*************************************************
* Geographically Weighted Regression *
* Release 3.0.1 *
* Dated: 06-vii-2003 *
* *
* Martin Charlton, Chris Brunsdon *
* Stewart Fotheringham *
* (c) University of Newcastle upon Tyne *
*************************************************
Program starts at: Wed Mar 26 17:40:14 2008
** Program limits:
** Maximum number of variables..... 52
** Maximum number of observations.. 80000
** Maximum number of fit locations. 80000
Untitled
** Observed data file: C:\GWR3\SampleData\fondidatiA.csv
** Prediction location file: Estimation at sample point locations
** Result output file:
** Variables in the data file...
ID LONGIT LATITU TOTCFS TOTPUB TOTPRI INIZRE LOGDIP
** Dependent (y) variable...... LOGDIP
** Easting (x-coord) variable.....LATITU
** Northing (y-coord) variable.....LONGIT
** No weight variable specified
** Independent variables in your model...
TOTPUB TOTPRI INIZRE
** Kernel type: Adaptive
** Kernel shape: Bi-Square
** Bandwidth selection by AICc minimisation
** Use all regression points
** Calibration history requested
** Prediction report requested
** No output estimates to be written to file
** Monte Carlo significance tests for spatial variation
** Casewise diagnostics to be printed
*** Analysis method ***
*** Geographically weighted multiple regression
** Cartesian coordinates: Euclidean Distance
***************************************************************
* *
* GEOGRAPHICALLY WEIGHTED GAUSSIAN REGRESSION *
* *
***************************************************************
Number of data cases read: 64
Observation points read...
Dependent mean= 0.0504999906
Number of observations, nobs= 64
Number of predictors, nvar= 3
Observation Easting extent: 1860669.
Observation Northing extent: 2069320.
*Finding bandwidth...
... using all regression points
This can take some time...
*Calibration will be based on 64 cases
*Adaptive kernel sample size limits: 10 64
*AICc minimisation begins...
Bandwidth AICc
26.686917730000 -321.283734667649
37.000000000000 -325.219991291447
47.313082270000 -330.627388020544
53.686917654526 -332.869108143495
57.626164568828 -333.243525902038
60.060753056870 -333.531446280979
61.565411494142 -333.334344583844
59.130823006101 -333.601278974608
** Convergence after 8 function calls
** Convergence: Local Sample Size= 59
**********************************************************
* GLOBAL REGRESSION PARAMETERS *
**********************************************************
Diagnostic information...
Residual sum of squares...... 0.020586
Effective number of parameters.. 4.000000
Sigma...... 0.018523
Akaike Information Criterion.... -322.031047
Coefficient of Determination.... 0.404340
Adjusted r-square...... 0.363956
Parameter Estimate Std Err T
------
Intercept -0.048564839079 0.017122973870 -2.836238622665
TOTPUB 0.001003830738 0.002625749613 0.382302522659
TOTPRI -0.001777679553 0.001685838700 -1.054477810860
INIZRE -0.022774278048 0.003872312331 -5.881312370300
**********************************************************
* GWR ESTIMATION *
**********************************************************
Fitting Geographically Weighted Regression Model...
Number of observations...... 64
Number of independent variables... 4
(Intercept is variable 1)
Number of nearest neighbours...... 59
Number of locations to fit model.. 64
Diagnostic information...
Residual sum of squares...... 0.013825
Effective number of parameters.. 8.866661
Sigma...... 0.015835
Akaike Information Criterion.... -334.778750
Coefficient of Determination.... 0.599982
Adjusted r-square...... 0.534462
**********************************************************
* CASEWISE DIAGNOSTICS *
**********************************************************
Obs Observed Predicted Residual Std Resid R-Square Influence Cook's D
------
1 0.10200 0.05204 0.04996 1.560477 0.800120 0.155303 0.050493
2 0.01100 0.03418 -0.02318 -0.701806 0.800208 0.101010 0.006241
3 0.03800 0.04079 -0.00279 -0.082299 0.798843 0.052438 0.000042
4 0.05800 0.06075 -0.00275 -0.082831 0.808743 0.088665 0.000075
5 0.06200 0.05887 0.00313 0.112093 0.792426 0.355350 0.000781
6 0.06500 0.06597 -0.00097 -0.030991 0.738955 0.194836 0.000026
7 0.07000 0.05309 0.01691 0.590991 0.739651 0.325160 0.018980
8 0.02400 0.04029 -0.01629 -0.479638 0.743323 0.048998 0.001337
9 0.04300 0.04078 0.00222 0.069509 0.740320 0.157486 0.000102
10 0.04600 0.04543 0.00057 0.016986 0.730793 0.074430 0.000003
11 -0.00200 0.04596 -0.04796 -1.429260 0.722453 0.072086 0.017898
12 0.03100 0.04093 -0.00993 -0.311286 0.766393 0.160450 0.002089
13 0.06000 0.06028 -0.00028 -0.009289 0.770761 0.225257 0.000003
14 -0.00600 0.00053 -0.00653 -0.217566 0.795933 0.257324 0.001850
15 0.02000 0.03290 -0.01290 -0.389103 0.794185 0.094097 0.001774
16 0.02600 0.02516 0.00084 0.025311 0.786081 0.083758 0.000007
17 0.01400 0.02228 -0.00828 -0.252621 0.783708 0.114460 0.000930
18 0.05200 0.05437 -0.00237 -0.069713 0.782914 0.047432 0.000027
19 0.03500 0.02909 0.00591 0.176040 0.796728 0.071746 0.000270
20 0.02300 0.03088 -0.00788 -0.236778 0.798554 0.086122 0.000596
21 0.02000 0.02678 -0.00678 -0.214692 0.800016 0.178517 0.001130
22 0.04300 0.05023 -0.00723 -0.213838 0.800613 0.057666 0.000316
23 0.04000 0.04078 -0.00078 -0.023884 0.766259 0.111088 0.000008
24 0.04700 0.04359 0.00341 0.100009 0.768849 0.039809 0.000047
25 0.03400 0.03595 -0.00195 -0.057224 0.767952 0.044755 0.000017
26 0.03700 0.03160 0.00540 0.161493 0.753249 0.077787 0.000248
27 0.04500 0.03601 0.00899 0.268597 0.758021 0.075942 0.000669
28 0.02800 0.04013 -0.01213 -0.354965 0.767584 0.037103 0.000548
29 0.03000 0.04498 -0.01498 -0.440719 0.797609 0.048069 0.001106
30 0.04100 0.05413 -0.01313 -0.387367 0.781414 0.052807 0.000943
31 0.01600 0.02956 -0.01356 -0.418556 0.783461 0.134334 0.003066
32 0.04500 0.03821 0.00679 0.200108 0.799641 0.050904 0.000242
33 0.05000 0.03358 0.01642 0.505562 0.816732 0.130985 0.004345
34 0.07000 0.05958 0.01042 0.318493 0.816483 0.117693 0.001526
35 0.05800 0.08241 -0.02441 -0.964069 0.814192 0.471459 0.093502
36 0.06000 0.05763 0.00237 0.070693 0.820755 0.074807 0.000046
37 0.05300 0.04084 0.01216 0.382641 0.818490 0.168169 0.003338
38 0.06300 0.05620 0.00680 0.203088 0.818940 0.075487 0.000380
39 0.05000 0.05059 -0.00059 -0.017489 0.820551 0.051445 0.000002
40 0.04400 0.05495 -0.01095 -0.331293 0.821350 0.100095 0.001377
41 0.06600 0.05663 0.00937 0.276746 0.818809 0.054542 0.000498
42 0.09800 0.06951 0.02849 0.866635 0.816244 0.108952 0.010357
43 0.04300 0.05098 -0.00798 -0.235731 0.815065 0.054925 0.000364
44 0.08300 0.07048 0.01252 0.373885 0.813861 0.076189 0.001300
45 0.09500 0.08965 0.00535 0.215590 0.812758 0.492217 0.005081
46 0.07200 0.07150 0.00050 0.015766 0.810473 0.165903 0.000006
47 0.05200 0.06338 -0.01138 -0.343952 0.810589 0.097236 0.001437
48 0.07200 0.07382 -0.00182 -0.055641 0.809960 0.118115 0.000047
49 0.02300 0.04334 -0.02034 -0.626509 0.812408 0.131112 0.006680
50 0.05300 0.06124 -0.00824 -0.256774 0.814528 0.151325 0.001326
51 0.06000 0.06059 -0.00059 -0.018165 0.807992 0.134066 0.000006
52 0.07200 0.06104 0.01096 0.328587 0.798775 0.082612 0.001097
53 0.03100 0.03697 -0.00597 -0.176938 0.802587 0.063194 0.000238
54 0.04100 0.04436 -0.00336 -0.098563 0.800026 0.043633 0.000050
55 0.06200 0.07320 -0.01120 -0.484459 0.728848 0.559243 0.033586
56 0.06200 0.05327 0.00873 0.265112 0.716979 0.106482 0.000945
57 0.09000 0.09631 -0.00631 -0.213394 0.806290 0.279854 0.001996
58 0.07600 0.05095 0.02505 0.771976 0.805879 0.132081 0.010228
59 0.06800 0.04715 0.02085 0.640407 0.806543 0.126576 0.006703
60 0.07900 0.03925 0.03975 1.193883 0.799649 0.086417 0.015206
61 0.07700 0.07483 0.00217 0.075246 0.798394 0.315038 0.000294
62 0.06800 0.06726 0.00074 0.024141 0.805638 0.215638 0.000018
63 0.07300 0.06173 0.01127 0.385840 0.805307 0.297422 0.007108
64 0.07000 0.05620 0.01380 0.419513 0.804137 0.108563 0.002417
Predictions from this model...
Obs Y(i) Yhat(i) Res(i) X(i) Y(i)
1 0.102 0.052 0.050 -70876.000 -372611.000 F
2 0.011 0.034 -0.023 -104129.000 -312755.000 F
3 0.038 0.041 -0.003 -157107.000 -376868.000 F
4 0.058 0.061 -0.003 395392.000 155516.000 F
5 0.062 0.059 0.003 252414.000-1029690.000 F
6 0.065 0.066 -0.001 -812502.000-1059538.000 F
7 0.070 0.053 0.017 -844388.000 -993796.000 F
8 0.024 0.040 -0.016 -903105.000 -904672.000 F
9 0.043 0.041 0.002 -931351.000 -971376.000 F
10 0.046 0.045 0.001-1037129.000 -858187.000 F
11 -0.002 0.046 -0.048-1130990.000-1101937.000 F
12 0.031 0.041 -0.010-1094418.000 -625432.000 F
13 0.060 0.060 0.000-1286298.000 -604193.000 F
14 -0.006 0.001 -0.007 -275560.000 -413878.000 F
15 0.020 0.033 -0.013 -198257.000 -525670.000 F
16 0.026 0.025 0.001 -224021.000 -678333.000 F
17 0.014 0.022 -0.008 -404630.000 -574113.000 F
18 0.052 0.054 -0.002 -252332.000 -715538.000 F
19 0.035 0.029 0.006 -485144.000 -356835.000 F
20 0.023 0.031 -0.008 -300064.000 -264330.000 F
21 0.020 0.027 -0.007 -360277.000 -158983.000 F
22 0.043 0.050 -0.007 -497685.000 -287475.000 F
23 0.040 0.041 -0.001 -446400.000 -829463.000 F
24 0.047 0.044 0.003 -290971.000-1015165.000 F
25 0.034 0.036 -0.002 -530591.000 -701870.000 F
26 0.037 0.032 0.005 -701481.000 -794121.000 F
27 0.045 0.036 0.009 -853950.000 -657072.000 F
28 0.028 0.040 -0.012 -617673.000 -644009.000 F
29 0.030 0.045 -0.015 -648000.000 -377986.000 F
30 0.041 0.054 -0.013 -637331.000 -509860.000 F
31 0.016 0.030 -0.014 -867220.000 -473202.000 F
32 0.045 0.038 0.007 -909669.000 -355764.000 F
33 0.050 0.034 0.016-1066770.000 -101731.000 F
34 0.070 0.060 0.010 -732322.000 -174918.000 F
35 0.058 0.082 -0.024 -661481.000 -194754.000 F
36 0.060 0.058 0.002 -802082.000 -84154.000 F
37 0.053 0.041 0.012 -689505.000 -63135.000 F
38 0.063 0.056 0.007 -691950.000 175802.000 F
39 0.050 0.051 -0.001 -792177.000 97647.000 F
40 0.044 0.055 -0.011 -869671.000 93446.000 F
41 0.066 0.057 0.009 -937987.000 185304.000 F
42 0.098 0.070 0.028 -880844.000 269037.000 F
43 0.043 0.051 -0.008-1064705.000 198476.000 F
44 0.083 0.070 0.013-1000109.000 328593.000 F
45 0.095 0.090 0.005-1092585.000 371088.000 F
46 0.072 0.071 0.001-1168323.000 345525.000 F
47 0.052 0.063 -0.011-1129224.000 548386.000 F
48 0.072 0.074 -0.002-1184675.000 470092.000 F
49 0.023 0.043 -0.020-1460838.000 478870.000 F
50 0.053 0.061 -0.008-1465277.000 281848.000 F
51 0.060 0.061 -0.001-1350538.000 -73165.000 F
52 0.072 0.061 0.011 -245942.000 -267226.000 F
53 0.031 0.037 -0.006 134349.000 -219384.000 F
54 0.041 0.044 -0.003 -113920.000 -288060.000 F
55 0.062 0.073 -0.011 -972937.000-1476560.000 F
56 0.062 0.053 0.009-1413245.000-1520934.000 F
57 0.090 0.096 -0.006 60108.000 219514.000 F
58 0.076 0.051 0.025 46372.000 198567.000 F
59 0.068 0.047 0.021 223848.000 134092.000 F
60 0.079 0.039 0.040 -211058.000 -118426.000 F
61 0.077 0.075 0.002 -288909.000 -208522.000 F
62 0.068 0.067 0.001 -67854.000 158133.000 F
63 0.073 0.062 0.011 246909.000 8019.000 F
64 0.070 0.056 0.014 -108190.000 69157.000 F
**********************************************************
* ANOVA *
**********************************************************
Source SS DF MS F
OLS Residuals 0.0 4.00
GWR Improvement 0.0 4.87 0.0014
GWR Residuals 0.0 55.13 0.0003 5.5407
**********************************************************
* PARAMETER 5-NUMBER SUMMARIES *
**********************************************************
Label Minimum Lwr Quartile Median Upr Quartile Maximum
------
Intrcept -0.099652 -0.087911 -0.064856 -0.058012 -0.030515
TOTPUB -0.002558 -0.000607 0.001687 0.006186 0.009907
TOTPRI -0.006045 -0.005039 -0.003615 -0.002318 -0.000321
INIZRE -0.029355 -0.028211 -0.026838 -0.024508 -0.020390
<------LOWER ------<------UPPER ------>
Label Far Out Outer Fence Outside Inner Fence Inner Fence Outside Outer Fence Far Out
------
Intrcept 0 -0.177606 0 -0.132758 -0.013164 0 0.031683 0
TOTPUB 0 -0.020985 0 -0.010796 0.016375 0 0.026564 0
TOTPRI 0 -0.013201 0 -0.009120 0.001763 0 0.005844 0
INIZRE 0 -0.039319 0 -0.033765 -0.018954 0 -0.013400 0
*************************************************
* *
* Test for spatial variability of parameters *
* *
*************************************************
Tests based on the Monte Carlo significance test
procedure due to Hope [1968,JRSB,30(3),582-598]
Parameter P-value
------
Intercept 0.06000 n/s
TOTPUB 0.00000 ***
TOTPRI 0.17000 n/s
INIZRE 0.53000 n/s
*** = significant at .1% level
** = significant at 1% level
* = significant at 5% level
Program terminates normally at: Wed Mar 26 17:40:14 2008