Chapter 7 Appendix

7.1 Ordinary Least Squares (OLS) Results

London North East West South
Residual Standard Error 0.4189 0.3848 0.4365 0.3804 0.3883
Multiple R-squared 0.1384 0.2322 0.21 0.3045 0.1451
Adjusted R-squared 0.1286 0.1899 0.1765 0.2722 0.1052
p-Value 2.20E-16 1.58E-05 1.59E-06 1.08E-09 0.001183

7.2 Spatial Lag Results

London North East West South
Rho 0.40297 0.32206 0.29468 0.45669 -0.13798
LR test value 49.379 7.3763 7.0177 17.906 1.1217
p-Value 2.11E-12 0.0066088 0.0080709 2.32E-05 0.28955
Log Likelihood -314.2866 -54.80725 -94.47798 -58.85549 -70.04624
AIC 648.57 129.61 208.96 137.71 160.09
AIC for OLS 695.95 134.99 213.97 153.62 159.21
Residual Autocorrelation-Test Value 0.25813 2.8071 0.50144 0.27107 1.5317
Residual Autocorrelation-p Value 0.61141 0.093845 0.45188 0.60262 0.21586

7.3 Spatial Error Results

London North East West South
Lambda 0.41608 0.27217 0.27668 0.46645 -0.090527
LR test value 47.572 3.2666 5.3636 14.224 0.43599
p-Value 5.30E-12 0.070703 0.020562 0.00016232 0.50906
Log Likelihood -315.1897 -56.86209 -95.30504 -70.38909 -70.38909
AIC 650.38 133.72 210.61 141.39 160.78
AIC for OLS 695.95 134.99 213.97 153.62 159.21

7.4 Spatial Durbin Results

London North East West South
Rho 0.37479 0.16363 0.24079 0.36453 -0.1142
LR test value 41.266 1.4741 4.4874 9.7043 0.7311
p-Value 1.33E-10 0.22469 0.034146 0.0018383 0.39253
Log Likelihood -302.6399 -48.56145 -89.76326 -54.65625 -65.65341
AIC 639.28 131.12 213.53 143.31 165.31
AIC for OLS 678.55 134.99 213.9736 151.02 159.21
Residual Autocorrelation-Test Value 1.9248 0.35131 0.18741 0.67823 1.8075
Residual Autocorrelation-p Value 0.16533 0.55337 0.66508 0.4102 0.17881

7.5 Geographically Weighted Regression Results

London North East West South
Fixed Bandwidth 5823.581 4941.289 10334.82 4850.866 11140.59
AICc 642.0675 127.0033 215.8062 129.3623 159.2444
AIC 5.65E+02 98.46093 196.742 93.19053 144.7065
Quasi-global R2 0.3487077 0.4189579 0.2682174 0.5426054 0.1824
Moran’s I 0.0403409 0.0175191 0.08093797 0.04163799 -0.04694458
p-Value 4.92E-06 0.0217 0.001437 0.001576 0.5284

7.5.1 Shapiro-Wilk Normality Tests before normalisation

Greens pace London North East West South
W 0.93963 0.89477 0.96168 0.95177 0.93639
p-Value 3.12E-15 2.59E-08 0.0001102 2.72E-05 1.65E-06

7.5.2 Shapiro-Wilk Normality Test after normalisation

ln(green space + 12) London North East West South
W 3.12E-15 0.98383 0.97935 0.98605 0.9928
p-Value 0.003074 0.1109 0.01124 0.1121 0.6184

7.5.3 Shapiro-Wlike Normality Test for OLS Residuals

London North East West South
W 0.99453 0.99526 0.03343 0.97689 0.99129
p-Value 0.02431 0.9386 0.98304 0.00907 0.4481

7.6 OLS with Spatial Filtering Results

London North East West
Residual Standard Error 0.3671 0.3526 0.4047 0.3218
Multiple R-squared 0.3758 0.3959 0.3415 0.5384
Adjusted R-squared 0.3308 0.3197 0.2922 0.4791
p-value 2.20E-16 7.43E-08 5.23E-10 5.762e-16
London North East West South
1 Observed Moran’s I -0.044942652 -0.044432333 -0.020959765 -0.067750899 -0.032591742
2 OLS -0.0508352899 -0.076417741 -0.050377136 -0.082645384 -0.030405068
3 Expectation 0.3952 0.2542 0.2472 0.3631 0.5179
4 p-value -0.044942652 -0.044432333 -0.020959765 -0.067750899 -0.032591742
London
Estimate Std. Error t value Pr(>|t|) Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.8709770 1.5843668 6.2302347 0.0000000 9.8709770 1.5843668 6.2302347 0.0000000
age 0.0296997 0.0060355 4.9208270 0.0000011 0.0296997 0.0060355 4.9208270 0.0000011
life_expectancy -0.0028445 0.0095016 -0.2993662 0.7647675 -0.0028445 0.0095016 -0.2993662 0.7647675
income -0.5967406 0.1408925 -4.2354336 0.0000265 -0.5967406 0.1408925 -4.2354336 0.0000265
asian -0.0340785 0.0241271 -1.4124571 0.1583499 -0.0340785 0.0241271 -1.4124571 0.1583499
black -0.0271910 0.0363927 -0.7471547 0.4552719 -0.0271910 0.0363927 -0.7471547 0.4552719
other -0.0497549 0.0282910 -1.7586823 0.0791570 -0.0497549 0.0282910 -1.7586823 0.0791570
mixed -0.0000851 0.0001007 -0.8453218 0.3982786 -0.0000851 0.0001007 -0.8453218 0.3982786
fitted(spatial_filter)vec2 -1.5704160 0.3671052 -4.2778364 0.0000221 -1.5704160 0.3671052 -4.2778364 0.0000221
fitted(spatial_filter)vec4 1.5795052 0.3671052 4.3025955 0.0000198 1.5795052 0.3671052 4.3025955 0.0000198
fitted(spatial_filter)vec29 -1.3490363 0.3671052 -3.6747949 0.0002600 -1.3490363 0.3671052 -3.6747949 0.0002600
fitted(spatial_filter)vec31 -1.1944495 0.3671052 -3.2536980 0.0012052 -1.1944495 0.3671052 -3.2536980 0.0012052
fitted(spatial_filter)vec27 -1.1368771 0.3671052 -3.0968701 0.0020499 -1.1368771 0.3671052 -3.0968701 0.0020499
fitted(spatial_filter)vec19 -1.0619286 0.3671052 -2.8927092 0.0039622 -1.0619286 0.3671052 -2.8927092 0.0039622
fitted(spatial_filter)vec16 -1.0325690 0.3671052 -2.8127332 0.0050780 -1.0325690 0.3671052 -2.8127332 0.0050780
fitted(spatial_filter)vec14 -0.9183091 0.3671052 -2.5014877 0.0126408 -0.9183091 0.3671052 -2.5014877 0.0126408
fitted(spatial_filter)vec58 -1.0035691 0.3671052 -2.7337371 0.0064525 -1.0035691 0.3671052 -2.7337371 0.0064525
fitted(spatial_filter)vec11 -0.7833354 0.3671052 -2.1338173 0.0332752 -0.7833354 0.3671052 -2.1338173 0.0332752
fitted(spatial_filter)vec60 0.9568675 0.3671052 2.6065211 0.0093810 0.9568675 0.3671052 2.6065211 0.0093810
fitted(spatial_filter)vec73 0.9855805 0.3671052 2.6847359 0.0074656 0.9855805 0.3671052 2.6847359 0.0074656
fitted(spatial_filter)vec28 -0.8128152 0.3671052 -2.2141205 0.0272073 -0.8128152 0.3671052 -2.2141205 0.0272073
fitted(spatial_filter)vec6 0.7074351 0.3671052 1.9270637 0.0544581 0.7074351 0.3671052 1.9270637 0.0544581
fitted(spatial_filter)vec42 0.8049051 0.3671052 2.1925735 0.0287333 0.8049051 0.3671052 2.1925735 0.0287333
fitted(spatial_filter)vec52 0.7899425 0.3671052 2.1518150 0.0318226 0.7899425 0.3671052 2.1518150 0.0318226
fitted(spatial_filter)vec65 -0.8335256 0.3671052 -2.2705359 0.0235397 -0.8335256 0.3671052 -2.2705359 0.0235397
fitted(spatial_filter)vec20 0.6684498 0.3671052 1.8208672 0.0691404 0.6684498 0.3671052 1.8208672 0.0691404
fitted(spatial_filter)vec66 0.7994872 0.3671052 2.1778150 0.0298206 0.7994872 0.3671052 2.1778150 0.0298206
fitted(spatial_filter)vec33 -0.6956081 0.3671052 -1.8948468 0.0586081 -0.6956081 0.3671052 -1.8948468 0.0586081
fitted(spatial_filter)vec71 0.8100255 0.3671052 2.2065215 0.0277373 0.8100255 0.3671052 2.2065215 0.0277373
fitted(spatial_filter)vec41 0.7046724 0.3671052 1.9195381 0.0554049 0.7046724 0.3671052 1.9195381 0.0554049
fitted(spatial_filter)vec126 1.0304371 0.3671052 2.8069259 0.0051692 1.0304371 0.3671052 2.8069259 0.0051692
fitted(spatial_filter)vec43 0.6870460 0.3671052 1.8715233 0.0617740 0.6870460 0.3671052 1.8715233 0.0617740
fitted(spatial_filter)vec21 0.5992589 0.3671052 1.6323900 0.1031383 0.5992589 0.3671052 1.6323900 0.1031383
fitted(spatial_filter)vec77 0.7427811 0.3671052 2.0233467 0.0434940 0.7427811 0.3671052 2.0233467 0.0434940
fitted(spatial_filter)vec102 0.7793232 0.3671052 2.1228879 0.0341847 0.7793232 0.3671052 2.1228879 0.0341847
fitted(spatial_filter)vec175 1.1738147 0.3671052 3.1974887 0.0014615 1.1738147 0.3671052 3.1974887 0.0014615
fitted(spatial_filter)vec94 -0.7414185 0.3671052 -2.0196349 0.0438791 -0.7414185 0.3671052 -2.0196349 0.0438791
fitted(spatial_filter)vec54 0.6296508 0.3671052 1.7151782 0.0868448 0.6296508 0.3671052 1.7151782 0.0868448
fitted(spatial_filter)vec112 -0.8062533 0.3671052 -2.1962459 0.0284681 -0.8062533 0.3671052 -2.1962459 0.0284681
fitted(spatial_filter)vec86 0.6941237 0.3671052 1.8908031 0.0591471 0.6941237 0.3671052 1.8908031 0.0591471
fitted(spatial_filter)vec8 -0.5089892 0.3671052 -1.3864940 0.1661270 -0.5089892 0.3671052 -1.3864940 0.1661270
fitted(spatial_filter)vec141 -0.8690080 0.3671052 -2.3671907 0.0182499 -0.8690080 0.3671052 -2.3671907 0.0182499
fitted(spatial_filter)vec114 0.6443810 0.3671052 1.7553032 0.0797335 0.6443810 0.3671052 1.7553032 0.0797335
West
Estimate Std. Error t value Pr(>|t|) Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.8317911 3.1023756 6.7147869 0.0000000 20.8317911 3.1023756 6.7147869 0.0000000
age 0.0503955 0.0120691 4.1755747 0.0000520 0.0503955 0.0120691 4.1755747 0.0000520
life_expectancy -0.0168003 0.0170229 -0.9869259 0.3253816 -0.0168003 0.0170229 -0.9869259 0.3253816
income -1.4774121 0.3119440 -4.7361453 0.0000053 -1.4774121 0.3119440 -4.7361453 0.0000053
asian 0.0137365 0.0514152 0.2671677 0.7897332 0.0137365 0.0514152 0.2671677 0.7897332
black -0.3282186 0.0812350 -4.0403581 0.0000876 -0.3282186 0.0812350 -4.0403581 0.0000876
other -0.0110186 0.0714357 -0.1542456 0.8776382 -0.0110186 0.0714357 -0.1542456 0.8776382
mixed 0.0003461 0.0002375 1.4570771 0.1473344 0.0003461 0.0002375 1.4570771 0.1473344
fitted(w_spatial_filter)vec2 1.4769840 0.3217963 4.5898100 0.0000098 1.4769840 0.3217963 4.5898100 0.0000098
fitted(w_spatial_filter)vec11 -1.0279445 0.3217963 -3.1943946 0.0017314 -1.0279445 0.3217963 -3.1943946 0.0017314
fitted(w_spatial_filter)vec4 0.7829903 0.3217963 2.4331859 0.0162277 0.7829903 0.3217963 2.4331859 0.0162277
fitted(w_spatial_filter)vec23 1.0302609 0.3217963 3.2015929 0.0016916 1.0302609 0.3217963 3.2015929 0.0016916
fitted(w_spatial_filter)vec8 0.6276460 0.3217963 1.9504447 0.0531208 0.6276460 0.3217963 1.9504447 0.0531208
fitted(w_spatial_filter)vec28 0.8203771 0.3217963 2.5493673 0.0118688 0.8203771 0.3217963 2.5493673 0.0118688
fitted(w_spatial_filter)vec24 0.7160523 0.3217963 2.2251723 0.0276694 0.7160523 0.3217963 2.2251723 0.0276694
fitted(w_spatial_filter)vec13 -0.5265725 0.3217963 -1.6363532 0.1040118 -0.5265725 0.3217963 -1.6363532 0.1040118
fitted(w_spatial_filter)vec3 0.4138796 0.3217963 1.2861537 0.2005124 0.4138796 0.3217963 1.2861537 0.2005124
fitted(w_spatial_filter)vec1 -0.3662773 0.3217963 -1.1382270 0.2569698 -0.3662773 0.3217963 -1.1382270 0.2569698
fitted(w_spatial_filter)vec45 0.5218438 0.3217963 1.6216587 0.1071264 0.5218438 0.3217963 1.6216587 0.1071264
North
Estimate Std. Error t value Pr(>|t|) Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.7756022 5.0005479 -0.7550377 0.4517181 -3.7756022 5.0005479 -0.7550377 0.4517181
age 0.0724045 0.0136346 5.3103482 0.0000005 0.0724045 0.0136346 5.3103482 0.0000005
life_expectancy 0.0474327 0.0196163 2.4180299 0.0171210 0.0474327 0.0196163 2.4180299 0.0171210
income -0.1171889 0.3785144 -0.3096023 0.7574049 -0.1171889 0.3785144 -0.3096023 0.7574049
asian -0.0008369 0.0824013 -0.0101570 0.9919130 -0.0008369 0.0824013 -0.0101570 0.9919130
black 0.4206325 0.1257478 3.3450488 0.0011009 0.4206325 0.1257478 3.3450488 0.0011009
other -0.0649742 0.0746259 -0.8706664 0.3856893 -0.0649742 0.0746259 -0.8706664 0.3856893
mixed -0.0005622 0.0002852 -1.9713209 0.0510080 -0.0005622 0.0002852 -1.9713209 0.0510080
fitted(n_spatial_filter)vec2 0.7660024 0.3525986 2.1724486 0.0318045 0.7660024 0.3525986 2.1724486 0.0318045
fitted(n_spatial_filter)vec6 -0.6123011 0.3525986 -1.7365384 0.0850566 -0.6123011 0.3525986 -1.7365384 0.0850566
fitted(n_spatial_filter)vec1 0.5496056 0.3525986 1.5587287 0.1217162 0.5496056 0.3525986 1.5587287 0.1217162
fitted(n_spatial_filter)vec18 0.7079633 0.3525986 2.0078448 0.0469249 0.7079633 0.3525986 2.0078448 0.0469249
fitted(n_spatial_filter)vec34 0.9992707 0.3525986 2.8340174 0.0054016 0.9992707 0.3525986 2.8340174 0.0054016
fitted(n_spatial_filter)vec19 0.6335987 0.3525986 1.7969402 0.0748816 0.6335987 0.3525986 1.7969402 0.0748816
fitted(n_spatial_filter)vec3 -0.4559080 0.3525986 -1.2929943 0.1985177 -0.4559080 0.3525986 -1.2929943 0.1985177
fitted(n_spatial_filter)vec47 0.7969061 0.3525986 2.2600942 0.0256340 0.7969061 0.3525986 2.2600942 0.0256340
East
Estimate Std. Error t value Pr(>|t|) Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.7045900 4.7859358 1.6098398 0.1094040 7.7045900 4.7859358 1.6098398 0.1094040
age 0.0118892 0.0154085 0.7716011 0.4414888 0.0118892 0.0154085 0.7716011 0.4414888
life_expectancy -0.0251986 0.0214599 -1.1742180 0.2420525 -0.0251986 0.0214599 -1.1742180 0.2420525
income -0.1075121 0.4431103 -0.2426305 0.8086024 -0.1075121 0.4431103 -0.2426305 0.8086024
asian -0.1683068 0.0735425 -2.2885655 0.0234130 -0.1683068 0.0735425 -2.2885655 0.0234130
black 0.0236404 0.0894777 0.2642041 0.7919627 0.0236404 0.0894777 0.2642041 0.7919627
other -0.0860340 0.1009896 -0.8519091 0.3955379 -0.0860340 0.1009896 -0.8519091 0.3955379
mixed 0.0005186 0.0002796 1.8548388 0.0654595 0.0005186 0.0002796 1.8548388 0.0654595
fitted(e_spatial_filter)vec8 1.1460230 0.4047321 2.8315591 0.0052275 1.1460230 0.4047321 2.8315591 0.0052275
fitted(e_spatial_filter)vec9 -1.1612723 0.4047321 -2.8692368 0.0046706 -1.1612723 0.4047321 -2.8692368 0.0046706
fitted(e_spatial_filter)vec13 -1.1268684 0.4047321 -2.7842324 0.0060127 -1.1268684 0.4047321 -2.7842324 0.0060127
fitted(e_spatial_filter)vec17 -1.0898204 0.4047321 -2.6926954 0.0078425 -1.0898204 0.4047321 -2.6926954 0.0078425
fitted(e_spatial_filter)vec1 0.3395594 0.4047321 0.8389732 0.4027361 0.3395594 0.4047321 0.8389732 0.4027361

7.6.1 Lagrange Multiplier Diagnostics for Spatial Dependence

London North East West South
LMlag 56.262 7.5719 7.2718 1.85E+01 0.96829
p-Value (LMlag) 6.34E-14 0.005928 0.007005 1.73E-05 0.3251
LMerr 52.139 2.5679 5.2787 13.204 0.36006
p-Value (LMerr) 5.17E-13 0.1091 0.02159 0.0002793 0.5485
RLMlag 4.1866 11.009 3.1031 6.2264 2.7989
p-Value (RLMlag) 0.04074 0.0009069 0.07814 0.01259 0.09433
RLMerr 0.063807 6.0046 1.11 0.96381 2.1907
p-Value (RLMerr) 0.8006 0.01427 0.2921 0.3262 0.1388