francia22<-francia
#We order all the data with respect to the Longitude X1
francia23<-francia22[order(francia22$X1),]
#We order all the data with respect to the Latitude X2
francia25<-francia22[order(francia22$X2),]
library(mgcv)
# Variable PER fit as a function of Longitude X1
v23<gam(round(francia23[,6]/1000,0)~s(francia23[,1],bs="cr",k=84),data=francia23,knots=list(franc
ia23[,1]),family=poisson,scale=-1,gamma=1.4)
# Variable PER fit as a function of Latitude X2
v25<gam(round(francia25[,6]/1000,0)~s(francia25[,2],bs="cr",k=84),data=francia25,knots=list(franc
ia25[,2]),family=poisson,scale=-1,gamma=1.4)
-------------------------------------------HAUTES-ALPES
2*(1-pnorm(abs(v23$coefficients[81]-v23$coefficients[80])/(0.001*abs(francia23[81,1]francia23[80,1])*sqrt(v23$Ve[81,81]+v23$Ve[80,80]-2*v23$Ve[81,80]))))
0.4100886
2*(1-pnorm(abs(v25$coefficients[23]-v25$coefficients[22])/(0.001*abs(francia25[23,2]francia25[22,2])*sqrt(v25$Ve[23,23]+v25$Ve[22,22]-2*v25$Ve[23,22]))))
0.2116123
PROBABILITY OF THE SLOPE AT HAUTES-ALPES
0.4100886*0.2116123
[1] 0.08677979
--------------------AIN
2*(1-pnorm(abs(v23$coefficients[74]-v23$coefficients[73])/(0.001*abs(francia23[74,1]francia23[73,1])*sqrt(v23$Ve[74,74]+v23$Ve[73,73]-2*v23$Ve[74,73]))))
0.9097573
2*(1-pnorm(abs(v25$coefficients[38]-v25$coefficients[37])/(0.001*abs(francia25[38,2]francia25[37,2])*sqrt(v25$Ve[38,38]+v25$Ve[37,37]-2*v25$Ve[38,37]))))
0.8569917
PROBABILITY OF THE SLOPE AT AIN
0.9097573* 0.8569917
[1] 0.7796545
--------------------ARDECHE
2*(1-pnorm(abs(v23$coefficients[64]-v23$coefficients[63])/(0.001*abs(francia23[64,1]francia23[63,1])*sqrt(v23$Ve[64,64]+v23$Ve[63,63]-2*v23$Ve[64,63]))))
0.1039388
2*(1-pnorm(abs(v25$coefficients[24]-v25$coefficients[23])/(0.001*abs(francia25[24,2]francia25[23,2])*sqrt(v25$Ve[24,24]+v25$Ve[23,23]-2*v25$Ve[24,23]))))
0.826492
PROBABILITY OF THE SLOPE AT ARDECHE
0.1039388 *0.826492
[1] 0.08590459
--------------------CORRECE
2*(1-pnorm(abs(v23$coefficients[36]-v23$coefficients[35])/(0.001*abs(francia23[36,1]francia23[35,1])*sqrt(v23$Ve[36,36]+v23$Ve[35,35]-2*v23$Ve[36,35]))))
0.9599223
2*(1-pnorm(abs(v25$coefficients[30]-v25$coefficients[29])/(0.001*abs(francia25[30,2]francia25[29,2])*sqrt(v25$Ve[30,30]+v25$Ve[29,29]-2*v25$Ve[30,29]))))
0.8900466
PROBABILITY OF THE SLOPE AT CORRECE
0.9599223 *0.8900466
[1] 0.8543756
---------------------------------------------------CREUSE
2*(1-pnorm(abs(v23$coefficients[37]-v23$coefficients[36])/(0.001*abs(francia23[37,1]francia23[36,1])*sqrt(v23$Ve[37,37]+v23$Ve[36,36]-2*v23$Ve[37,36]))))
0.7703166
2*(1-pnorm(abs(v25$coefficients[37]-v25$coefficients[36])/(0.001*abs(francia25[37,2]francia25[36,2])*sqrt(v25$Ve[37,37]+v25$Ve[36,36]-2*v25$Ve[37,36]))))
0.4341633
PROBABILITY OF THE SLOPE AT CREUSE
0.7703166 * 0.4341633
[1] 0.3344432
---------------------------------------------------INDRE
2*(1-pnorm(abs(v23$coefficients[35]-v23$coefficients[34])/(0.001*abs(francia23[35,1]francia23[34,1])*sqrt(v23$Ve[35,35]+v23$Ve[34,34]-2*v23$Ve[35,34]))))
0.9294258
2*(1-pnorm(abs(v25$coefficients[45]-v25$coefficients[44])/(0.001*abs(francia25[45,2]francia25[44,2])*sqrt(v25$Ve[45,45]+v25$Ve[44,44]-2*v25$Ve[45,44]))))
0.8653942
PROBABILITY OF THE SLOPE AT INDRE
0.9294258*0.8653942
[1] 0.8043197
---------------------------------------------------ISERE
2*(1-pnorm(abs(v23$coefficients[75]-v23$coefficients[74])/(0.001*abs(francia23[75,1]francia23[74,1])*sqrt(v23$Ve[75,75]+v23$Ve[74,74]-2*v23$Ve[75,74]))))
0.7544629
2*(1-pnorm(abs(v25$coefficients[29]-v25$coefficients[28])/(0.001*abs(francia25[29,2]francia25[28,2])*sqrt(v25$Ve[29,29]+v25$Ve[28,28]-2*v25$Ve[29,28]))))
0.3878305
PROBABILITY OF THE SLOPE AT ISERE
0.7544629* 0.3878305
[1] 0.2926037
---------------------------------------------------JURA
2*(1-pnorm(abs(v23$coefficients[76]-v23$coefficients[75])/(0.001*abs(francia23[76,1]francia23[75,1])*sqrt(v23$Ve[76,76]+v23$Ve[75,75]-2*v23$Ve[76,75]))))
0.926961
2*(1-pnorm(abs(v25$coefficients[44]-v25$coefficients[43])/(0.001*abs(francia25[44,2]francia25[43,2])*sqrt(v25$Ve[44,44]+v25$Ve[43,43]-2*v25$Ve[44,43]))))
2(P{Z> 16'54776}) = 0
PROBABILITY OF THE SLOPE AT JURA
0.926961*2(P{Z> 16'54776}) = 0
[1] 0
---------------------------------------------------LOIRE
2*(1-pnorm(abs(v23$coefficients[62]-v23$coefficients[61])/(0.001*abs(francia23[62,1]francia23[61,1])*sqrt(v23$Ve[62,62]+v23$Ve[61,61]-2*v23$Ve[62,61]))))
0.7613716
2*(1-pnorm(abs(v25$coefficients[33]-v25$coefficients[32])/(0.001*abs(francia25[33,2]francia25[32,2])*sqrt(v25$Ve[33,33]+v25$Ve[32,32]-2*v25$Ve[33,32]))))
0.7220238
PROBABILITY OF THE SLOPE AT LOIRE
0.7613716*0.7220238
[1] 0.5497284
---------------------------------------------------RHONE
2*(1-pnorm( abs(v23$coefficients[67]-v23$coefficients[66])/(0.001*abs(francia23[67,1]francia23[66,1])*sqrt(v23$Ve[67,67]+v23$Ve[66,66]-2*v23$Ve[67,66])) ))
0.8732205
2*(1-pnorm( abs(v25$coefficients[35]-v25$coefficients[34])/(0.001*abs(francia25[35,2]francia25[34,2])*sqrt(v25$Ve[35,35]+v25$Ve[34,34]-2*v25$Ve[35,34])) ))
= 2(P{Z>13'83688}) = 0
PROBABILITY OF THE SLOPE AT RHONE
0.8732205*2(P{Z>13'83688}) = 0
[1] 0
---------------------------------------------------SAONE-ET-LOIRE
2*(1-pnorm(abs(v23$coefficients[66]-v23$coefficients[65])/(0.001*abs(francia23[66,1]francia23[65,1])*sqrt(v23$Ve[66,66]+v23$Ve[65,65]-2*v23$Ve[66,65]))))
0.8155472
2*(1-pnorm(abs(v25$coefficients[42]-v25$coefficients[41])/(0.001*abs(francia25[42,2]francia25[41,2])*sqrt(v25$Ve[42,42]+v25$Ve[41,41]-2*v25$Ve[42,41]))))
0.5629717
PROBABILITY OF THE SLOPE AT SAONE-ET-LOIRE
0.8155472*0.5629717
[1] 0.45913
---------------------------------------------------SEINE
2*(1-pnorm(abs(v23$coefficients[43]-v23$coefficients[42])/(0.001*abs(francia23[43,1]francia23[42,1])*sqrt(v23$Ve[43,43]+v23$Ve[42,42]-2*v23$Ve[43,42]))))
0.1365352
2*(1-pnorm(abs(v25$coefficients[72]-v25$coefficients[71])/(0.001*abs(francia25[72,2]francia25[71,2])*sqrt(v25$Ve[72,72]+v25$Ve[71,71]-2*v25$Ve[72,71]))))
2(P{Z> 131'8917}) = 0
PROBABILITY OF THE SLOPE AT SEINE
0.1365352*2(P{Z> 131'8917}) = 0
[1] 0
---------------------------------------------------HAUTE-VIENNE
2*(1-pnorm(abs(v23$coefficients[29]-v23$coefficients[28])/(0.001*abs(francia23[29,1]francia23[28,1])*sqrt(v23$Ve[29,29]+v23$Ve[28,28]-2*v23$Ve[29,28]))))
0.02489112
2*(1-pnorm(abs(v25$coefficients[36]-v25$coefficients[35])/(0.001*abs(francia25[36,2]francia25[35,2])*sqrt(v25$Ve[36,36]+v25$Ve[35,35]-2*v25$Ve[36,35]))))
0.7964547
PROBABILITY OF THE SLOPE AT HAUTE-VIENNE
0.02489112*0.7964547
[1] 0.01982465
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------library(mgcv)
# Variable PROP fit as a function of the Longitude X1
v33<gam(round(francia23[,7]/1000,0)~s(francia23[,1],bs="cr",k=84),data=francia23,knots=list(franc
ia23[,1]),family=poisson,scale=-1,gamma=1.4)
# Variable PROP fit as a function of the Latitude X2
v35<gam(round(francia25[,7]/1000,0)~s(francia25[,2],bs="cr",k=84),data=francia25,knots=list(franc
ia25[,2]),family=poisson,scale=-1,gamma=1.4)
---------------------------------------------------HAUTES-ALPES
2*(1-pnorm(abs(v33$coefficients[81]-v33$coefficients[80])/(0.001*abs(francia23[81,1]francia23[80,1])*sqrt(v33$Ve[81,81]+v33$Ve[80,80]-2*v33$Ve[81,80]))))
0.8348357
2*(1-pnorm(abs(v35$coefficients[23]-v35$coefficients[22])/(0.001*abs(francia25[23,2]francia25[22,2])*sqrt(v35$Ve[23,23]+v35$Ve[22,22]-2*v35$Ve[23,22]))))
0.8800091
PROBABILITY OF THE SLOPE AT HAUTES-ALPES
0.8348357*0.8800091
[1] 0.734663
--------------------------------------------------AIN
2*(1-pnorm(abs(v33$coefficients[74]-v33$coefficients[73])/(0.001*abs(francia23[74,1]francia23[73,1])*sqrt(v33$Ve[74,74]+v33$Ve[73,73]-2*v33$Ve[74,73]))))
0.9878527
2*(1-pnorm(abs(v35$coefficients[38]-v35$coefficients[37])/(0.001*abs(francia25[38,2]francia25[37,2])*sqrt(v35$Ve[38,38]+v35$Ve[37,37]-2*v35$Ve[38,37]))))
0.915027
PROBABILITY OF THE SLOPE AT AIN
0.9878527*0.915027
[1] 0.9039119
------------------------------------------------ARDECHE
2*(1-pnorm(abs(v33$coefficients[64]-v33$coefficients[63])/(0.001*abs(francia23[64,1]francia23[63,1])*sqrt(v33$Ve[64,64]+v33$Ve[63,63]-2*v33$Ve[64,63]))))
0.7953353
2*(1-pnorm(abs(v35$coefficients[24]-v35$coefficients[23])/(0.001*abs(francia25[24,2]francia25[23,2])*sqrt(v35$Ve[24,24]+v35$Ve[23,23]-2*v35$Ve[24,23]))))
0.7350154
PROBABILITY OF THE SLOPE AT ARDECHE
0.7953353 * 0.7350154
[1] 0.5845837
----------------------------------------------------CORRECE
2*(1-pnorm(abs(v33$coefficients[36]-v33$coefficients[35])/(0.001*abs(francia23[36,1]francia23[35,1])*sqrt(v33$Ve[36,36]+v33$Ve[35,35]-2*v33$Ve[36,35]))))
0.9772881
2*(1-pnorm(abs(v35$coefficients[30]-v35$coefficients[29])/(0.001*abs(francia25[30,2]francia25[29,2])*sqrt(v35$Ve[30,30]+v35$Ve[29,29]-2*v35$Ve[30,29]))))
0.9905769
PROBABILITY OF THE SLOPE AT CORRECE
0.9772881 *0.9905769
[1] 0.968079
---------------------------------------------------CREUSE
2*(1-pnorm(abs(v33$coefficients[37]-v33$coefficients[36])/(0.001*abs(francia23[37,1]francia23[36,1])*sqrt(v33$Ve[37,37]+v33$Ve[36,36]-2*v33$Ve[37,36]))))
0.9177886
2*(1-pnorm(abs(v35$coefficients[37]-v35$coefficients[36])/(0.001*abs(francia25[37,2]francia25[36,2])*sqrt(v35$Ve[37,37]+v35$Ve[36,36]-2*v35$Ve[37,36]))))
0.9301495
PROBABILITY OF THE SLOPE AT CREUSE
0.9177886*0.9301495
[1] 0.8536806
---------------------------------------------------INDRE
2*(1-pnorm(abs(v33$coefficients[35]-v33$coefficients[34])/(0.001*abs(francia23[35,1]francia23[34,1])*sqrt(v33$Ve[35,35]+v33$Ve[34,34]-2*v33$Ve[35,34]))))
0.9882307
2*(1-pnorm(abs(v35$coefficients[45]-v35$coefficients[44])/(0.001*abs(francia25[45,2]francia25[44,2])*sqrt(v35$Ve[45,45]+v35$Ve[44,44]-2*v35$Ve[45,44]))))
0.9476407
PROBABILITY OF THE SLOPE AT INDRE
0.9882307 *0.9476407
[1] 0.9364876
---------------------------------------------------ISERE
2*(1-pnorm(abs(v33$coefficients[75]-v33$coefficients[74])/(0.001*abs(francia23[75,1]francia23[74,1])*sqrt(v33$Ve[75,75]+v33$Ve[74,74]-2*v33$Ve[75,74]))))
0.8999697
2*(1-pnorm(abs(v35$coefficients[29]-v35$coefficients[28])/(0.001*abs(francia25[29,2]francia25[28,2])*sqrt(v35$Ve[29,29]+v35$Ve[28,28]-2*v35$Ve[29,28]))))
0.8749544
PROBABILITY OF THE SLOPE AT ISERE
0.8999697* 0.8749544
[1] 0.7874324
---------------------------------------------------JURA
2*(1-pnorm(abs(v33$coefficients[76]-v33$coefficients[75])/(0.001*abs(francia23[76,1]francia23[75,1])*sqrt(v33$Ve[76,76]+v33$Ve[75,75]-2*v33$Ve[76,75]))))
0.9894166
2*(1-pnorm(abs(v35$coefficients[44]-v35$coefficients[43])/(0.001*abs(francia25[44,2]francia25[43,2])*sqrt(v35$Ve[44,44]+v35$Ve[43,43]-2*v35$Ve[44,43]))))
0.006266475
PROBABILITY OF THE SLOPE AT JURA
0.9894166*0.006266475
[1] 0.006200154
---------------------------------------------------LOIRE
2*(1-pnorm(abs(v33$coefficients[62]-v33$coefficients[61])/(0.001*abs(francia23[62,1]francia23[61,1])*sqrt(v33$Ve[62,62]+v33$Ve[61,61]-2*v33$Ve[62,61]))))
0.9539984
2*(1-pnorm(abs(v35$coefficients[33]-v35$coefficients[32])/(0.001*abs(francia25[33,2]francia25[32,2])*sqrt(v35$Ve[33,33]+v35$Ve[32,32]-2*v35$Ve[33,32]))))
0.9230121
PROBABILITY OF THE SLOPE AT LOIRE
0.9539984*0.9230121
[1] 0.8805521
---------------------------------------------------RHONE
2*(1-pnorm( abs(v33$coefficients[67]-v33$coefficients[66])/(0.001*abs(francia23[67,1]francia23[66,1])*sqrt(v33$Ve[67,67]+v33$Ve[66,66]-2*v33$Ve[67,66]))))
0.9468413
2*(1-pnorm( abs(v35$coefficients[35]-v35$coefficients[34])/(0.001*abs(francia25[35,2]francia25[34,2])*sqrt(v35$Ve[35,35]+v35$Ve[34,34]-2*v35$Ve[35,34]))))
0.3860541
PROBABILITY OF THE SLOPE AT RHONE
0.9468413*0.3860541
[1] 0.365532
--------------------------------------------------SAONE-ET-LOIRE
2*(1-pnorm(abs(v33$coefficients[66]-v33$coefficients[65])/(0.001*abs(francia23[66,1]francia23[65,1])*sqrt(v33$Ve[66,66]+v33$Ve[65,65]-2*v33$Ve[66,65]))))
0.9742965
2*(1-pnorm(abs(v35$coefficients[42]-v35$coefficients[41])/(0.001*abs(francia25[42,2]francia25[41,2])*sqrt(v35$Ve[42,42]+v35$Ve[41,41]-2*v35$Ve[42,41]))))
0.8323817
PROBABILITY OF THE SLOPE AT SAONE-ET-LOIRE
0.9742965*0.8323817
[1] 0.8109866
---------------------------------------------------SEINE
2*(1-pnorm(abs(v33$coefficients[43]-v33$coefficients[42])/(0.001*abs(francia23[43,1]francia23[42,1])*sqrt(v33$Ve[43,43]+v33$Ve[42,42]-2*v33$Ve[43,42]))))
0.8173481
2*(1-pnorm(abs(v35$coefficients[72]-v35$coefficients[71])/(0.001*abs(francia25[72,2]francia25[71,2])*sqrt(v35$Ve[72,72]+v35$Ve[71,71]-2*v35$Ve[72,71]))))
2(P{Z> 26'32592}) = 0
PROBABILITY OF THE SLOPE AT SEINE
0.1365352*2(P{Z> 26'32592}) = 0
[1] 0
---------------------------------------------------HAUTE-VIENNE
2*(1-pnorm(abs(v33$coefficients[29]-v33$coefficients[28])/(0.001*abs(francia23[29,1]francia23[28,1])*sqrt(v33$Ve[29,29]+v33$Ve[28,28]-2*v33$Ve[29,28]))))
0.7261238
2*(1-pnorm(abs(v35$coefficients[36]-v35$coefficients[35])/(0.001*abs(francia25[36,2]francia25[35,2])*sqrt(v35$Ve[36,36]+v35$Ve[35,35]-2*v35$Ve[36,35]))))
0.9614115
PROBABILITY OF THE SLOPE AT HAUTE-VIENNE
0.7261238* 0.9614115
[1] 0.6981038
-----------------------------------------------------------------------------------------------------------------------------------------------
Department
Probability
PER
PROP
HAUTES-ALPES 0.08677979
0.734663
AIN
0.7796545
0.9039119
ARDECHE
0.08590459
0.5845837
CORREZE
0.8543756
0.968079
CREUSE
0.3344432
0.8536806
INDRE
0.8043197
0.9364876
ISERE
0.2926037
0.7874324
JURA
0.926961*2(P{Z> 16'54776}) = 0
LOIRE
RHONE
0.5497284
0.8732205*2(P{Z>13'83688}) = 0
SAONE-ET-LOIRE
SEINE
0.45913
0.1365352*2(P{Z> 131'8917}) = 0
HAUTE-VIENNE
0.01982465
0.006200154
0.8805521
0.365532
0.8109866
0.1365352*2(P{Z> 26'32592}) = 0
0.6981038