Calibrate a basic GWR model

Usage

gwr_basic(
  formula,
  data,
  bw = NA,
  adaptive = FALSE,
  kernel = c("gaussian", "exp", "bisquare", "tricube", "boxcar"),
  longlat = FALSE,
  p = 2,
  theta = 0,
  optim_bw_range = c(0, Inf),
  hatmatrix = TRUE,
  parallel_method = c("no", "omp", "cuda"),
  parallel_arg = c(0),
  verbose = FALSE
)

# S3 method for gwrm
step(
  object,
  ...,
  criterion = c("AIC"),
  threshold = 3,
  bw = NA,
  optim_bw = c("no", "AIC", "CV")
)

# S3 method for gwrm
plot(x, y, ..., columns)

# S3 method for gwrm
coef(object, ...)

# S3 method for gwrm
fitted(object, ...)

# S3 method for gwrm
residuals(object, ...)

# S3 method for gwrm
predict(object, regression_points, verbose = FALSE, ...)

Arguments

formula: Regresison model.
data: A sf objects.
bw: The bandwidth used in selecting models. If NA or missing, the bandwidth value will be derived from the gwrm object.
adaptive: Whether the bandwidth value is adaptive or not.
kernel: Kernel function used.
longlat: Whether the coordinates
p: Power of the Minkowski distance, default to 2, i.e., Euclidean distance.
theta: Angle in radian to roate the coordinate system, default to 0.
optim_bw_range: Bounds on bandwidth optimization, a vector of two numeric elements. Set to NA_real_ to enable default values selected by the algorithm.
hatmatrix: If TRUE, great circle will be caculated.
parallel_method: Parallel method.
parallel_arg: Parallel method argument.
verbose: Whether to print additional message.
object: A "gwrm" object.
...: Additional arguments.
criterion: The model-selection method. Currently there is only AIC available.
threshold: The threshold of criterion changes. Default to 3.0.
optim_bw: Whether optimize bandwidth after selecting models. Avaliable values are no, AIC, and CV. If no is specified, the bandwidth specified by argument bw is used in calibrating selected models.
x: A "gwrm" object.
y: Ignored.
columns: Column names to plot. If it is missing or non-character value, all coefficient columns are plottd.
regression_points: Data of new locations.

Value

A gwrm object.

Functions

step(gwrm): Model selection for basic GWR model
plot(gwrm): Plot the result of basic GWR model.
coef(gwrm): Get coefficients of a basic GWR model.
fitted(gwrm): Get fitted values of a basic GWR model.
residuals(gwrm): Get residuals of a basic GWR model.
predict(gwrm): Predict on new locations.

Examples

data(LondonHP)

# Basic usage
gwr_basic(PURCHASE ~ FLOORSZ + UNEMPLOY, LondonHP, 64, TRUE)
#> Geographically Weighted Regression Model
#> ========================================
#>   Formula: PURCHASE ~ FLOORSZ + UNEMPLOY
#>      Data: LondonHP
#>    Kernel: gaussian
#> Bandwidth: 64 (Nearest Neighbours) 
#> 
#> 
#> Summary of Coefficient Estimates
#> --------------------------------
#>  Coefficient         Min.      1st Qu.       Median      3rd Qu.       Max. 
#>    Intercept    13522.222    32504.015    40577.746    48200.526  58693.596 
#>      FLOORSZ     1121.663     1227.720     1319.804     1626.053   1829.647 
#>     UNEMPLOY  -337280.108  -219604.691  -193278.555  -128408.592  50585.573 
#> 
#> 
#> Diagnostic Information
#> ----------------------
#>   RSS: 652228895037
#>   ENP: 11.04545
#>   EDF: 304.9546
#>    R2: 0.63579
#> R2adj: 0.6225549
#>   AIC: 7682.378
#>  AICc: 7693.041
#> 
#> 

# Bandwidth Optimization
m <- gwr_basic(PURCHASE ~ FLOORSZ + UNEMPLOY + PROF, LondonHP, 'AIC', TRUE)
m
#> Geographically Weighted Regression Model
#> ========================================
#>   Formula: PURCHASE ~ FLOORSZ + UNEMPLOY + PROF
#>      Data: LondonHP
#>    Kernel: gaussian
#> Bandwidth: 20 (Nearest Neighbours) (Optimized accroding to AIC)
#> 
#> 
#> Summary of Coefficient Estimates
#> --------------------------------
#>  Coefficient         Min.      1st Qu.       Median      3rd Qu.         Max. 
#>    Intercept  -283403.492  -202450.678  -146322.221   -26250.365    75680.532 
#>      FLOORSZ      908.249     1095.711     1411.257     1864.155     2482.376 
#>     UNEMPLOY  -982984.259    -5935.799   575766.002  1029212.413  1780751.157 
#>         PROF   -16595.354   143221.798   303155.382   379563.029   480351.828 
#> 
#> 
#> Diagnostic Information
#> ----------------------
#>   RSS: 348701748965
#>   ENP: 40.26956
#>   EDF: 275.7304
#>    R2: 0.8052821
#> R2adj: 0.7767406
#>   AIC: 7506.818
#>  AICc: 7546.36
#> 
#> 

step(m, threshold = 100.0, bw = Inf, optim_bw = "AIC")
#> Geographically Weighted Regression Model
#> ========================================
#>   Formula: PURCHASE ~ FLOORSZ + PROF
#>      Data: LondonHP
#>    Kernel: gaussian
#> Bandwidth: 20 (Nearest Neighbours) (Optimized accroding to AIC)
#> 
#> 
#> Summary of Coefficient Estimates
#> --------------------------------
#>  Coefficient         Min.      1st Qu.      Median     3rd Qu.        Max. 
#>    Intercept  -152579.638  -118714.514  -90913.980  -34294.832   40062.236 
#>      FLOORSZ      911.526     1101.292    1398.171    1856.190    2455.689 
#>         PROF    15980.626   153433.054  240159.824  305365.434  374968.876 
#> 
#> 
#> Diagnostic Information
#> ----------------------
#>   RSS: 370110146208
#>   ENP: 34.53499
#>   EDF: 281.465
#>    R2: 0.7933274
#> R2adj: 0.7678789
#>   AIC: 7521.104
#>  AICc: 7554.126
#> 
#> 

plot(m)


coef(m)
#>       Intercept   FLOORSZ    UNEMPLOY       PROF
#> 0    -23859.461 1107.8783  -68568.676 143091.277
#> 1    -19273.643 1099.6911 -105774.018 137317.019
#> 2    -22341.033 1101.6762  -78733.418 139576.718
#> 3    -16587.207 1091.7319 -127715.686 131959.645
#> 4     -4548.212 1071.6907 -236130.771 118805.428
#> 5     36721.681 1025.9964 -574801.771  69162.505
#> 6     41385.027 1015.8069 -621772.017  64587.380
#> 7     41586.375  980.2804 -702105.052  72971.834
#> 8     57682.066  985.6583 -778290.440  47493.741
#> 9     71221.072  928.7546 -982984.259  43974.217
#> 10    71221.072  928.7546 -982984.259  43974.217
#> 11    74619.469  937.5908 -981068.792  35656.125
#> 12   -36611.744 1293.7533  118242.876 111337.546
#> 13   -41112.698 1326.8599  143987.685 114779.442
#> 14   -40110.478 1320.6462  138194.762 113819.779
#> 15   -33091.101 1294.2362   85744.274 105303.803
#> 16   -23071.257 1285.1642  -11537.358  89797.524
#> 17   -25340.399 1292.3173    9974.365  92655.220
#> 18   -23664.457 1290.9835   -7325.338  90061.119
#> 19   -40788.103 1339.5933  133977.982 112868.944
#> 20   -20594.143 1293.7927  -43903.820  84688.294
#> 21   -19987.938 1293.1533  -51824.798  83716.671
#> 22   -31732.566 1325.2556   56141.817  99498.249
#> 23   -19925.638 1298.6693  -54305.801  83082.941
#> 24   -29725.451 1338.4512   26254.767  95071.690
#> 25   -24568.662 1305.8243   -4546.260  89908.455
#> 26   -34640.129 1347.4549   69428.751 102184.662
#> 27   -30890.868 1345.7680   32633.917  96348.212
#> 28   -32685.382 1338.3860  -49922.575 124119.833
#> 29   -25031.866 1318.5557  -73244.469 112769.198
#> 30   -28116.265 1121.2863   43412.634 129466.851
#> 31   -26149.241 1357.6589  -85303.026 108194.827
#> 32   -28815.881 1363.0023  -76497.373 112363.623
#> 33   -24015.706 1147.3150   39287.822 113082.394
#> 34   -26379.748 1137.6319   53964.126 119851.269
#> 35   -26034.543 1088.9505    2927.169 135083.755
#> 36   -23218.692 1378.8505 -104683.173  98601.243
#> 37   -36255.268 1134.3452  120112.460 139922.245
#> 38   -15897.099 1404.6278 -143720.880  79841.433
#> 39   -21289.621 1413.4258 -124270.598  88403.005
#> 40    -8452.456 1029.1179 -185083.061 128044.334
#> 41    -4320.913 1025.9978 -215601.270 122376.737
#> 42    -4320.913 1025.9978 -215601.270 122376.737
#> 43    -5809.548 1036.7680 -186788.099 122370.745
#> 44    -4341.754 1028.1755 -208168.502 121619.580
#> 45   -10383.573 1409.0873 -165291.742  68025.326
#> 46    -8824.776 1021.5504 -188262.545 129078.178
#> 47   -10137.012 1037.5851 -150487.877 128097.150
#> 48    16566.925 1217.5195 -212082.833  47962.183
#> 49   -18834.233 1038.5697  -92604.819 141155.663
#> 50   -21084.132 1047.5924  -64879.463 143221.798
#> 51   -21084.132 1047.5924  -64879.463 143221.798
#> 52   -27308.114 1047.4202  -27747.822 152371.073
#> 53   -26071.929 1047.7922  -31162.659 150660.710
#> 54     4523.811 1189.1320 -139133.905  73502.804
#> 55    18450.195 1230.7297 -211385.065  40595.420
#> 56   -78025.383 1354.7924  435490.767 178018.253
#> 57   -93045.927 1420.6569  517467.533 196609.487
#> 58  -124481.080 1530.2091  695353.082 238166.572
#> 59  -103520.116 1432.8200  578416.543 214480.538
#> 60  -193744.426 1836.5844 1195282.350 313344.383
#> 61  -193274.433 1827.4748 1186073.610 314044.847
#> 62  -193735.300 1825.3512 1180397.449 315575.882
#> 63  -195926.529 1854.6350 1208500.148 314192.406
#> 64  -197873.004 1886.5766 1239754.544 312166.889
#> 65  -194683.519 1830.6797 1182174.626 316625.208
#> 66  -198909.405 1899.4295 1250951.410 311810.090
#> 67  -197964.562 1879.5361 1230244.102 313695.386
#> 68  -196984.343 1861.0807 1211169.372 315231.984
#> 69  -199370.654 1899.3408 1248412.783 312758.159
#> 70  -195286.393 1830.4182 1177983.402 318069.911
#> 71  -201488.734 1916.1275 1258174.219 313959.437
#> 72  -201075.847 1899.3392 1238432.960 316410.372
#> 73  -122966.902 1459.8109  647646.765 252063.226
#> 74  -204142.372 1958.3516 1295831.472 311457.756
#> 75  -201754.049 1904.2279 1240770.944 316919.889
#> 76  -111809.258 1416.8823  578410.941 239681.550
#> 77  -140907.059 1526.6295  740957.406 274837.743
#> 78  -131236.761 1494.6460  684095.951 262915.812
#> 79   -76973.771 1131.9787  312000.704 225259.894
#> 80  -166798.513 1610.4826  878728.070 309109.787
#> 81   -86408.882 1146.9463  341470.102 244299.111
#> 82  -157393.834 1588.5383  786840.399 300532.618
#> 83   -91026.229 1160.3658  357390.550 252453.030
#> 84   -25368.714 1130.8292   81559.990 128297.807
#> 85   -42356.065 1213.7833   99044.118 153624.002
#> 86   -41753.667 1212.7656   98886.546 152150.647
#> 87   -52290.457 1195.5067  148326.050 176003.075
#> 88   -53536.422 1204.0584  147749.251 177443.631
#> 89   -53110.102 1194.8885  152241.799 177626.600
#> 90   -42906.561 1136.7366  148773.176 162973.927
#> 91   -32589.425 1217.6497   67368.699 131583.483
#> 92   -40843.722 1177.7670  120739.369 153760.651
#> 93  -145324.943 1519.6628  546163.529 313250.136
#> 94   -40386.797 1184.1628  116057.451 151812.256
#> 95   -40386.797 1184.1628  116057.451 151812.256
#> 96   -63693.673 1393.2761   57803.458 167024.604
#> 97  -146913.332 1527.2560  524210.507 318967.579
#> 98   -25772.967 1362.7696  -28933.103  91071.393
#> 99  -150526.185 1539.6434  543690.461 323316.529
#> 100 -144832.760 1486.5406  507171.097 322256.518
#> 101 -151929.878 1551.6849  542438.980 325106.777
#> 102 -146354.685 1477.7322  505330.717 327697.663
#> 103 -141004.141 1404.4299  478929.579 329343.642
#> 104  -54724.575 1397.8204   31856.728 145557.540
#> 105 -151899.631 1525.4163  520851.615 332052.394
#> 106 -136652.717 1343.7679  463386.721 329991.761
#> 107  -65783.213 1384.1013   67412.271 171642.120
#> 108 -163943.930 1649.6199  573121.062 335345.387
#> 109  -34302.484 1363.7123   -1879.183 105520.383
#> 110  -61906.708 1379.5745   59876.558 163408.921
#> 111  -63902.406 1383.8854   62257.153 167059.742
#> 112  -63298.209 1367.4527   70201.259 168259.170
#> 113 -183968.599 1906.1663 1114035.672 308271.037
#> 114 -209792.314 2143.1224 1458701.054 300109.720
#> 115 -213246.943 2166.3855 1468408.666 302170.075
#> 116 -213246.943 2166.3855 1468408.666 302170.075
#> 117 -210074.356 2140.1829 1440752.767 302284.363
#> 118 -183629.433 1906.6000 1139288.166 306983.913
#> 119 -183993.702 1906.1384 1109886.220 309212.354
#> 120 -211804.106 2143.6217 1419408.634 306323.115
#> 121 -253005.740 2265.0371 1370802.789 355680.491
#> 122 -253005.740 2265.0371 1370802.789 355680.491
#> 123 -274609.504 2261.1436 1550146.420 384463.687
#> 124 -273937.830 2273.4631 1546274.739 380747.174
#> 125 -253697.283 2246.2771 1388624.390 358241.762
#> 126 -206840.192 2098.9941 1361132.055 307846.578
#> 127 -206840.192 2098.9941 1361132.055 307846.578
#> 128 -263024.542 2195.0258 1465714.426 381322.743
#> 129 -270635.461 2219.7017 1526105.795 386272.348
#> 130 -272066.870 2214.6770 1540644.182 388321.284
#> 131 -272066.870 2214.6770 1540644.182 388321.284
#> 132 -272079.659 2198.1240 1553363.326 388180.809
#> 133 -235777.875 2061.2737 1263976.447 369054.706
#> 134 -261706.572 2110.3258 1445845.135 393564.654
#> 135 -254731.596 2113.1494 1412781.954 384817.765
#> 136 -259503.610 2064.1820 1419938.337 397565.035
#> 137 -258036.926 2101.5268 1431673.539 390736.463
#> 138 -264122.205 2208.2201 1597252.244 375067.867
#> 139 -265448.390 2130.8937 1523111.088 392814.994
#> 140 -248885.929 1984.5707 1303652.667 399801.952
#> 141 -279219.764 2268.7836 1780751.157 379345.412
#> 142 -106422.532 1255.2841  307829.406 281862.698
#> 143  -90130.375  975.2943  296861.750 303719.651
#> 144   32993.857  912.6665  -25733.363  46812.090
#> 145 -102823.614 1248.8238  290192.497 275297.248
#> 146   33310.199  915.6290   34428.970  25819.327
#> 147   -6129.054  916.6483  200930.983  93245.565
#> 148  -87080.550  967.1367  280205.225 301798.130
#> 149   34926.743  913.5507   14063.087  27206.439
#> 150   32979.912  916.9892   31195.599  27460.728
#> 151 -101418.346 1247.6201  281882.055 272619.900
#> 152  -65242.960  935.8904  211718.575 263563.062
#> 153   23783.236  917.5440   81913.187  39732.241
#> 154   38912.204  917.1887  -22495.545  25687.728
#> 155   69882.546  924.8565 -186561.929 -16241.233
#> 156   69882.546  924.8565 -186561.929 -16241.233
#> 157 -220114.101 2250.7113 1615287.068 302591.113
#> 158   75680.532  922.7330 -237153.620 -16595.354
#> 159   44065.949  922.1580  -57014.463  20137.213
#> 160   24849.866  921.0858   61272.655  42016.637
#> 161   44226.644  925.5689  -57629.253  19454.057
#> 162   -2678.568  908.2490  195129.322  86609.356
#> 163 -218354.071 2203.3357 1586624.357 308106.132
#> 164   66702.201  927.2640 -182038.638  -9238.404
#> 165  -24796.663  911.6317  263383.579 131323.332
#> 166 -225630.587 2452.7718 1723723.295 279479.326
#> 167  -39282.423  923.0486  298060.889 161755.717
#> 168  -84730.694 1167.1956  259336.935 244247.937
#> 169  -81907.907 1171.5208  241881.914 237374.318
#> 170  -94606.134 1238.2614  243879.824 259861.513
#> 171 -226743.760 2482.3762 1725632.703 276027.308
#> 172  -83365.769 1166.4158  248518.543 241734.199
#> 173 -226340.398 2317.8543 1638659.114 305914.122
#> 174  -84759.759 1160.6337  257348.335 245823.797
#> 175 -221668.705 2329.8940 1548044.956 299929.659
#> 176 -194759.918 1752.7725  929105.573 381505.707
#> 177 -195129.656 1768.9584  981662.174 375850.711
#> 178 -194052.703 1759.3443  927403.697 379638.693
#> 179 -190654.570 1707.9721  772953.463 394178.986
#> 180 -191406.417 1695.9069  716261.396 402051.169
#> 181 -203763.265 2017.7502 1177656.835 338238.264
#> 182 -201277.267 2001.1566 1128376.805 339155.284
#> 183 -198474.694 1972.8412 1059310.587 343715.421
#> 184 -197355.796 1958.8821 1027800.199 345957.172
#> 185 -202800.333 2008.4550 1144348.189 341545.231
#> 186 -195930.789 1939.1237 1014551.587 349062.843
#> 187 -207768.636 2021.9519 1197288.304 346653.332
#> 188 -207768.636 2021.9519 1197288.304 346653.332
#> 189 -197802.413 1530.0578  609933.161 450072.555
#> 190 -207169.882 2028.6115 1178984.359 346520.414
#> 191 -206509.952 2026.5245 1172478.286 346034.942
#> 192 -206715.400 2027.6282 1167953.120 347149.886
#> 193 -199057.268 1966.2572 1063461.707 347107.596
#> 194 -137105.753 1166.7426  439383.656 374397.109
#> 195 -186608.841 1702.2111  660546.619 409356.648
#> 196 -210597.354 1612.6948  678233.643 457423.506
#> 197 -179454.934 1810.6647 1012255.350 333165.630
#> 198 -180583.931 1810.2878 1025736.258 335130.899
#> 199 -180763.373 1809.4881 1028900.351 335532.599
#> 200 -181077.182 1811.0613 1029524.475 335929.559
#> 201 -179160.823 1812.5585  997629.218 333135.218
#> 202 -179757.639 1813.6065 1002948.396 334034.891
#> 203  -35983.237 1050.9548 -113582.373 182970.385
#> 204 -189019.300 1421.9912  602838.237 445342.324
#> 205  -97599.864 1085.9401  275072.660 310360.048
#> 206  -97599.864 1085.9401  275072.660 310360.048
#> 207  -81675.314 1065.7517  188765.366 279896.365
#> 208 -216979.592 1852.1494  963569.328 409713.895
#> 209 -213844.462 1864.4895  986102.144 399738.351
#> 210 -215403.146 1863.6802  976209.171 403501.341
#> 211  -31362.918 1040.5642 -144789.201 176802.658
#> 212 -187188.101 1705.5391  932200.737 383427.364
#> 213 -217765.714 1868.9346 1003802.364 404267.257
#> 214  -69403.675 1058.7749  102299.099 259040.239
#> 215 -220352.915 1871.1802 1022873.382 406704.731
#> 216 -217480.886 1876.0205 1011974.207 401622.418
#> 217 -220302.356 1874.8819 1032789.661 404909.517
#> 218 -232148.420 1681.0334  819255.932 480122.068
#> 219  -35639.926 1048.8612 -139004.580 190818.451
#> 220  -34927.508 1047.3951 -142988.884 189338.564
#> 221 -219310.812 1878.9996 1024412.293 403118.191
#> 222  -28792.693 1032.5003 -167373.719 175356.373
#> 223 -197143.739 1863.8215  830769.405 385106.338
#> 224 -222930.980 1881.9983 1058135.931 405661.593
#> 225 -223762.909 1882.2014 1063980.614 406556.337
#> 226 -214215.939 1582.0998  719084.024 465381.389
#> 227 -197105.159 1869.0983  817972.033 385155.706
#> 228 -183318.261 1665.6276  900696.888 385187.193
#> 229 -261068.589 1858.6649 1125415.789 476082.591
#> 230 -260606.969 1846.7319 1110739.467 478518.264
#> 231 -183259.555 1672.2453  894299.371 384170.578
#> 232 -259683.437 1834.0735 1094408.425 480351.828
#> 233 -214961.134 1584.4408  728919.631 465726.368
#> 234 -179031.339 1639.6687  896171.238 380794.541
#> 235 -231327.932 1664.8498  829707.490 478625.995
#> 236 -178427.128 1634.7771  892493.508 380680.128
#> 237 -270840.653 1894.2030 1222331.222 476733.970
#> 238 -268653.461 1879.6219 1194730.439 478190.768
#> 239 -201339.902 1917.6566  790984.172 385170.956
#> 240   -5446.985  957.6556 -295179.152 143081.881
#> 241   -5561.775  958.6462 -290121.835 142075.296
#> 242   -5561.775  958.6462 -290121.835 142075.296
#> 243   -7071.014  966.4910 -272207.741 141290.505
#> 244   -7184.705  965.4910 -302102.017 149148.883
#> 245   -9970.831  977.8190 -297961.533 155349.564
#> 246   -8414.991  972.3714 -296203.396 150675.239
#> 247 -179877.745 1682.9628  854011.738 376944.324
#> 248   -9480.627  981.9215 -255100.428 142425.559
#> 249 -182318.374 1702.2505  831173.282 380777.741
#> 250 -201977.508 1939.8453  753373.831 385070.046
#> 251  -15317.128 1000.3804 -280517.834 165480.605
#> 252  -11759.616  988.2017 -285874.615 156691.195
#> 253  -11759.616  988.2017 -285874.615 156691.195
#> 254 -182472.544 1709.1154  833648.576 379487.366
#> 255  -19526.312 1016.5120 -263485.794 173308.195
#> 256  -14713.160 1000.0623 -278727.278 162985.122
#> 257  -13155.596  997.1770 -270715.811 156059.324
#> 258 -180571.694 1705.9064  853153.275 373788.166
#> 259  -25680.657 1054.0299  -99288.854 142302.914
#> 260 -205513.210 1965.4399  758691.628 385355.120
#> 261  -15848.140 1012.0292 -250764.029 157492.917
#> 262  -26351.489 1056.1317  -96430.753 143581.961
#> 263  -28583.728 1061.0439  -85538.406 147793.302
#> 264 -202101.022 1941.5929  763743.561 383015.182
#> 265  -73808.560 1079.9328  138050.080 269583.248
#> 266  -17572.732 1019.2257 -249939.278 162049.727
#> 267 -181868.033 1730.2769  854140.191 371618.790
#> 268 -183290.591 1741.4968  836831.704 374254.228
#> 269  -63506.859 1078.5385   71984.022 248822.673
#> 270  -17789.174 1024.6133 -224816.708 155019.202
#> 271  -55335.689 1077.7769   16587.753 232435.701
#> 272  -19483.285 1033.1694 -223354.243 159090.889
#> 273  -26510.244 1059.3551  -97114.373 144078.606
#> 274  -14369.313 1014.3687 -319467.143 169451.681
#> 275  -28185.003 1063.5982  -89241.103 147349.031
#> 276  -87681.452 1100.4286  232686.961 293368.822
#> 277  -39965.296 1080.8956  -90548.886 201044.788
#> 278 -275800.381 2045.3834 1308612.532 441037.442
#> 279 -283403.492 2002.1007 1390993.773 454040.616
#> 280 -179587.437 1805.0297  648027.534 370759.072
#> 281 -261940.811 2005.8321 1237007.218 429356.415
#> 282 -179608.874 1787.1464  676652.178 371229.855
#> 283 -179608.874 1787.1464  676652.178 371229.855
#> 284 -179075.247 1815.4151  635910.576 368599.877
#> 285 -178835.912 1848.1077  595288.781 365933.284
#> 286 -178835.912 1848.1077  595288.781 365933.284
#> 287 -180713.578 1803.7210  675375.160 370697.690
#> 288 -180359.295 1858.7331  605414.898 366348.047
#> 289 -257315.936 2014.6814 1196296.513 422838.600
#> 290 -257315.936 2014.6814 1196296.513 422838.600
#> 291 -271949.791 1961.9545 1335905.853 444561.271
#> 292 -164178.612 1300.9616  603010.389 411755.380
#> 293 -164178.612 1300.9616  603010.389 411755.380
#> 294 -203905.629 1946.0869  803361.083 376399.740
#> 295 -162543.882 1299.1293  596652.152 408245.055
#> 296 -159553.339 1286.8513  590452.314 403798.940
#> 297 -200857.248 1922.7553  803543.763 374637.196
#> 298 -242352.959 1724.8751 1180500.148 442819.355
#> 299 -172513.554 1332.4961  689527.592 416352.409
#> 300 -203628.168 1932.7010  818126.619 375991.424
#> 301 -163085.568 1303.7578  601060.564 407992.721
#> 302 -170817.621 1327.4445  678172.767 414333.092
#> 303 -237430.009 1712.1826 1129331.641 441340.212
#> 304 -146289.758 1244.6034  532502.169 383851.304
#> 305 -231497.044 1713.4655 1061125.192 437716.510
#> 306 -231497.044 1713.4655 1061125.192 437716.510
#> 307 -167186.917 1318.7074  645874.061 410358.176
#> 308 -159834.006 1292.9478  596615.062 402152.013
#> 309 -164364.712 1315.3763  612881.176 407084.355
#> 310 -217285.056 1640.7157  935289.417 434958.416
#> 311 -216815.581 1633.8806  932161.097 435410.293
#> 312 -213511.226 1604.3888  915380.591 434951.474
#> 313 -210782.000 1537.2801 1011121.106 427192.580
#> 314 -208633.633 1520.0156 1020292.826 424077.075
#> 315 -209256.550 1529.6582 1005234.147 425801.420

fitted(m)
#>   [1] 127499.16 125164.02 112173.27 145740.98 158572.52 158491.40 139519.98
#>   [8] 206972.84 158200.85 310010.65 227351.49 218960.30 143220.87 129807.56
#>  [15]  89995.81 130354.15  90211.23 112505.24 100529.15 135172.39 222632.44
#>  [22] 144012.54 109387.37 181885.59 137308.40  74666.91  82799.36  69315.74
#>  [29] 210992.36 129999.13  84123.75 138678.51 111355.96  91975.56  69502.30
#>  [36] 194693.87 210217.83 134452.03 178036.27 224789.37 245500.73  95455.14
#>  [43]  88273.16 133334.56 124413.89 241427.40  74161.21  78136.69 218928.78
#>  [50] 106340.82 169987.75  95608.69  58249.97  77885.82 184405.09 214704.59
#>  [57]  88850.94 110309.07 126240.73 125366.84 200586.18 139873.13  95789.07
#>  [64]  92625.71 150260.92 126808.83 127488.29 137083.02 198577.49  76197.29
#>  [71] 271355.74 225056.12 186411.25 133664.75  85402.28 104651.96 117459.04
#>  [78] 128036.70 121716.49 152546.57 158933.80  82575.00 238878.12 100010.44
#>  [85]  85791.93 182472.53 120449.76 118575.72  92099.87 113849.31 110690.83
#>  [92] 174556.92  80145.58 136588.43 169086.76 150140.16 115737.39 101469.37
#>  [99] 145227.66 118511.82 167107.16 109243.29  88585.50 242955.79  79378.95
#> [106] 127614.29 121545.07 221263.43  80682.45 113378.86 145492.05 119319.93
#> [113] 116681.58  82661.75 172999.72 138764.74 190757.99 222518.95  85506.44
#> [120]  64904.09 178798.15 190168.79 110892.50 143761.39 154277.19  97604.29
#> [127] 291461.55 257877.64  94640.19 208159.72 165224.00 165224.00 151290.31
#> [134] 167588.66 217979.40 226493.64 171776.77 155648.95 364497.82 167899.98
#> [141] 266448.48 223277.77  96409.28 136769.53 133117.59 146731.33 124868.29
#> [148] 112214.28  89341.76  92785.94 195532.44 159246.64  98452.35 133977.09
#> [155]  92730.06 101848.38 122195.22  99402.13  85875.64 139685.29 151761.46
#> [162] 122298.83  91801.67  71759.19 103465.56 162734.57 191940.83 109429.59
#> [169] 142043.58 105635.98 115799.61 190189.77 153476.63  96799.46  69744.52
#> [176]  59887.01 236669.12 123338.65 258327.69 154163.26 128833.96 266028.69
#> [183] 172463.07 101087.43 168896.74 211663.47 267993.41 157508.20 189859.43
#> [190]  98483.36 182981.98 324772.61 284562.80 111690.74 190104.97 229384.54
#> [197] 102329.40 203315.69  98257.16 199011.39 189526.16  29301.32  85444.79
#> [204] 102182.68 101199.14 126970.15 157376.48 116600.51 201941.58 473638.83
#> [211] 238476.13  69947.46  98368.29 249977.84  94705.44 298782.50 163373.63
#> [218] 259588.75 170418.05 203631.46 128055.58 187735.57  54584.57 116050.19
#> [225] 150223.92 251893.98 151317.37 139859.38  92479.20 184030.61 223807.81
#> [232] 249585.05 136484.75 167951.05 101563.89 243140.99 124537.19 195726.52
#> [239] 392094.05 252110.12  66016.73  59265.33  60223.98  49354.09  83946.82
#> [246]  82585.35 139290.60 145358.97 101306.71 233300.88 105597.50 108233.26
#> [253]  64887.09 120226.38 202500.01 151900.23 123070.09  81415.24 148013.39
#> [260] 108686.92 107389.62 106171.85  97151.90 102545.61 212435.41 156584.38
#> [267] 118789.70 292908.48 234944.84 237834.63 126033.01 134768.95 116266.56
#> [274] 113266.15 117398.56 123036.64 189083.55 177843.09 177311.27 153847.32
#> [281]  95360.61 480631.66 124282.88 106411.42 148410.65  74269.14  76117.24
#> [288]  53838.43 168657.63 186187.34 190216.70 111677.61 129698.53 111485.06
#> [295] 139138.38 119943.11  93029.78 183253.13 165111.37  98423.79 334041.46
#> [302] 157366.98  94506.98 182319.80 132068.58 184899.80 184899.80 100360.59
#> [309]  55561.10  93337.84 148125.06 116780.66 218463.36 237880.69 109360.91
#> [316] 395050.44

residuals(m)
#>   [1]   29500.83727  -11664.02426  -30423.26922    4259.02140   31427.47974
#>   [6]    1458.60153   10475.01914   32977.16014   -5200.85365  -60060.65054
#>  [11]   19648.50946   42039.70312  -40220.86616   -6307.56374   13004.18953
#>  [16]  -30354.14691    -261.23411  -17505.24130  -11029.14767     827.61462
#>  [21]   47367.56215   -9012.53917    5612.62733   13114.41458  -13308.40429
#>  [26]    9333.08684    4200.64287   -5365.73785   19007.64109   12000.86749
#>  [31]   11876.25385  -11678.51497     644.03992    3024.44188     497.70342
#>  [36]  -34693.86840  -23717.82544  -14452.02807   41963.72638   12710.63149
#>  [41]  -15500.72828  -18455.14279  -43273.15800   -8334.55778   50586.11427
#>  [46]  118572.59862  -18661.21422    6863.31313   30071.22026  -36390.82376
#>  [51]  -20037.74660   11391.31341    8250.03190   -8385.82244   10594.91023
#>  [56]   30295.41072   16149.05531   14690.92630   53709.27003   -2366.84458
#>  [61]   24413.81773    7126.86790   13210.92960   -2675.71484  -15260.91514
#>  [66]    2191.17388    7511.71464     -83.02417  -83577.48930    3752.71245
#>  [71]   77644.26079  -45056.12000   19588.74655   -3665.74732    3597.72233
#>  [76]   28348.03682    6040.96237  -46036.70433  -21716.49448  -58046.57171
#>  [81]   42066.20239  -11575.00237    6121.87664    8489.56446    2158.06727
#>  [86]  -60972.52874  -11449.76430  -13580.71536    7850.13103  -15849.30625
#>  [91]  -20690.82730   -5556.92344   49849.42386   -6588.42967  -42086.76106
#>  [96]  -25140.15628   18262.61008  -11469.36813  -10727.66002  -21011.82295
#> [101]    -607.15697   13756.71300    8914.49642   30044.20529    4621.05071
#> [106]   24385.70853  -41545.07111   13736.57301   33817.54901  -14428.85818
#> [111]   12507.95395  -31319.92980    3318.41500    6838.24848    7000.27804
#> [116]  -23764.73635  -45757.98853   27431.05153   29493.55597   22095.90660
#> [121]  -23798.15003  -13168.79464   52107.50309  -58761.39491     722.80916
#> [126]   43395.70695   46538.45119   12122.35639   13359.81497   58340.28028
#> [131]  -20224.00234  -20224.00234  -41290.30711  -15088.66099  -87979.40051
#> [136]    8506.36157  -15276.76663   22851.05298  155502.18157    4100.01917
#> [141]  -56448.48261  -33277.76779    3590.72106  -22658.52640   38882.40555
#> [146]   23268.66954   15131.71422  -12219.28425   -2341.75756   -9785.93731
#> [151]  -33532.43734  -16246.64019  -10952.34853  -43977.08509   21269.94500
#> [156]    5651.62323  -24195.22027   24597.86640  -13375.63822   -1185.29078
#> [161]   26738.54439    9701.17116  -21801.67345   31240.80745      34.44375
#> [166]   35265.43006  -81940.82576   19570.40738  -12048.57904  -30635.97991
#> [171]  -20804.61369   26810.22622  -24476.62995     200.53866   -4744.51983
#> [176]   50112.99191  -56669.11801   48661.34974   36672.30628  130836.74240
#> [181]   48666.04336    8971.30916  -34963.06768   12912.57329   44353.26324
#> [186]  -36663.47176  -47993.40677    -508.19717  -16859.42707   86516.64054
#> [191]    7018.02355  100227.39363   95437.19629    9309.25936    9895.02655
#> [196]   -9384.54294   62670.59588   42184.31393   16692.84121  -44011.39370
#> [201]  -52526.15594   23698.67980   16555.20583  -10187.68443   47300.86169
#> [206]    4029.84765  -22376.47570  -21600.50987    9058.41689  -83638.83347
#> [211]   -3476.13277    3552.53670    -368.29161   28022.16433   -6705.44183
#> [216]  -28782.50157  -21373.63361    8411.24766   39581.94822    9368.53761
#> [221]   -4055.58195  -14235.56999   -9584.57147  -33050.18664    8776.07788
#> [226]   43106.01529  -24817.37303     140.61709    5020.80237    5919.38837
#> [231]  -33807.81101  -31585.05478  -21484.75357   -2951.04855   32436.10747
#> [236]   37059.00542    7462.81223   -5726.51639  107905.95358  -72110.11678
#> [241]    3978.27173   -1515.33438   -5223.98055   10145.90697  -10446.81953
#> [246]   -6585.35271  -49290.60190  -40358.96573    5193.29488    4699.11568
#> [251]   -1597.50184    1766.73731   -5387.08841   12273.61640  -12500.01008
#> [256]  -26900.22933    4929.91373     584.75547  -16013.38840  -48691.91674
#> [261]   10610.37923   11828.15318   -2651.89966  -23545.61219   10064.59155
#> [266]   28415.61857   14460.30451    -908.48419    8055.15919  -22834.63155
#> [271]     966.99243   13231.04831   19733.44492   21733.84751    7601.43516
#> [276]     963.36391  -19583.55483   32656.90947  -17311.26945    1152.67859
#> [281]  -20360.61001   86868.33594   -4332.88121   12588.58283   -8410.65382
#> [286]   25680.86406   22382.75640   27111.57215   -1657.62824  -24187.33794
#> [291]   -7216.70066    7322.38576   13301.47221  -14535.06494   -4138.38479
#> [296]   37556.88659   14970.22256  -68253.12808  -61611.36563   37076.21451
#> [301]   75958.54098   22633.01610  -17506.98100  -40069.80488  -48068.58408
#> [306]  -24899.80140  -24899.80140   12639.41200   12438.90329   -9337.84319
#> [311]    1874.94495   -6780.65807   19036.63999   17119.30687   20639.08727
#> [316] -115050.44316

predict(m, LondonHP)
#> Simple feature collection with 316 features and 6 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 507400 ymin: 159400 xmax: 552300 ymax: 194900
#> CRS:           NA
#> First 10 features:
#>    Intercept   FLOORSZ   UNEMPLOY      PROF     yhat   residual
#> 0 -23859.461 1107.8783  -68568.68 143091.28 127499.2  29500.837
#> 1 -19273.643 1099.6911 -105774.02 137317.02 125164.0 -11664.024
#> 2 -22341.033 1101.6762  -78733.42 139576.72 112173.3 -30423.269
#> 3 -16587.207 1091.7319 -127715.69 131959.65 145741.0   4259.021
#> 4  -4548.212 1071.6907 -236130.77 118805.43 158572.5  31427.480
#> 5  36721.681 1025.9964 -574801.77  69162.51 158491.4   1458.602
#> 6  41385.027 1015.8069 -621772.02  64587.38 139520.0  10475.019
#> 7  41586.375  980.2804 -702105.05  72971.83 206972.8  32977.160
#> 8  57682.066  985.6583 -778290.44  47493.74 158200.9  -5200.854
#> 9  71221.072  928.7546 -982984.26  43974.22 310010.7 -60060.651
#>                geometry
#> 0 POINT (533200 159400)
#> 1 POINT (533300 159700)
#> 2 POINT (532000 159800)
#> 3 POINT (531900 160100)
#> 4 POINT (532800 160300)
#> 5 POINT (535700 161700)
#> 6 POINT (535600 161800)
#> 7 POINT (533400 161900)
#> 8 POINT (535500 162200)
#> 9 POINT (534200 162500)