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*             Semiparametric Geographically Weighted Regression             *
*                         Release 1.0.90 (GWR 4.0.90)                       *
*                               12 May 2015                                 *
*                 (Originally coded by T. Nakaya: 1 Nov 2009)               *
*                                                                           *
*              Tomoki Nakaya(1), Martin Charlton(2), Chris Brunsdon (2)     *
*              Paul Lewis (2), Jing Yao (3), A Stewart Fotheringham (4)     *
*                       (c) GWR4 development team                           *
* (1) Ritsumeikan University, (2) National University of Ireland, Maynooth, *
*         (3) University of Glasgow, (4) Arizona State University           *
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Program began at 7/25/2016 2:04:40 AM

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Session: 
Session control file: C:\Users\IEUser\Desktop\georgia_BS_F.ctl
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Data filename: C:\Users\IEUser\Desktop\georgia\georgia\GData_utm.csv
Number of areas/points: 159

Model settings---------------------------------
Model type: Gaussian
Geographic kernel: fixed bi-square
Method for optimal bandwidth search: Golden section search
Criterion for optimal bandwidth: AICc
Number of varying coefficients: 4
Number of fixed coefficients:   0

Modelling options---------------------------------
Standardisation of independent variables: OFF
Testing geographical variability of local coefficients: OFF
Local to Global Variable selection: OFF
Global to Local Variable selection: OFF
Prediction at non-regression points: OFF

Variable settings---------------------------------
Area key: field1: AreaKey
Easting (x-coord): field12 : X
Northing (y-coord): field13: Y
Cartesian coordinates: Euclidean distance
Dependent variable: field6: PctBach
Offset variable is not specified
Intercept: varying (Local) intercept
Independent variable with varying (Local) coefficient: field5: PctRural
Independent variable with varying (Local) coefficient: field9: PctPov
Independent variable with varying (Local) coefficient: field10: PctBlack
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  Global regression result
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  < Diagnostic information >
Residual sum of squares:                 2639.559476
Number of parameters:                        4
 (Note: this num does not include an error variance term for a Gaussian model)
ML based global sigma estimate:             4.074433
Unbiased global sigma estimate:             4.126671
-2 log-likelihood:                        897.927089
Classic AIC:                              907.927089
AICc:                                     908.319245
BIC/MDL:                                  923.271610
CV:                                        18.100197
R square:                                   0.485273
Adjusted R square:                          0.471903

Variable                  Estimate    Standard Error      t(Est/SE) 
-------------------- --------------- --------------- ---------------
Intercept                  23.854615        1.173043       20.335661
PctRural                   -0.111395        0.012878       -8.649661
PctPov                     -0.345778        0.070863       -4.879540
PctBlack                    0.058331        0.029187        1.998499

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  GWR (Geographically weighted regression) bandwidth selection
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Bandwidth search <golden section search>
  Limits: 108972.626308445,  558903.094487309
 Golden section search begins...
 Initial values
  pL            Bandwidth: 108972.626 Criterion:    948.618
  p1            Bandwidth: 280830.773 Criterion:    898.912
  p2            Bandwidth: 387044.948 Criterion:    903.831
  pU            Bandwidth: 558903.094 Criterion:    906.526
 iter    1 (p1) Bandwidth: 280830.773 Criterion:    898.912 Diff: 106214.176
 iter    2 (p1) Bandwidth: 215186.802 Criterion:    895.030 Diff:  65643.971
 iter    3 (p2) Bandwidth: 215186.802 Criterion:    895.030 Diff:  40570.205
 iter    4 (p1) Bandwidth: 215186.802 Criterion:    895.030 Diff:  25073.766
 iter    5 (p2) Bandwidth: 215186.802 Criterion:    895.030 Diff:  15496.439
 iter    6 (p1) Bandwidth: 215186.802 Criterion:    895.030 Diff:   9577.326
 iter    7 (p1) Bandwidth: 209267.689 Criterion:    894.983 Diff:   5919.113
 iter    8 (p2) Bandwidth: 209267.689 Criterion:    894.983 Diff:   3658.213
Best bandwidth size 209267.689
Minimum AICc      894.983

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  GWR (Geographically weighted regression) result
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  Bandwidth and geographic ranges
Bandwidth size:               209267.688808
Coordinate                Min              Max           Range
--------------- --------------- --------------- ---------------
X-coord           635964.300000  1059706.000000   423741.700000
Y-coord          3401148.000000  3872640.000000   471492.000000

  Diagnostic information
Residual sum of squares:          2012.563924
Effective number of parameters (model: trace(S)):                    16.722876
Effective number of parameters (variance: trace(S'S)):               11.612295
Degree of freedom (model: n - trace(S)):                            142.277124
Degree of freedom (residual: n - 2trace(S) + trace(S'S)):           137.166544
ML based sigma estimate:             3.557757
Unbiased sigma estimate:             3.830458
-2 log-likelihood:                 854.805884
Classic AIC:                       890.251635
AICc:                              894.982602
BIC/MDL:                           944.641443
CV:                                 18.254062
R square:                            0.607540
Adjusted R square:                   0.544612

***********************************************************
 << Geographically varying (Local) coefficients >>
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Estimates of varying coefficients have been saved in the following file.
    Listwise output file: C:\Users\IEUser\Desktop\georgia_BS_F_listwise.csv

Summary statistics for varying (Local) coefficients 
Variable                      Mean             STD 
-------------------- --------------- ---------------
Intercept                  23.100425        4.102437
PctRural                   -0.115556        0.038728
PctPov                     -0.284599        0.131956
PctBlack                    0.058275        0.075808

Variable                       Min              Max           Range
-------------------- --------------- --------------- ---------------
Intercept                  17.723650       30.349333       12.625683
PctRural                   -0.197305       -0.054520        0.142786
PctPov                     -0.772356       -0.072209        0.700147
PctBlack                   -0.075941        0.308952        0.384893

Variable               Lwr Quartile          Median    Upr Quartile
-------------------- --------------- --------------- ---------------
Intercept                  18.856279       23.103493       27.099926
PctRural                   -0.150482       -0.106458       -0.082746
PctPov                     -0.339158       -0.271117       -0.198485
PctBlack                    0.000226        0.057840        0.110329

Variable             Interquartile R     Robust STD
-------------------- --------------- ---------------
Intercept                   8.243647        6.110932
PctRural                    0.067736        0.050212
PctPov                      0.140673        0.104280
PctBlack                    0.110103        0.081618
 (Note: Robust STD is given by (interquartile range / 1.349) )

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 GWR ANOVA Table
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Source                           SS          DF             MS           F
----------------- ------------------- ---------- --------------- ----------
Global Residuals              2639.559    155.000
GWR Improvement                626.996     17.833          35.158
GWR Residuals                 2012.564    137.167          14.672   2.396224

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Program terminated at 7/25/2016 2:04:40 AM
