM +m MiB}+ / b2 M2+2b `B K2Mi2 /2 + mb HB/ /X G + mb HB/ / 2Mi`2 H b p `B #H2b bm2H2 b2` mM Tm2bi /2H BMp2biB; /Q` +QM # b2 2M bm +QMQ+BKB2MiQ Q BMimB+BƦM bQ#`2 HQb T`Q+2bQb [m2 /QKBM M H b + ` +i2`Å&#x2018;biB+ b /2 H b p `B #H2b H2 iQ`B b U:B##QMb v Pp2`K M- kyRkVX 1H +Q2}+B2Mi2 /2 +Q``2H +BƦM /2 S2 `bQM 2b mb /Q T ` + ` +i2`Bx ` H 7m2`x /2 `2H +BQM2b HBM2 H2b- KB2Mi` b [m2 2H +Q2}+B2Mi2 /2 +Q``2H +BƦM /2 aT2 `K M 2b mb /Q T ` + ` +i2`Bx ` `2H +BQM2b MQ HBM2 H2bX 1biQb +Q2}+B2Mi2b bQM MÂ&#x20AC;HBbBb 2}+ +2b T ` b2H2++BQM ` p `B #H2b + M/B/ i b b2` BM+HmB/ b 2M KQ/2HQb /2 `2;`2bBƦM- i MiQ T ` b2H2++BQM ` H b p `B #H2b [m2 iB2M2M `2H +BƦM 7m2`i2 +QM H p `B #H2 T`2/2+B`- +QKQ H BM/2T2M/2M+B HBM2 H /2 H b p `B #H2b 2tTHB+ iBp b- +QM/B+BQM2b M2+2b `B b T ` [m2 HQb KûiQ/Qb /2 Dmbi2 /2 T `Â&#x20AC;K2i`Qb /2 HQb KQ/2HQb HBM2 H2b U:B##QMb v Pp2`K M- kyRkVX GQb +Q2}+B2Mi2b /2 +Q``2H +BƦM- +QKQ 2bi /Å&#x2018;biB+ /2 `2bmK2M- MQ Tm2/2M `22KTH x ` 2H 2t K2M pBbm H /2 HQb / iQb v H +QMbi`m++BƦM /2 `2H +BQM2b [m2 i2M; M mM 7mM/ K2MiQ i2Ʀ`B+QX GQb KQ/2HQb /2 `2;`2bBƦM HBM2 H bQM KTHB K2Mi2 mb /Qb 2M H 2+QMQK2i`Å&#x2018; T ` +QMb@ i`mB` KQ/2HQb 2tTHB+ iBpQb +QM iû`KBMQb [m2 /2b+`B#2M +QKTQM2Mi2b i2Ʀ`B+Qb /2 HQb T`Q+2bQb /2 2bim/BQ 2 BM72`B` 2H +QKTQ`i KB2MiQ Q i2M/2M+B b 2M mM TQ#H +BƦM +QM # b2 2M mM Km2bi` X .2 2bi 7Q`K b2 T`2i2M/2 +m MiB}+ ` 2H + K#BQ /2 H p `B #H2 /2T2M/B2Mi2 Y Mi2 mK2MiQb Q /BbKBMm+BQM2b /2H p HQ` /2 mM /2 H b p p `B #H2b /2@ T2M/B2Mi2b xj /QM/2 j = 1...pX * / mM /2 H b Q#b2`p +BQM2b i - i = 1...n /2H p2+iQ` Xp /2MQKBM / b xij 7Q`K M mM bBbi2K /2 2+m +BQM2b HBM2 H2b /QM/2 2H T `Â&#x20AC;K2i`Q βj T2b 2H TQ`i2 2tTHB+ iBpQ /2 H p `B #H2 +Q``2bTQM/B2Mi2 H 2biBK `HQ U2+m +BƦM UkXeV v UkXdVVX bÅ&#x2018;- HQb +Q2}+B2Mi2b 2biBK /Qb `2T`2b2Mi M H BKTQ`i M+B /2 mM p `B #H2 BM/2T2M/B2Mi2 2M HQb + K#BQb /2 H /2T2M/B2Mi2X GQb KûiQ/Qb T ` `2bQHp2` bQM 2biBK @ /Q`2b /2 KÅ&#x2018;MBKQb +m /` /Qb UPGa Q`/BM `v H2 bi@b[m `2V Q /2 KÂ&#x20AC;tBK p2`QbBKBHBim/ UJG K tBKmK HBF2HB?QQ/VX aB HQb iû`KBMQb /2H 2``Q`- i K#BûM HH K /Qb `2bB/mQb- iB2M2M mM /Bbi`B#m+BƦM MQ`K H v mM p `B Mx +QMbi Mi2 U?QKQ+2/ biB+B/ /V- 2MiQM+2b 2H 2b@ iBK /Q` 2b ƦTiBKQ 2Mi`2 iQ/Qb HQb 2biBK /Q`2b MQ b2b; /Qb HBM2 H2b v MQ HBM2 H2bX 1b k3
BKTQ`i Mi2 BM/ ; ` 2H +mKTHBKB2MiQ /2 H b +QM/B+BQM2b /2 MQ`K HB/ /- 2M 2bT2+B H 2M HQb `2bB/mQb U:B##QMb v Pp2`K M- kyRkVX KQ/2HQ HBM2 H /2 H B@2bBK Q#b2`p +BƦM
yi = β0 + β1 · xi1 + ... + βj · xij + ... + βp · xip + ei
UkXeV
7Q`K K i`B+B H /2H bBbi2K /2 2+m +BQM2b `2bQHp2`
YnÃ&#x2014;1 = XnÃ&#x2014;p βpÃ&#x2014;1 + e(nÃ&#x2014;1)
UkXdV
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1M7Q[m2 ;2Q2bi /Å&#x2018;biB+Q
*m M/Q b2 M HBx HQb `2bB/mQb ei 2M mM `2;`2bBƦM HBM2 H b2 2bT2` 2biQb b2 M B/2 HK2Mi2 `mB/QX aBM 2K# `;Q bB b2 2M+m2Mi` [m2 2tBbi2 H;ȹM iBTQ /2 `2H +BƦM /2 HQb `2bB/mQb +QM H TQbB+BƦM /2 H b Q#b2`p +BQM2b i 2M TH MQ ;2Q;`Â&#x20AC;}+Q- 2MiQM+2b b2 Tm2/2 mb ` p `B @ +BQM2b 2M 2H KQ/2HQ HBM2 H- [m2 +QMbBbi2 2M BM+HmB` mM iû`KBMQ HBM2 H mb M/Q H p `B #H2 /2T2M/B2Mi2 UKQ/2HQ miQ`2;`2bBpQ a _- 2+m +BƦM UkX3VV- H b BM/2T2M/B2Mi2b UbT iB H H ;
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Q `2i `/Q 2bT +B H 2M X aGs- 2+m +BƦM UkXRyVV- 2M 2H 2``Q` UKQ/2HQ 2bT +B H /2H 2``Q` a1J-2+m +BƦM UkXNVV Q mb M/Q mM +QK#BM +BƦM /2H KQ/2HQ /2 2``Q` v miQ`2;`2bBpQ UKQ/2HQ 2bT +B H /2 .m`#BM a.-2+m +BƦM UkXRRVVX hQ/ b 2bi b T`QtBK +BQM2b BMi`Q/m@ +2M mM K i`Bx /2 Wn×n - /QM/2 n 2b 2H MȹK2`Q /2 bBiBQb- [m2 + Tim` H BM~m2M+B /2 H b p `B #H2b 2M `2H +BƦM +QM bm T`QtBKB/ /X JQ/2HQ 2bT +B H miQ`2;`2bBpQ Ua _V
Y = Xβ + ρW Y + e
UkX3V
JQ/2HQ /2 2``Q` 2bT +B H Ua1JV
Y = Xβ + u /QM/2 u = ρW u + e
UkXNV
JQ/2HQ /2 `2i `/Q 2bT +B H 2M HQb i2`KBMQb BM/2T2M/B2Mi2 UaGsV
Y = Xβ + W Xλ + e
UkXRyV
JQ/2HQ 2bT +B H /2 .m`#BM a.
Y = Xβ + ρW Y + W Xλ + e
UkXRRV
1biQ bB;MB}+ [m2 b2 T`QTQM2 T`BQ`B mM `2H +BƦM 2bT +B H H / ` 2bi`m+im` W - TQ` 2D2KTHQ mb M/Q bQHQ p HQ`2b /2 R Up2+BMQV v y UMQ p2+BMQV H b mMB/ /2b 2bT +B H2b +QMiB;m b Q T ` 2tT`2b ` mM `2H +BƦM ;HQ# H mb M/Q mM Kûi`B+ /2 /Bbi M+B 2M HQb p HQ`2b /2 H K i`Bx W - TQ` 2D2KTHQ wij = 1/dij /QM/2 dij 2b H /Bbi M+B 2m+HB/B M 2Mi`2 HQb +2Mi`QB/2b /2 HQb bBiBQb i v jX G B/2 2b [m2 HQb p2+BMQb K b +2`+ MQb BM~m2M+B M HQb 72MƦK2MQb 2M H mMB/ / i- # b /Qb 2M H T`BK2` H2v /2 H ;2Q;` 7ő Q G2v /2 hQ#H2`R UhQ#H2`- RNdyVX 1bi2 2b mM bmTm2biQ 7m2`i2- v /2#2 b2` +Q?2`2Mi2 +QM 2H 72MƦK2MQ v HQb R
dzhQ/ b H b +Qb b 2bi M `2H +BQM / b 2Mi`2 bő- T2`Q H b +Qb b K b T`ƦtBK b 2M 2H 2bT +BQ iB2M2M mM `2H +BƦM K vQ` [m2 H b /Bbi Mi2bXǴ
jy
/ iQb [m2 HQ `2T`2b2Mi MX *QM H K i`Bx W b2 + H+mH 2H +Q2}+B2Mi2 /2 JQ` MǶA UJQ` M- RN8yV- [m2 b2 mb T ` T`Q# ` mM bQ+B +BƦM ;HQ# H 2Mi`2 mM p `B #H2 v bm TQbB+BƦM 2M 2H TH MQX aB HQb `2bB/mQb ei Km2bi` M mM bQ+B +BƦM 7m2`i2 +QM H 2bi`m+im` /2 W 2M H T`m2# /2 JQ` MǶA- b2 bm;B2`2 mb ` H;mMQ /2 HQb KQ/2HQb 2bT +B H2b Ua _-aGs-a1J Q a.V- Tm2b 2biQ bB;MB}+ [m2 MQ b2 Tm2/2 +QM} ` 2M HQb +Q2}+B2Mi2b 2biBK /Qb TQ` H `2;`2bBƦM HBM2 HX a2 /m+2 [m2 W Tm2/2 vm/ ` 2tTHB+ ` 2H T`Q+2bQ [m2 b2 2biÂ&#x20AC; KQ/2H M/QX .2 HQ +QMi` `BQ 2b K2DQ` mb ` mM KQ/2HQ HBM2 H m Qi` iû+MB+ X Mb2HBM UkyykV- SÂ&#x20AC;2x v a+Qii Ukyy8V v EBbbHBM; v * `H Ukyy3V ? +2M mM `2pBbBƦM /2 HQb T`Q+2bQb 2bT +B H2b- bmb bmTm2biQ v HQb +`Bi2`BQb /2 Dmbi2 +QKQ 2``Q`2b +m /`Â&#x20AC;iB+Qb v +`Bi2`BQ /2 BM7Q`K +BƦM /2 F BF2 T ` H b2H2++BƦM /2 mM KQ/2HQ v /Bb2Æ¢Q #B2M 7Q`KmH /Q v Dmbi /QX 1bim/BQb +QKQ 2H /2 G M/`v v *? F` #Q`iv UkyyNV- w?Qm v EBK UkyRjV- a? M ? M 2i HX UkyR9V v a+?r `x 2i HX UkyR8V ? +2M mbQ /2 KQ/2HQb miQ``2;`2bBpQb v /2 `2i `/Q 2bT +B H T ` 2tTHB+ ` HQb 2``Q`2b 2M 2H KQ/2HQ HBM2 H v K2DQ` ` 2H Dmbi2 +QKT ` M/Q KQ/2HQb [m2 `2H +BQM M H b p `B #H2b K#B2Mi H2b U+Q#2`im` /2 +QT v ++2bQ 1oV +QM BM/B+ /Q`2b bQ+BQ2+QMƦKB+QbX EBbbHBM; v * `H Ukyy3V- :B##QMb v Pp2`K M UkyRkV v G2a ;2 v S +2 UkyR9V ? +2M mM +`Å&#x2018;iB+ HQb KQ/2HQb 2bT +B H2b- v Km2bi` M [m2 H BM+HmbBƦM /2 HQb iû`KBMQb /2 miQ@ `2;`2bBƦM Ua _V MQ TQ`i M Km+?Q H + T +B/ / 2tTHB+ iBp 2 BMi2`T`2i +BƦM- Tm2b 2tBbi2 mM +QTH2 2Mi`2 HQb 2biBK /Q`2b /2 HQb +Q2}+B2Mi2b [m2 MQ T2`KBi2 BMi2`T`2i ` HQb +Q2}+B2Mi2b +QKQ 7 +iQ`2b /2H 272+iQ BbH /Q /2 + / mM /2 H b p `B #H2b 2tTHB+ iBp bX a2 Km2bi` [m2 2H Dmbi2 MQ bm2H2 b2` Kmv b2MbB#H2 p `B +BQM2b 2M q- HQ [m2 +m2biBQM 2H mbQ /2 H 2bi`m+im` 2bT +B H /2}MB/ T`BQ`BX aBM 2K# `;Q- G2a ;2 v S +2 UkyR9V T`QTQM2M [m2 bB H K2i /2 mb ` KQ/2HQb /2 `2;`2bBƦM 2bT +B H 2b i2M2` K2/B/ b 2b+ @ H `2b T`QtBK / K2Mi2 +Q``2+i b /2 HQb 272+iQb /B`2+iQb 2 BM/B`2+iQb bQ#`2 H p `B #H2 /2T2M/B2Mi2- bQ+B /Qb + K#BQb 2M H b p `B #H2b 2tTHB+ iBp b- 2MiQM+2b- bÅ&#x2018; 2b /2+m /Q 2H mbQ /2 2biQb KQ/2HQbX /2KÂ&#x20AC;b /2H mbQ /2H MÂ&#x20AC;HBbBb /2 miQ+Q``2H +BƦM 2bT +B H ;HQ# H- b2 Tm2/2 2tTHQ` ` KûiQ@ jR
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4km â&#x2C6;&#x2019;76.45
Long Datos en grados decimales, sistema de coordenas WGS84
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área de copa
cobertura de copa [%]
deciles 1
2
3
4
5
6
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afrocolombianos
con alguna limitación
con estudios superiores
ningún estudio
deciles 1
2
3
4
5
6
7
8
9
10
NA
6B;m` jXd, J T b /2 H b p `B #H2b /2 TQ#H +BƦM b2H2++BQM / b U2M /2+BH2bVX
9d
afrocolombianos [%]
con alguna limitación [%]
densidad de población
ningun estudio [%]
con estudios superiores [%]
deciles 1
2
3
4
5
6
7
8
9
10
NA
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vivienda tipo cuarto [%] 0.0
0.2
0.4
uso de vivienda [%]
0.6
0.00
uso de unidad económica [%] 0.00
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0.75
0.25
0.50
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1.00
uso de LEA [%] 1.00
0.00
0.05
0.10
0.15
0.20
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[m22MV 2M H +Bm/ / /2 * HBX G b `2;`2bBQM2b b2 `2 HBx M bQ#`2 mM bm#+QMDmMiQ /2 HQb alb- v TQ` i MiQ H 2bi`m+im` /2 2bi K i`Bx impQ 2biQ 2M +m2Mi X
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S ` BM/ ; ` bQ#`2 H BM7Q`K +BƦM Q T i`QM2b 2bT +B H2b /2 HQb `2bB/mQb /2 HQb KQ/2HQb /2 `2;`2bBƦM b2 mbƦ 2H Å&#x2018;M/B+2 /2 JQ` MǶA U2+m +BƦM UjXjVVX 1H Å&#x2018;M/B+2 /2 JQ` MǶA 2b 2H +Q2}+B2Mi2 /2 +Q``2H +BƦM T ` H `2H +BƦM 2Mi`2 mM p `B #H2 v bmb p HQ`2b +B`+mM/ Mi2bX *m M/Q b2 2M+m2Mi` mM +Q``2H +BƦM 2bT +B H bB;MB}+ iBp 2M HQb `2bB/mQb- 2biQ bm;B2`2 [m2 ;`2; M/Q 2b 2bi`m+im` /2 p2+BM/ / H KQ/2HQ 2b TQbB#H2 Q#i2M2` mM 2biBK +BƦM KÂ&#x20AC;b 2}+B2Mi2 /2 HQb +Q2}+B2Mi2b- v 2M +QMb2+m2M+B mM 2biBK +BƦM KÂ&#x20AC;b +QM} #H2 /2 HQb +Q2}+B2Mi2bX 1M 2bi2 2bim/BQ MQ b2 ? +2 BM72`2M+B /2 mM TQ#H +BƦM TQ` mM Km2bi` b2 + H+mH `QM +Q2}+B2Mi2b bQ#`2 2H iQi H /2 H TQ#H +BƦM- v TQ` i MiQ HQb +Q2}+B2Mi2b Tm2/2M BMi2`T`2i `b2 +QKQ H 7m2`x /2 2b `2H +BƦMX
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/QM/2 N 2b 2H MȹK2`Q /2 mMB/ /2b 2bT +B H2b BM/2t /Qb TQ` i v jc X 2b H p `B #H2 /2 BMi2`ûbc XÌ&#x201E; 2b H K2/B /2 Xc v wij 2b mM 2H2K2MiQ /2 mM K i`Bx /2 T2bQb 2bT +B H2b W X lM p HQ` /2 y /2 JQ` MǶA BM/B+ mM T i`ƦM 2bT +B H H2 iQ`BQX aB 2tBbi2 miQ+Q``2H +BƦM HQb p HQ`2b bQM TQbBiBpQb v 2H KÂ&#x20AC;tBKQ 2b RX aB HQb p HQ`2b bQM M2; iBpQb b2 /B+2 [m2 2tBbi2 /BbT2`bBƦM- bB2M/Q @R 2H KÅ&#x2018;MBKQ p HQ` TQbB#H2 `2T`2b2Mi M/Q H /BbT2`bBƦM T2`72+i X 1H p HQ` p /2H i2bi 2tT`2b 2H ;` /Q /2 +2`i2x bQ#`2 2H p HQ` /2H 2bi /Å&#x2018;biB+Q- bB 2H p HQ` HÅ&#x2018;KBi2 /2 bB;MB}+ M+B 2b K2MQ` [m2 α = 0,05
jXjXeXjX
AM/B+ /Q`2b GQ+ H2b /2 bQ+B +BƦM 1bT +B H UGAa V
. /Q [m2 JQ`Â&#x20AC;MǶA 2b mM bmK /2 T`Q/m+iQb +`mx /Qb BM/BpB/m H2b 2b 2tTHQi /Q T ` 7Q`KmH ` HQb BM/B+ /Q`2b HQ+ H2b /2 bQ+B +BƦM 2bT +B H UGAa VX 1biQb T2`KBi2M 2p Hm `
88
H ;`mT +BƦM /2 H b mMB/ /2b BM/BpB/m H2b K2/B Mi2 2H +Â&#x20AC;H+mHQ /2 H JQ` M HQ+ H T ` + / mMB/ / 2bT +B H v H 2p Hm +BƦM /2 H bB;MB}+ +BƦM 2bi /Å&#x2018;biB+ /2 2bi2 BM/B+ /Q` U Mb2HBM- RNN8VX 1biQb K T b 2M +QMDmMiQ +QM 2H `2bmHi /Q MmKû`B+Q /2 HQb GAa x@MQ`K HBx /Q v 2H p@p HQ` T2`KBi2M B/2MiB}+ ` ;`mT +BQM2b 2bT +B H2bX G b `2;BQM2b `2b Hi / b 2M `QDQ iB2M2M p HQ`2b HiQb /2 H p `B #H2 v iB2M2M p2+BMQb +QM p HQ`2b HiQb i K#BûM U?B;?@ ?B;?VX 1H Â&#x20AC;`2 xmH UHQr@HQrV bQM HQb ;`mTQb [m2 T`2b2Mi M p HQ`2b # DQb H B;m H [m2 bmb p2+BMQbX JB2Mi` b [m2 H b `2;BQM2b xmH TÂ&#x20AC;HB/Q bQM HQr@?B;? v H b Â&#x20AC;`2 b `Qb / b bQM ?B;?@ HQr Km2bi` M +Q``2H +BƦM M2; iBp - 2b /2+B` p HQ`2b Kmv /B72`2Mi2b HQb /2 bmb p2+BMQbX G b `2;BQM2b 7m2`i2K2Mi2 +QHQ`2 / b bQM [m2HH b [m2 +QMi`B#mv2M bB;MB}+ iBp K2Mi2 mM `2bmHi /Q TQbBiBpQ /2 miQ+Q``2H +BƦM 2bT +B H ;HQ# H- KB2Mi` b [m2 HQb +QHQ`2b KÂ&#x20AC;b +H `Qb +QMi`B#mv2M bB;MB}+ iBp K2Mi2 mM `2bmHi /Q /2 miQ+Q``2H +BƦM M2; iBpQX
8e
* TőimHQ 9 _2bmHi /Qb 9XRX 9XRXRX
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1H T`Q+2bQ /2 b2H2++BƦM /2 H b p `B #H2b BM+HmB` 2M HQb KQ/2HQb BMB+B +QM H BMbT2+@ +BƦM pBbm H /2 H b /Bbi`B#m+BQM2b #Bp `B / b /2 H b + M/B/ i b T`2/B+iQ`2bX a2 #mb+ B/2MiB}+ ` H b p `B #H2b +Q``2H +BQM / b 2Mi`2 bő T ` 2pBi ` BM+HmB` BM7Q`K +BƦM `2/mM@ / Mi2 2M HQb KQ/2HQbX 1M H };m` 9XR b2 2tTHQ` H b `2H +BQM2b 2Mi`2 H b p `B #H2b /2 TQ#H +BƦM UMȹK2`Q /2 T2`bQM b 2M mM al +QM mM +QM/B+BƦM 2bT2+ő}+ VX G K i`Bx i`B M;mH ` bmT2`BQ` Km2bi` HQb +Q2}+B2Mi2b /2 +Q``2H +BƦM /2 S2 `bQM- H /B ;QM H +QM@ iB2M2 2H ?BbiQ;` K /2 7`2+m2M+B b /2 H p `B #H2 v H K i`Bx i`B M;mH ` BM72`BQ` Km2bi` mM ;` }+Q /2 /BbT2`bBƦM v H HőM2 /2 i2M/2M+B mb M/Q mM KQ/2HQ HBM2 H 2Mi`2 + / T ` /2 p `B #H2bX 1b MQiQ`B H Hi +Q``2H +BƦM 2Mi`2 TQ#H +BƦM +QM MBM;ȹM 2bim/BQ v i2M2` H;mM HBKBi +BƦM 7őbB+ U≃ 0,88Vc T2`i2M2+2` mM +QKmMB/ / 7`Q/2b+2M/B2Mi2 v + `2+2` /2 2bim/BQb U≃ 0,92V Q b2` 7`Q/2b+2M/B2Mi2 v i2M2` H;mM HBKBi +BƦM U≃ 0,88VX 1biQ `2T`2b2Mi mM bmK /2 +QM/B+BQM2b /2b7 pQ` #H2b `2H +BQM / b 2Mi`2 bő- [m2 /2b/2 2H TmMiQ /2 pBbi /2H KQ/2HQ bƦHQ TQ/` M b2` `2T`2b2Mi / b TQ` H p `B #H2 [m2 K2DQ` b2 `2H +BQM2 +QM H +Q#2`im` /2 +QT v 2pBi ` bő +QHBM2 HB/ / 2Mi`2 HQb T`2/B+iQ`2bX
8d
ningún estudio
con alguna limitación
afrocolombianos
Corr: 0.0231
Corr: 0.267
Corr: 0.0862
con estudios superiores
Corr: 0.881
Corr: 0.919
ningún estudio
Corr: 0.881
con alguna limitación
con estudios superiores
60 40 20 0
2000
1000
0
2000
1000
0 15000 afrocolombianos
10000 5000 0 0
2000
4000
60000
1000
2000
0
1000
2000
0
5000 10000 15000
6B;m` 9XR, *QKT ` +BƦM TQ` T `2b 2Mi`2 T`2/B+iQ`2b /2 TQ#H +BƦM
G b KBbK b p `B #H2b 2tT`2b / b +QKQ TQ`+2Mi D2 /2 H TQ#H +BƦM /2 mM al Km2bi` M T i`QM2b bBKBH `2b Up2` };m` 9XkV, 2tBbi2 mM Hi +Q``2H +BƦM M2; iBp 2Mi`2 2H TQ`+2M@ i D2 /2 TQ#H +BƦM 7`Q /2 mM b2+iQ` v H i2M2M+B /2 2bim/BQb bmT2`BQ`2b U≃ −0,71V- mM
7m2`i2 bQ+B +BƦM TQbBiBp 2Mi`2 2H TQ`+2Mi D2 /2 T2`bQM b 7`Q /2 mM b2+iQ` v 2H TQ`@ +2Mi D2 /2 T2`bQM b [m2 + `2+2M /2 2bim/BQb U≃ 0,68VX h K#BûM ? v mM 7m2`i2 `2H +BƦM BMp2`b 2Mi`2 2H TQ`+2Mi D2 /2 T2`bQM b /2 mM b2+iQ` bBM 2bim/BQb v 2H TQ`+2Mi D2 /2 2HHQb [m2 iB2M2 2bim/BQb bmT2`BQ`2b U≃ −0,8VX 1biQb `2bmHi /Qb `27m2`x M H +QM+2Mi` +BƦM /2 +QM/B+BQM2b /2b7 pQ` #H2b T ` H TQ#H +BƦM 2tTHB+ / b TQ` H +QM/B+BƦM ` +B HX
83
densidad de población
con alguna limitación [%]
ningun estudio [%]
con estudios superiores [%]
afrocolombianos [%]
Corr: 0.34
Corr: 0.375
Corr: −0.513
Corr: 0.472
Corr: 0.483
Corr: −0.492
Corr: 0.439
Corr: −0.797
Corr: 0.682
30
10
densidad de población
20
0 con alguna limitación [%]
0.10
0.05
0.00
ningun estudio [%]
0.15 0.10 0.05 0.00
con estudios superiores [%]
0.6 0.4
Corr: −0.71
0.2 0.0
afrocolombianos [%]
0.6 0.4 0.2 0.0 0.00 0.02 0.04 0.06 0.00
0.05
0.10
0.00 0.05 0.10 0.15
0.0
0.2
0.4
0.6 0.0
0.2
0.4
0.6
6B;m` 9Xk, *QKT ` +BƦM TQ` T `2b 2Mi`2 T`2/B+iQ`2b /2 TQ#H +BƦM TQ`+2Mim H2b
GQb ;` }+Qb /2 xmH2DQb bQM mM 7Q`K `2bmKB/ T ` +QMbmHi ` H BMi2MbB/ / /2 2bi b `2H +BQM2b U};m` 9XjV HBM2 H2b 2Mi`2 H b p `B #H2b /2T2M/B2Mi2b mb M/Q 2H +Q2}+B2Mi2 /2 +Q``2H +BƦM /2 S2 `bQM- v H b MQ HBM2 H2b K2/B Mi2 2H +Q2}+B2Mi2 /2 aT2 `K M U};m` 9X9VX *QM # b2 2M HQb +Q2}+B2Mi2b /2 +Q``2H +BƦM /2 S2 `bQM U};m` 9X8V v aT2 `K M U};m` 9XeV 2Mi`2 H b p `B #H2b /2T2M/B2Mi2b 2 BM/2T2M/B2Mi2b- v i2MB2M/Q 2M +m2Mi H b `2bi`B+@ +BQM2b /2 +QHBM2 HB/ / 2Mi`2 H b p `B #H2b /2T2M/B2Mi2b- b2 b2H2++BQM `QM H b bB;mB2Mi2b p `B #H2b T ` HQb KQ/2HQb HBM2 H2b, 8N
S ` 2H `2 /2 +QT U `2 n+QT V HQb T`2/B+iQ`2b b2H2++BQM /Qb bQM, +QM 2bim/BQb bmT2`BQ`2b- /2MbB/ / /2 TQ#H +BƟM- +QM H;mM HBKBi +BƟM ( W)- 7`Q+QHQK#B MQb ( W)X S ` H +Q#2`im` /2 +QT U+Q#2`im` n+QT X TV HQb T`2/B+iQ`2b b2H2++BQM /Qb bQM, +QM 2bim/BQb bmT2`BQ`2b ( W)- /2MbB/ / /2 TQ#H +BƟM- +QM H;mM HBKBi +BƟM ( W)- 7`Q+QHQK#B MQb ( W) S ` H b2H2++BƦM /2 p `B #H2b bQ#`2 mbQ /2 HQb T`2/BQb- HQb iBTQb /2 pBpB2M/ v `2 /2 2bT +BQ Tȹ#HB+Q b2 THB+Ʀ 2H KBbKQ T`Q+2bQX S ` 2H `2 /2 +QT b2 b2H2++BQM `QM 2H `2 /2 2bT +BQb p2`/2b v 2H TQ`+2Mi D2 /2 pBpB2M/ b iBTQ +m `iQX S ` 2H KQ/2HQ /2 TQ`+2Mi D2 /2 +Q#2`im` b2 b2H2++BQM `QM 2H TQ`+2Mi D2 /2 pBpB2M/ b iBTQ T `i K2MiQ2H TQ`+2Mi D2 /2 pBpB2M/ b iBTQ +m `iQ v TQ`+2Mi D2 /2 `2 /2 2bT +BQb p2`/2bX afrocolombianos
0.09
−0.44
0.33
0.48
0.64
0.41
0.88
0.92
ningún estudio
0.02
−0.48
0.32
0.57
0.53
0.41
0.88
1
con alguna limitación
0.27
−0.4
0.42
0.36
0.44
0.43
1
densidad de población
−0.04
−0.51
0.34
0.38
0.47
1
1
pearson 1.0 0.5
afrocolombianos [%]
−0.31
−0.71
0.44
0.68
1
0.0 ningun estudio [%]
−0.43
−0.8
0.48
con alguna limitación [%]
−0.16
−0.49
1
con estudios superiores [%]
0.42
1
−0.5 −1.0
afrocolombianos
ningún estudio
con alguna limitación
densidad de población
afrocolombianos [%]
ningun estudio [%]
con alguna limitación [%]
con estudios superiores [%]
1 con estudios superiores
con estudios superiores
1
6B;m` 9Xj, *Q2}+B2Mi2 S2 `bQM 2Mi`2 p `B #H2b /2 TQ#H +BƦM
ey
afrocolombianos [%]
−0.33
−0.76
0.55
0.45
0.63
0.74
0.48
0.72
ningun estudio [%]
−0.52
−0.93
0.46
0.4
0.7
0.57
0.53
1
con alguna limitación [%]
−0.16
−0.53
0.36
0.53
0.47
0.44
1
afrocolombianos
0.22
−0.61
0.66
0.89
0.93
1
ningún estudio
0.14
−0.69
0.63
0.89
1
1
spearman 1.0 0.5 0.0
con alguna limitación
0.46
−0.43
0.56
densidad de población
−0.01
−0.52
1
con estudios superiores [%]
0.53
1
−0.5 −1.0
afrocolombianos [%]
ningun estudio [%]
con alguna limitación [%]
afrocolombianos
ningún estudio
con alguna limitación
densidad de población
con estudios superiores [%]
1 con estudios superiores
con estudios superiores
1
6B;m` 9X9, *Q2}+B2Mi2 aT2 `K M 2Mi`2 p `B #H2b /2 TQ#H +BƦM
eR
−0.29
−0.28
−0.59
0.68
−0.46
área de copa
0.66
−0.04
0.1
−0.02
−0.34
−0.21
−0.37
0.42
−0.31
con estudios superiores
ningún estudio
pearson −1.0
0.0
ningun estudio [%]
densidad de población −0.5
0.5
afrocolombianos [%]
−0.32
con estudios superiores [%]
−0.28
con alguna limitación [%]
−0.36
afrocolombianos
0.31
con alguna limitación
cobertura de copa [%]
1.0
0.43
−0.49
−0.25
−0.37
−0.25
−0.33
−0.72
0.72
−0.5
área de copa
0.74
−0.03
0.23
0.06
−0.34
−0.24
−0.51
0.52
−0.34
ningún estudio
con alguna limitación
afrocolombianos
densidad de población
con estudios superiores [%]
afrocolombianos [%]
spearman −1.0
−0.5
0.0
ningun estudio [%]
con alguna limitación [%]
cobertura de copa [%]
con estudios superiores
6B;m` 9X8, *Q2}+B2Mi2 S2 `bQM 2Mi`2 +Q#2`im` /2 +QT v p `B #H2b /2 TQ#H +BƦM
0.5
1.0
6B;m` 9Xe, *Q2}+B2Mi2 aT2 `K M 2Mi`2 +Q#2`im` /2 +QT v p `B #H2b /2 TQ#H +BƦM
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9XRXkX
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Mi2b /2 2p Hm ` HQb KQ/2HQb b2 THB+ `QM p `B b i` Mb7Q`K +BQM2b 2M #mb+ /2 MQ`K HB@ x ` H b /Bbi`B#m+BQM2b /2 H b p `B #H2b /2T2M/B2Mi2bX G b [m2 K2DQ` `2bmHi /Q ``QD `QM 2M H 7Q`KmH +BƦM /2 HQb KQ/2HQb 7m2`QM H i` Mb7Q`K +BƦM HQ; `Å&#x2018;iKB+ T ` 2H + bQ /2H Â&#x20AC;`2 /2 +QT v H p `B #H2 bBM i` Mb7Q`K ` 2M 2H + bQ /2 H +Q#2`im` /2 +QT X G i #H 9XR `2bmK2 HQb +Q2}+B2Mi2b /2 H `2;`2bBƦM T ` 2H Â&#x20AC;`2 /2 +QT - H i #H 9Xk `2bmK2 HQb +Q2}+B2Mi2b /2 H `2;`2bBƦM T ` H +Q#2`im` /2 +QT - v H i #H 9Xj `2bmK2 H b Kûi`B+ b /2 Dmbi2 /2 K#Qb KQ/2HQbX GQb `2bmHi /Qb /2 HQb i2bi a? TB`Q@qBHF BM/B+ M MQ MQ`K HB/ / 2M HQb `2bB/mQb 2M K#Qb KQ/2HQb- ?2i2`Q+2/ biB+B/ / +QKQ Km2bi` 2H i2bi "`2mb+?@S ; M v TQbB#H2b MQ HBM2 HB@ / /2b +QKQ b2 Q#b2`p 2M H b ;`Â&#x20AC;}+ b /B ;MƦbiB+ b /2 H `2;`2bBƦM /2 K#Qb KQ/2HQbU p2` };m` b 9Xd v 9X3VX aBM 2K# `;Q- 2H Dmbi2 /2 K#Qb KQ/2HQb iB2M2 K2/B /2 HQb `2bB/mQb Kmv +2`+ M b y- H B;m H [m2 2H 2``Q` +m /`Â&#x20AC;iB+Q K2/BQ UJa1VX 1M 2H + bQ /2H Â&#x20AC;`2 /2 +QT b2 Q#iB2M2 mM /D_@b[m `2 /2 eyX8 W- [m2 2b +2Ti #H2X G b p `B #H2b bB;MB}+ iBp b T ` 2H Â&#x20AC;`2 /2 +QT bQM, +QM 2bim/BQb bmT2`BQ`2b- /2MbB/ / /2 TQ#H +BÆ&#x;M- pBpB2M/ iBTQ +m `iQ ( W)- {`2 /2 1oX GQb `2bmHi /Qb +QM}`K M [m2 H MBp2H /2 iQ/ 2H Â&#x20AC;`2 /2 2bim/BQ- H b +QM/B+BQM2b /2 ++2bQ H 2/m+ +BƦM /2 H TQ#H +BƦM- H /2MbB/ / /2 TQ#H +BƦM- 2H iBTQ /2 pBpB2M/ v H /BbTQMB#BHB/ / /2 1o b2 +Q``2H +BQM +QM 2H ++2bQ b2`pB+BQb K#B2Mi H2b /2H lX S ` H +Q#2`im` /2 +QT H ȹMB+ p `B #H2 bB;MB}+ iBp 2b +QM 2bim/BQb bmT2`BQ`2b ( W)X 1bi2 ȹMB+Q BM/B+ /Q` TQ`+2Mim H- [m2 ? +2 mM /2b+`BT+BƦM HQ+ H v +QKT ` #H2 2Mi`2 HQb al- 2tTHB+ 2H 98XN W /2 H p `B #BHB/ / /2 HQb / iQb- `27Q`x M/Q H BKTQ`i M+B /2H BM/B+ /Q` /2 ++2bQ 2/m+ +BƦM bmT2`BQ` +QKQ T`2/B+iQ` /2H ++2bQ b2`pB+BQb K#B2Mi H2b /2H lX S ` H bB;mB2Mi2b 7 b2b b2 B;MQ` `QM H b p `B #H2b MQ bB;MB}+ iBp b /2 HQb KQ/2HQb HBM2 @ H2bX
ej
h #H 9XR, *Q2}+B2Mi2b PGa /2 Â&#x20AC;`2 /2 +QT @ GQ;U *V hû`KBMQ
1biBK /Q
1``Q` bi/X
AMi2`+2TiQ
yXd33
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ekXk8e
yXyyy
+QM 2bim/BQb bmT2`BQ`2b
yXjRk
yXyk9
RjXyRj
yXyyy
/2MbB/ / /2 TQ#H +BƦM
@yXR9e
yXyky
@dXk3j
yXyyy
+QM H;mM HBKBi +BƦM ( W)
@yXyky
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yXyyyyy
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e9
h #H 9Xj, _2bmK2M Kรปi`B+ b /2 Dmbi2 PGa T ` 2H ย `2 /2 +QT U *V v +Q#2`im` /2 +QT U**V K2/B/ b}i
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yXyyyyy
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yXyyyyy
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A* GQ; HBF2HB?QQ/
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log.area_copa.mxn ~ superior_postgrado.mxn + densidad_poblacion.mxn + con_alguna_limitacion.porcentaje.mxn + afro.porcentaje.mxn + cuarto.porcentaje.mxn + area_ep.mxn
Residuos
0.1
0.0
−0.1
288
114 14
−0.2
0.6
0.8
Residuos estandarizados
Residuos vs Valores Ajustados
1.0
Gráfico Q−Q 2
0
−2
114 288 14 −3
−2
2.0 1.5
Gráfico Escala−Locacion 14 288 114
1.0 0.5
0
1
2
3
Cuantiles teóricos
Distancia de Cook 0.20
Distancia de Cook
|Residuosestandarizados|
Valores ajustados
−1
288
0.15 0.10
74
0.05
177
0.00
0.0 0.6
0.8
1.0
0
Valores ajustados
100
200
300
Índice de la observación
6B;m` 9Xd, :` }+ b /B ;MƦbiB+ b T ` 2H M HBbBb /2 `2;`2bBƦM HBM2 H /2 `2 /2 +QT
ee
cobertura_copa.ap.mxn ~ superior_postgrado.porcentaje.mxn + densidad_poblacion.mxn + con_alguna_limitacion.porcentaje.mxn + afro.porcentaje.mxn + apartamento.porcentaje.mxn + cuarto.porcentaje.mxn + area_ep.porcentaje.mxn
Residuos
0.50
Residuos estandarizados
Residuos vs Valores Ajustados 21 238 36
0.25 0.00 â&#x2C6;&#x2019;0.25 0.0
0.1
0.2
0.3
GrĂĄfico Qâ&#x2C6;&#x2019;Q 21 5.0
238 36 2.5
0.0
â&#x2C6;&#x2019;2.5
0.4
â&#x2C6;&#x2019;3
GrĂĄfico Escalaâ&#x2C6;&#x2019;Locacion 21
2.5
0
1
2
3
Distancia de Cook 21
238 36
2.0
â&#x2C6;&#x2019;1
Cuantiles teĂłricos
Distancia de Cook
|Residuosestandarizados|
Valores ajustados
â&#x2C6;&#x2019;2
1.5 1.0 0.5
0.09 0.06
314 233
0.03 0.00
0.0 0.0
0.1
0.2
0.3
0.4
0
Valores ajustados
100
200
300
Ă?ndice de la observaciĂłn
6B;m` 9X3, :`Â&#x20AC;}+ b /B ;MĆŚbiB+ b T ` 2H MÂ&#x20AC;HBbBb /2 `2;`2bBĆŚM HBM2 H /2 TQ`+2Mi D2 /2 +Q#2`im` /2 +QT
9XRXjX
JQ/2H /Q 2bT +B H l
G b K i`B+2b /2 p2+BM/ / +QMbi`mB/ b T ` 2H MÂ&#x20AC;HBbBb 2bT +B H bQM H [m22M Wq - [m2 +QMbB/2` p2+BMQ iQ/Qb HQb b2+iQ`2b [m2 +QKT `i2M mM H /Q Q mM 2b[mBM +QM mM alc v mM K i`Bx /2 /Bbi M+B BMp2`b b 2Mi`2 HQb +2Mi`QB/2b /2 HQb al- `2bi`BM;B2M/Q H p2+BM/ / [m2HHQb +2Mi`QB/2b [m2 2biÂ&#x20AC;M K2MQb /2 R FK UWd VX 1H p HQ` /2 mM FBHĆŚK2i`Q 2b `#Bi` `BQ- mM[m2 ` xQM #H2 2M H 2b+ H ?mK M X GQb ;` 7Qb [m2 `2T`2b2Mi M H b k K i`B+2b W b2 Km2bi` M 2M H };m` 9XNX
ed
Queen
Distancia inversa a 1 Km
6B;m` 9XN, J i`B+2b /2 p2+BM/ / /2H MÂ&#x20AC;HBbBb 2bT +B H
9XRXjXRX
miQ+Q``2H +BƦM p `B #H2b /2T2M/B2Mi2b
a2 M HBxƦ H miQ+Q``2H +BƦM /2 H b p `B #H2b /2T2M/B2Mi2b T ` 2M+QMi` ` ;`mT +BQM2b 2tBbi2Mi2b 2M HQb / iQb [m2 Tm2/2M b2` 2tTHB+ /Qb TQ` H 2bi`m+im` /2 p2+BM/ /X GQb `2bmHi /Qb /2 HQb i2bi /2 JQ` MǶA T ` K# b p `B #H2b /2T2M/B2Mi2b Km2bi` M [m2 2tBbi2M T i`QM2b /2 ;`mT KB2MiQ v [m2 Tm2/2 `2+? x `b2 H ?BTƦi2bBb MmH /2 [m2 HQb T`Q+2bQb 2bT +B H2b bm#v +2Mi2b bQM H2 iQ`BQb Up2` i #H b 9X9 v 9X8VX K#Qb /Bb2Æ¢Qb /2 K i`Bx `2p2H M T`2b2M+B +H ` /2 miQ+Q``2H +BƦM 2bT +B HX G K i`Bx Wq + Tim` K2DQ` H miQ+Q``2H +BƦM /2H Â&#x20AC;`2 /2 +QT X 1M 2H + bQ /2 H +Q#2`im` /2 +QT H K i`Bx Wd T`2b2Mi mM p HQ` HB;2` K2Mi2 K vQ` /2 miQ+Q``2H +BƦMX GQb K T b GAa Km2bi` M HQb ;`mTQb /2 b2+iQ`2b [m2 +QM};m` M H miQ+Q``2H +BƦM e3
/2H `2 /2 +QT mb M/Q H K i`Bx T ` Wq U};m` 9XRyV v HQb ;`mTQb /2 H p `B #H2 +Q#2`im` /2 +QT mb M/Q H K i`Bx Wd U};m` 9XRjVX GQb ;`mTQb [m2 b2 7Q`K M Km2bi` M T i`QM2b /BbiBMiQb 2M HQb /Qb BM/B+ /Q`2b b2H2++BQ@ M /Qb T ` + ` +i2`Bx ` HQb #2M2}+BQb /2H `#QH /Q m`# MQX aBM 2K# `;Q- 2tBbi2M al +QKmM2b 2M HQb ;`mTQb +QM7Q`K /Qb T2`Q +QM /B72`2M+B b 2M H 2ti2MbBƦM /2 HQb +QM@ ;HQK2` /Qb B/2MiB}+ /QbX 1biQ b2 /2#2 [m2 + / mMQ /2 HQb BM/B+ /Q`2b 2tT`2b mM +QM+2TiQ /BbiBMiQ /2H /Bb7`mi2 /2 2b2 #2M2}+BQ, 2H `2 /2 +QT Km2bi` H b /B72`2M+B b /2b/2 mM T2`bT2+iBp ;HQ# H- 2b /2+B`- +QM # b2 2M 2H p HQ` #bQHmiQ /2 `2 /2 +QT /2 mM al 2M `2H +BƦM H iQi H /2 `2 /BbTQMB#H2 2M iQ/ H +Bm/ /X 1H BM/B+ /Q` /2 +Q#2`im` /2 +QT 2tT`2b 2H #2M2}+BQ /2 7Q`K `2H iBp 2Mi`2 HQb al H /BpB/B` 2H `2 /2 +QT /BbTQMB#H2 2M mM al 2Mi`2 2H `2 Tȹ#HB+ /2 2b2 alX 1b +H ` H bBKBHBim/ 2Mi`2 HQb ;`mTQb Q#i2MB/Qb T ` mM KBbK p `B #H2 /2T2M/B2Mi2 +QM K#Qb /Bb2ƢQb /2 K i`Bx W U};m` 9XRy v };m` 9XRR T ` 2H `2 /2 +QT v 9XRk v 9XRj T ` H +Q#2`im` /2 +QT V- TQbB#H2K2Mi2 TQ`[m2 MQ 2tBbi2M /B72`2M+B b MQi #H2b 2Mi`2 HQb /Qb iBTQb /2 2bi`m+im` /2 p2+BM/ / T`QTm2bi b U};m` 9XNVX h #H 9X9, h2bi /2 JQ` M @ `2 /2 +QT T ` Wq v Wd
1bi /őbiB+Q JQ` M A 1tT2+i iBp
Wq
Wd
yXjd933
yXk3Rd9
@yXyyjRy @yXyyjRk
o `B Mx .2bpB +BƦM 2bi M/ ` /2 JQ` M A T@p HQ`
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yXyyyyy
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h #H 9X8, h2bi /2 JQ` M @ SQ`+2Mi D2 /2 +Q#2`im` /2 +QT T ` Wq v Wd
1bi /Å&#x2018;biB+Q JQ` M A 1tT2+i iBp o `B Mx .2bpB +BƦM 2biÂ&#x20AC;M/ ` /2 JQ` M A T@p HQ`
Moran Local Normalizado â&#x2C6;&#x2019;4
0
4
8
Wq
Wd
yX93Ry9
yX8ykk8
@yXyyjRy
@yXyyjRk
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ReXN8d9d
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yXyyyyy
Pâ&#x2C6;&#x2019;valor 0001
.001
Cuadrantes .01
.05
not signif.
NA
hâ&#x2C6;&#x2019;h
hâ&#x2C6;&#x2019;l
no signif.
lâ&#x2C6;&#x2019;h
6B;m` 9XRy, J T b GAa T ` H K i`Bx Wq /2H BM/B+ /Q` Â&#x20AC;`2 /2 +QT
dy
lâ&#x2C6;&#x2019;l
NA
Moran Local Normalizado 0
4
8
Pâ&#x2C6;&#x2019;valor 12
0001
.001
Cuadrantes .01
.05
not signif.
NA
hâ&#x2C6;&#x2019;h
hâ&#x2C6;&#x2019;l
no signif.
lâ&#x2C6;&#x2019;h
lâ&#x2C6;&#x2019;l
NA
lâ&#x2C6;&#x2019;l
NA
6B;m` 9XRR, J T b GAa T ` H K i`Bx Wd /2H BM/B+ /Q` Â&#x20AC;`2 /2 +QT
Moran Local Normalizado 0
4
8
Pâ&#x2C6;&#x2019;valor 12
0001
.001
Cuadrantes .01
.05
not signif.
NA
hâ&#x2C6;&#x2019;h
hâ&#x2C6;&#x2019;l
no signif.
lâ&#x2C6;&#x2019;h
6B;m` 9XRk, J T b GAa T ` H K i`Bx Wq /2H BM/B+ /Q` +Q#2`im` /2 +QT
dR
Moran Local Normalizado 0
10
20
30
Pâ&#x2C6;&#x2019;valor 0001
.001
Cuadrantes .01
.05
not signif.
NA
hâ&#x2C6;&#x2019;h
hâ&#x2C6;&#x2019;l
no signif.
lâ&#x2C6;&#x2019;h
lâ&#x2C6;&#x2019;l
NA
6B;m` 9XRj, J T b GAa T ` H K i`Bx Wd /2 /2H BM/B+ /Q` +Q#2`im` /2 +QT
9XRXjXkX
miQ+Q``2H +BƦM `2bB/mQb /2 HQb PGa
S ` 2p Hm ` H miBHB/ / /2 THB+ ` KQ/2HQb 2bT +B H2b /2 `2;`2bBƦM b2 2t KBMƦ H 2tBb@ i2M+B /2 miQ+Q``2H +BƦM 2M HQb `2bB/mQb /2 HQb KQ/2HQb /2 `2;`2bBƦM HBM2 HX a2 +QKT `Ʀ bB H;mMQ /2 H b 2bi`m+im` b /2 p2+BM/ / T`Q/m+2 `2bmHi /Qb bB;MB}+ iBp K2Mi2 K2DQ`2b 2M H /2i2++BƦM /2 miQ+Q``2H +BƦM 2bT +B HX G i #H 9Xe Km2bi` K#Qb /Bb2Æ¢Qb /2 K i`Bx W T`2b2Mi M mM p HQ` /2 JQ` M :HQ# H K vQ` [m2 y v bB;MB}+ iBpQ T ` HQb `2bB/mQb /2H PGa /2 Â&#x20AC;`2 /2 +QT - H B;m H [m2 T ` HQb `2bB/mQb /2H PGa /2H TQ`+2Mi D2 /2 +Q#2`im` Up2` i #H 9XdVX 1M K#Qb KQ/2HQb 2H `2bmHi /Q /2 miQ+Q``2H +BƦM 2bT +B H bm;B2`2 [m2 H BMi`Q/m+B` `2i `/Qb 2bT +B H2b v H 2bi`m+im` /2 p2+BM/ / Tm2/2M K2DQ` ` H 2biBK +BƦM /2 HQb +Q2}+B2Mi2b /2 H `2;`2bBƦM v H b Kûi`B+ b /2 /2b2KT2Æ¢Q /2H Dmbi2X
dk
h #H 9Xe, h2bi /2 JQ` M @ _2bB/mQb /2 PGa `2 /2 +QT T ` Wq v Wd Wq
Wd
yXyNeey
yXRR8dN
@yXyyjRy
@yXyyjRk
o `B Mx
yXyyRRN
yXyyyNy
.2bpB +BƦM 2biÂ&#x20AC;M/ ` /2 JQ` M A
kX3NReR
jXNdR3k
T@p HQ`
yXyyRNk
yXyyyy9
1bi /Å&#x2018;biB+Q JQ` M A 1tT2+i iBp
h #H 9Xd, h2bi /2 JQ` M @ _2bB/mQb /2 PGa SQ`+2Mi D2 /2 +Q#2`im` /2 +QT T ` Wq v Wd Wq
Wd
yXRN9je
yXR33kR
@yXyyjRy
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8Xd3Ryd
eX98Rky
T@p HQ`
yXyyyyy
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1bi /Å&#x2018;biB+Q JQ` M A 1tT2+i iBp
9XRXjXjX
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0.1
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6
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7.5
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área de EV [%]
razón área−distancia
deciles 1
2
3
4
5
6
7
8
9
10
6B;m` 9XRe, Jûi`B+ b /2 ++2bQ 2bT +BQ p2`/2b b2H2++BQM / b
Histograma 60
Cantidad SU
Promedio: 5.77% 40
20
0 0.00
0.25
0.50
0.75
Porcentaje de área de EV en un SU 6B;m` 9XRd, .Bbi`B#m+BQM /2H BM/B+ /Q` /2 ++2bQ HQ+ H 1o
3R
Histograma
Cantidad SU
80 60 40
Promedio del índice: 13.0
20 0 0
50
100
150
200
250
Razón área distancia 6B;m` 9XR3, .Bbi`B#m+BQM /2H BM/B+ /Q` /2 ++2bQ 1o `2 @/Bbi M+B
9XkXRX
*Q``2H +BQM2b v /Bbi`B#m+BQM2b #Bp `B / b
G b };m` b 9XRN v 9Xky `2bmK2M HQb `2bmHi /Qb /2H + H+mHQ /2 HQb +Q2}+B2Mi2b /2 S2 `bQM v aT2 `K M `2bT2+iBp K2Mi2 /2 H b p `B #H2b TQ#H +BQM H2b v HQb BM/B+ /Q`2b /2 ++2bQX 1bi `2H +BƦM 2b Kmv /û#BH- v 2M iQ/ b H b p `B #H2b Uv T ` K#Qb +Q2}+B2Mi2b /2 +Q``2@ H +BƦMV 2b BM72`BQ` yXj- mM p HQ` +QMbB/2` /Q # DQ T ` b2H2++BQM ` mM p `B #H2 +QKQ + M/B/ i T`2/B+iQ` /2 mM `2;`2bBƦM HBM2 HX aBM 2K# `;Q- +QKQ T `i2 /2H T`Q+2bQ T ` BM/ ; ` bQ#`2 2H 272+iQ 2M H 2biBK +BƦM /2 T ` K2i`Qb /2 HQb KQ/2HQb ;2Q2bi @ /őbiB+Qb- b2 BM+Hmv2`QM H b /2 K2DQ` +Q``2H +BƦM, /2MbB/ / /2 TQ#H +BƟM- +QM H;mM HBKBi +BƟM ( W) T ` 2H őM/B+2 /2 ++2bQ ` xƟM {`2 @/Bbi M+B v MBM;ȯM 2bim/BQ ( W) T ` {`2 /2 1o ( W)X
3k
−0.08
−0.12
−0.1
−0.23
−0.26
−0.07
0.1
−0.14
área de EV [%]
0.02
−0.04
−0.03
0.01
−0.12
−0.13
−0.07
0.09
0
con estudios superiores
ningún estudio
con alguna limitación
afrocolombianos
pearson −1.0
0.0
0.5
afrocolombianos [%]
con alguna limitación [%]
densidad de población −0.5
con estudios superiores [%]
−0.07
ningun estudio [%]
razón área−distancia
1.0
−0.1
−0.12
−0.11
−0.2
−0.15
−0.04
0.01
−0.09
área de EV [%]
0.15
−0.06
0.02
0.05
−0.06
−0.11
−0.19
0.17
0
ningún estudio
con alguna limitación
afrocolombianos
densidad de población
ningun estudio [%]
con estudios superiores [%]
spearman −1.0
−0.5
0.0
0.5
afrocolombianos [%]
−0.1
con alguna limitación [%]
razón área−distancia
con estudios superiores
6B;m` 9XRN, *Q2}+B2Mi2 S2 `bQM 2Mi`2 ++2bQ 1o v p `B #H2b /2 TQ#H +BƦM
1.0
6B;m` 9Xky, *Q2}+B2Mi2 aT2 `K M 2Mi`2 ++2bQ 1o v p `B #H2b /2 TQ#H +BƦM
1H +QMDmMiQ /2 p `B #H2b bQ#`2 2H mbQ /2 HQb T`2/BQb v bmb +Q2}+B2Mi2b /2 +Q``2H +BƦM +QM H b p `B #H2b /2T2M/B2Mi2b b2 Km2bi` M 2M H b };m` b 9XkR v 9XkkX .2 Mm2pQ H b +Q``2H +BQM2b bQM # D b- v T `2Mi2K2Mi2 TQ+Q 2tTHB+ iBp b /2 HQb őM/B+2b /2 ++2bQX 3j
G b p `B #H2b /2 mbQ /2 HQb T`2/BQb [m2 K2DQ` b2 `2H +BQM M +QM HQb őM/B+2b bQM, mbQ /2
−0.08
0.16
−0.13
−0.07
−0.22
0.22
0.07
0
0
−0.18
−0.02
−0.07
−0.15
0
0.05
−0.15
−0.05
0.05
−0.08
uso de vivienda
uso de unidad económica
uso de LEA
pearson −1.0
0.0
0.5
uso de vivienda [%]
vivienda tipo casa [%]
−0.5
uso de LEA [%]
−0.05
uso de unidad económica [%]
−0.12
vivienda tipo cuarto [%]
−0.1
vivienda tipo apartamento [%]
−0.11
vivienda tipo cuarto
área de EV [%]
−0.09
vivienda tipo apartamento
razón área−distancia
vivienda tipo casa
mMB/ / 2+QMƟKB+ ( W) v 2H pBpB2M/ b iBTQ +m `iQ ( W)X
1.0
−0.07
−0.15
−0.07
−0.16
−0.16
−0.02
0.01
−0.12
0.18
−0.18
−0.13
área de EV [%]
0.01
0.08
−0.28
0.07
−0.11
−0.13
−0.02
0.09
−0.43
0.22
−0.22
−0.12
vivienda tipo apartamento
vivienda tipo cuarto
uso de vivienda
uso de unidad económica
uso de LEA
uso de vivienda [%]
uso de unidad económica [%]
uso de LEA [%]
spearman −1.0
vivienda tipo casa [%] −0.5
0.0
vivienda tipo cuarto [%]
−0.08
vivienda tipo apartamento [%]
razón área−distancia
vivienda tipo casa
6B;m` 9XkR, *Q2}+B2Mi2 S2 `bQM 2Mi`2 ++2bQ 1o v p `B #H2b /2 mbQ /2 HQb T`2/BQb
0.5
1.0
6B;m` 9Xkk, *Q2}+B2Mi2 aT2 `K M 2Mi`2 ++2bQ 1o v p `B #H2b /2 mbQ /2 HQb T`2/BQb 1H ȹHiBKQ #HQ[m2 /2 p `B #H2b BM/ ; bQ#`2 H b `2 b v T`QTQ`+BQM2b /2 H b K Mx M b /2 + / b2+iQ` +2Mb H v H pQ+ +BƦM +QKQ Tȹ#HB+ Q T`Bp / /2 HQb 2bT +BQb /2Mi`Q /2 39
mM b2+iQ` m`# MQX G b };m` b 9Xkj v 9Xk9 Km2bi` M [m2 2H Â&#x20AC;`2 K2/B /2 H b K Mx M b U{`2 K2/B /2 K Mx M V /2 HQb b2+iQ`2b m`# MQb b2 `2H +BQM /2 7Q`K TQbBiBp +QM K#Qb Å&#x2018;M/B+2b /2 ++2bQ- Km+?Q KÂ&#x20AC;b 7m2`i2K2Mi2 [m2 H b p `B #H2b TQ#H +BQM H2b v /2 mbQ /2 T`2/BQbX mM[m2 T `2+2 ? #2` mM 7m2`i2 +Q``2H +BƦM /2 HQb BM/B+ /Q`2b /2 ++2bQ +QM H b Â&#x20AC;`2 b T`Bp / b- Tȹ#HB+ b v /2H b2+iQ` m`# MQ- 2bi b ? +2M T `i2 /2 HQb +Â&#x20AC;H+mHQb [m2 ;2M2` M 2biQb Å&#x2018;M/B+2b- T`Q/m+B2M/Q 2M 272+iQ }+iB+BQ 2M H +Q``2H +BƦM- ` xƦM TQ` H
0.37
0.49
â&#x2C6;&#x2019;0.06
0.46
0.11
â&#x2C6;&#x2019;0.12
0.12
â&#x2C6;&#x2019;0.25
0.38
área de EV [%]
0.54
0.15
â&#x2C6;&#x2019;0.03
â&#x2C6;&#x2019;0.04
0.06
0.6
â&#x2C6;&#x2019;0.6
â&#x2C6;&#x2019;0.06
0.13
área de manzanas
número de manzanas
área privada
área privada [%]
área de las calles [%]
área del SU
pearson â&#x2C6;&#x2019;1.0
área de las calles
área pública [%]
razón áreaâ&#x2C6;&#x2019;distancia
área media de manzana
[m2 b2 BM+Hmv2M 2M H KQ/2H +BƦMX
â&#x2C6;&#x2019;0.5
0.0
0.5
1.0
6B;m` 9Xkj, *Q2}+B2Mi2 S2 `bQM 2Mi`2 ++2bQ 1o v p `B #H2b bQ#`2 bT2+iQb 7Å&#x2018;bB+Qb /2 H b K Mx M b v al
38
0.16
0.17
−0.02
0.13
0.13
0.07
−0.07
−0.11
0.17
área de EV [%]
0.07
0.13
0.02
0.04
0.14
0.5
−0.5
0.08
0.14
área media de manzana
área de manzanas
número de manzanas
área privada
área de las calles
área de las calles [%]
área del SU
spearman −1.0
−0.5
0.0
área privada [%]
área pública [%]
razón área−distancia
0.5
1.0
6B;m` 9Xk9, *Q2}+B2Mi2 aT2 `K M 2Mi`2 ++2bQ 1o v p `B #H2b bQ#`2 bT2+iQb 7őbB+Qb /2 H b K Mx M b v al
1M `2bmK2M- H b p `B #H2b BM/2T2M/B2Mi2b 2b+Q;B/ b T ` HQb KQ/2HQb HBM2 H2b bQM, S ` 2H `2 /2 1o ( W) HQb T`2/B+iQ`2b b2H2++BQM /Qb bQM MBM;mM 2bim/BQ ( W){`2 K2/B /2 K Mx M - pBpB2M/ iBTQ +m `iQ ( W)X S ` ` xƦM `2 @/Bbi M+B HQb T`2/B+iQ`2b b2H2++BQM /Qb bQM /2MbB/ / /2 TQ#H +BƟM- +QM H;mM HBKBi +BƟM ( W)- mbQ /2 mMB/ / 2+QMƟKB+ ( W){`2 K2/B /2 K Mx M X
9XkXkX
JQ/2HQb /2 `2;`2bBƦM HBM2 H 1o
G i #H 9XR3 Km2bi` HQb +Q2}+B2Mi2b /2 H `2;`2bBƦM T ` 2H TQ`+2Mi D2 /2 1oc H i #H 9XRN Km2bi` HQb +Q2}+B2Mi2b /2 H `2;`2bBƦM T ` őM/B+2 `2 b@/Bbi M+B - v H i #H 9Xky `2bmK2 H b Kûi`B+ b /2 Dmbi2 /2 K#Qb KQ/2HQbX GQb `2bmHi /Qb /2 HQb i2bi a? TB`Q@qBHF BM/B+ M MQ MQ`K HB/ / 2M HQb `2bB/mQb 2M K#Qb KQ/2HQb- ?2i2`Q+2/ biB+B/ / +QKQ Km2bi` 2H i2bi "`2mb+?@S ; M v TQbB#H2b MQ HBM2 HB@ / /2b +QKQ b2 Q#b2`p 2M H b ;` }+ b /B ;MƦbiB+ b /2 H `2;`2bBƦM /2 K#Qb KQ/2HQb 3e
Up2` };m` b 9Xk8 v 9XkeVX 1H MBp2H 2tTHB+ iBpQ /2 H p `B #BHB/ / /2 HQb / iQb /2 K#Qb KQ/2HQb 2b # DQX aBM 2K# `;Q- 2H Dmbi2 /2 K#Qb KQ/2HQb iB2M2 K2/B /2 HQb `2bB/mQb Kmv +2`+ M b y- H B;m H [m2 2H 2``Q` +m /`Â&#x20AC;iB+Q K2/BQ UJa1VX G b p `B #H2b bB;MB}+ iBp b T ` 2H Â&#x20AC;`2 /2 1o ( W) bQM {`2 K2/B /2 K Mx M pBpB2M/ iBTQ +m `iQ ( W)X 1biQb `2bmHi /Qb Km2bi` M [m2 MQ 2tBbi2 2pB/2M+B bB;MB}+ iBp /2 [m2 2H ++2bQ 1o 2M mM al 2biû `2H +BQM /Q +QM p `B #H2b ûiMB+ b- /2 /Bb+ T +B/ / Q /2 ++2bQ H 2/m+ +BƦMX aBM 2K# `;Q 2b Kmv BKTQ`i Mi2 H `2H +BƦM TQbBiBp +QM bT2+iQb 2bi`m+im` H2b `2T`2b2Mi /Qb TQ` 2H Â&#x20AC;`2 K2/B /2 H b K Mx M b v mM `2H +BƦM M2; iBp +QM 2H TQ`+2Mi D2 /2 pBpB2M/ b iBTQ +m `iQ- 2bi b ȹHiBK b +QM+2Mi` / b 2M H xQM +2Mi`Q v /2 H /2` /2H Â&#x20AC;`2 m`# M /2 a MiB ;Q /2 * HB Up2` };m` jXNVX S ` H `2H +BƦM /2 Â&#x20AC;`2 /Bbi M+B b2 +QM}`K H bB;MB}+ M+B /2 {`2 K2/B /2 K Mx M v- 2M mb2M+B /2 H p `B #H2 pBpB2M/ iBTQ +m `iQ ( W)- b2 BM+Q`TQ` mbQ /2 mMB/ / 2+QMÆ&#x;KB+ ( W) [m2 2t?B#2 mM T i`ƦM 2bT +B H bBKBH `X /B72`2M+B /2H Å&#x2018;M/B+2 HQ+ H /2 ++2bQ- 2M ` xÆ&#x;M {`2 @/Bbi M+B b2 2pB/2M+BƦ mM `2H +BƦM M2; iBp +QM 2H TQ`+2Mi D2 /2 T2`bQM b +QM H;mM HBKBi +BƦMX S ` H bB;mB2Mi2b 7 b2b b2 B;MQ` `QM H b p `B #H2b MQ bB;MB}+ iBp b /2 HQb KQ/2HQb HBM2 @ H2bX h #H 9XR3, *Q2}+B2Mi2b PGa /2 SQ`+2Mi D2 /2 1o hû`KBMQ
1biBK /Q 1``Q` bi/X
i@p HQ` S`U=%i%V
AMi2`+2TiQ
yXyjNd3
yXyy3ke
9X3RdNN
yXyyyyy
MBM;mM 2bim/BQ ( W)
yXy8dNe
yXyjee8
RX83R8y
yXRR9d9
Â&#x20AC;`2 K2/B /2 K Mx M
yXd8dNk
yXye8eR
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yXyyyyy
pBpB2M/ iBTQ +m `iQ ( W)
@yXRk3yR
yXy9jjk
@kXN89d3
yXyyjje
3d
h #H 9XRN, *Q2}+B2Mi2b PGa /2 Â&#x20AC;`2 b@/Bbi M+B hû`KBMQ
1biBK /Q
1``Q` bi/X
yXy33dN
yXykyek
9Xjy8de
yXyyyyk
/2MbB/ / /2 TQ#H +BƦM
@yXykkej
yXyjRjd
@yXdkRke
yX9dRkd
+QM H;mM HBKBi +BƦM ( W)
@yXRydyN
yXyjdyR
@kX3NjkR
yXyy9yd
mbQ /2 mMB/ / 2+QMƦKB+ ( W)
yXy33jR
yXyj3j3
kXjyRk8
yXykkyR
Â&#x20AC;`2 K2/B /2 K Mx M
yX9eR3e
yXy3ejk
8Xj8yde
yXyyyyy
AMi2`+2TiQ
i@p HQ` S`U=%i%V
h #H 9Xky, _2bmK2M Kûi`B+ b /2 Dmbi2 PGa AM/B+2 +QMi2M2/Q` U1oV v /2 ++2bQ Â&#x20AC;`2 @ /Bbi M+B K2/B/ b}i
1o `2 @.Bbi M+B
a? TB`Q@qBHF
yXded3k
yX88jyk
aq T@p Hm2
yXyyyyy
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8RXeykRj
"S T@p Hm2
yXyyR8R
yXyyyyy
J2/B _2bB/mQb
yXyyyyy
yXyyyyy
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yXyyeyd
yXyyNkj
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"`2mb+?@S ; M
A* GQ; HBF2HB?QQ/
33
area_ep.porcentaje.mxn ~ cuarto.porcentaje.mxn + area_media_manzana.mxn
Residuos estandarizados
Residuos vs Valores Ajustados 98 Residuos
0.50
160 259
0.25
0.00
−0.25 0.0
0.2
0.4
0.6
Gráfico Q−Q 98 5
160 259
0
0.8
−3
−2
3
2
Gráfico Escala−Locacion 98
0.6
2
3
10
5
0.8
Valores ajustados
267
40
0
0 0.4
1
287
1
0.2
0
Distancia de Cook
160 259
0.0
−1
Cuantiles teóricos
Distancia de Cook
|Residuosestandarizados|
Valores ajustados
0
100
200
Índice de la observación
6B;m` 9Xk8, :` }+ b /B ;MƦbiB+ b T ` PGa /2H TQ`+2Mi D2 /2 1o
3N
300
ia.areas.dist.mxn ~ unidad_economica.porcentaje.mxn + area_media_manzana.mxn + con_alguna_limitacion.porcentaje.mxn
Residuos estandarizados
Residuos
0.6
Residuos vs Valores Ajustados 268 20 269
0.3 0.0 â&#x2C6;&#x2019;0.3 0.0
0.2
0.4
GrĂĄfico Qâ&#x2C6;&#x2019;Q 268 20 269
5
0
â&#x2C6;&#x2019;5
0.6
â&#x2C6;&#x2019;3
3
2
GrĂĄfico Escalaâ&#x2C6;&#x2019;Locacion 268 20 269
2
3
287
10
5
20
0 0.4
1
Distancia de Cook
0 0.2
0
15
1
0.0
â&#x2C6;&#x2019;1
Cuantiles teĂłricos
Distancia de Cook
|Residuosestandarizados|
Valores ajustados
â&#x2C6;&#x2019;2
0.6
0
Valores ajustados
268 100
200
300
Ă?ndice de la observaciĂłn
6B;m` 9Xke, :`Â&#x20AC;}+ b /B ;MĆŚbiB+ b T ` PGa /2 Ĺ&#x2018;M/B+2 Â&#x20AC;`2 @/Bbi M+B
9XkXjX
JQ/2H /Q 2bT +B H /2 2bT +BQb p2`/2b
1H T`Q+2bQ /2 Dmbi2 /2 HQb KQ/2HQb ;2Q2bi /Ĺ&#x2018;biB+Qb T ` 2H MÂ&#x20AC;HBbBb /2 2bT +BQb p2`/2b ? +2 mbQ /2 HQb KBbKQb 2H2K2MiQb K2iQ/QHĆŚ;B+Qb mb /Qb T ` H +Q#2`im` /2 +QT X a2 mb `QM H b /Qb K i`B+2b /2 p2+BM/ / mb M/Q mM F2`M2H /2 p2+BM/ / Zm22M Wq v Qi`Q +QM # b2 2M mM ` /BQ /2 #Čšb[m2/ /2 R FBHĆŚK2i`Q Wd mb / b 2M 2H MÂ&#x20AC;HBbBb /2H l Up2` };m` 9XNVX
Ny
9XkXjXRX
miQ+Q``2H +BƦM p `B #H2b /2T2M/B2Mi2b
a2 M HBxƦ H miQ+Q``2H +BƦM /2 H b p `B #H2b /2T2M/B2Mi2b T ` 2M+QMi` ` ;`mT +BQM2b 2tBbi2Mi2b 2M HQb / iQb [m2 Tm2/2M b2` 2tTHB+ /Qb TQ` H 2bi`m+im` /2 p2+BM/ /X GQb `2bmHi /Qb /2 HQb i2bi /2 JQ` MǶA T ` K# b p `B #H2b /2T2M/B2Mi2b Km2bi` M [m2 2tBb@ i2M T i`QM2b /2 ;`mT KB2MiQ v Tm2/2 `2+? x `b2 H ?BTƦi2bBb MmH /2 [m2 HQb T`Q+2bQb 2bT +B H2b bm#v +2Mi2b bQM H2 iQ`BQb Up2` i #H b 9XkR v 9XkkVX K#Qb /Bb2Æ¢Qb /2 K i`Bx `2p2H M T`2b2M+B +H ` /2 miQ+Q``2H +BƦM 2bT +B HX G K @ i`Bx Wq + Tim` K2DQ` H miQ+Q``2H +BƦM /2 K#Qb BM/B+ /Q`2bX 1H BM/B+ /Q` ` xÆ&#x;M {`2 @/Bbi M+B 2t?B#2 mM p HQ` /2 miQ+Q``2H +BƦM Km+?Q KÂ&#x20AC;b HiQ [m2 {`2 /2 1o ( W)X 1H +Â&#x20AC;H+mHQ /2H Å&#x2018;M/B+2 ` xÆ&#x;M {`2 @/Bbi M+B 2M bm +QMbi`m++BƦM mb mM /Bbi M+B /2 ` /BQ /2 #ȹb[m2/ /2 R FBHƦK2i`QX 1M bm /2}MB+BƦM 2H BM/B+ /Q` 2biÂ&#x20AC; BM~m2M+B /Q TQ` bmb p2+BMQb TQ` HQ [m2 b2 7Q`K M ;`mTQb Q +Hmbi2`b H`2/2/Q` /2 +B2`iQb b2+iQ`2b m`# MQbX _2bmHi Tm2b BMi2`2b Mi2 MQ b2 Wd H [m2 + Tim`2 K2DQ` 2H ;`mT KB2MiQX GQb K T b GAa T ` K#Qb BM/B+ /Q`2b /2 ++2bQ 1o mb M/Q H K i`Bx Wq Km2bi` M HQb ;`mTQb /2 b2+iQ`2b miQ+Q``2H +BQM /Qb U};m` b 9Xkd v 9Xk3VX GQb ;`mTQb 7Q`K /Qb Km2bi` M ;`mT +BQM2b /2 HiQ ++2bQ 1o 2M `2H +BƦM H `2biQ /2 H +Bm/ /X a2 T`2+B [m2 b2 7Q`K M +Hmbi2`b H`2/2/Q` /2 +m i`Q xQM b 2M 2H + bQ /2H TQ`+2Mi D2 /2 Â&#x20AC;`2 /2 1o v /Qb T ` 2H BM/B+ /Q` /2 `2H +BƦM Â&#x20AC;`2 b@/Bbi M+B - +QBM+B/2Mi2b +QM 2H Mi2`BQ`X 1bQb b2+iQ`2b H#2`; M 2[mBT KB2MiQb /2 +Bm/ / +QKQ mM +2K2Mi2`BQ /2 ;` M i K Æ¢Q- H b mMBp2`bB/ /2b v xQM b +QMb2`p / b /2 `B#2` b /2 `Å&#x2018;QbX 1H ;`mTQ [m2 b2 7Q`K H Q`B2Mi2 /2 H +Bm/ / 2b /QM/2 b2 2M+m2Mi` H H ;mM /2H SQM/ D2X h #H 9XkR, h2bi /2 JQ` M @ SQ`+2M iD2 /2 1o T ` Wq v Wd Wq
Wd
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yXyyRyR
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jXjNjde
kXyeyR3
T@p HQ`
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