Here is how you should use the code
RefDB.StatCA <- read.csv(paste(dir, "RefDB.caStat.csv", sep=""))
RefDB.StatCB <- read.csv(paste(dir, "RefDB.cbStat.csv", sep=""))
RefDB.StatCB <- RefDB.StatCB[which(RefDB.StatCB$Residue!="Gly"),] # Remove the glycine
CarbonCov.t <- read.csv(paste(dir, "CarbonCovTable_BC.csv", sep=""))Here are the inversed matrix
## $`A-H`
## [,1] [,2]
## [1,] 1.0222703358175891 0.4095366246510062
## [2,] 0.4095366246510062 1.4553887464345199
##
## $`A-B`
## [,1] [,2]
## [1,] 0.5113544996325828 0.1208720966881067
## [2,] 0.1208720966881067 0.2665249008911861
##
## $`A-C`
## [,1] [,2]
## [1,] 0.4032493996046403 0.1465713523806098
## [2,] 0.1465713523806098 0.6831567052007056
##
## $`A-A`
## [,1] [,2]
## [1,] 0.4527728203473753 0.3051857131338516
## [2,] 0.3051857131338516 0.5213232312552896
##
## $`R-H`
## [,1] [,2]
## [1,] 0.416234421975495206 -0.001012179240670737
## [2,] -0.001012179240670737 0.769469989840048774
##
## $`R-B`
## [,1] [,2]
## [1,] 0.4255154591713081 0.1377426899648212
## [2,] 0.1377426899648212 0.3532303638849228
##
## $`R-C`
## [,1] [,2]
## [1,] 0.28004449906066520 0.07361991219253594
## [2,] 0.07361991219253594 0.37791798797544540
##
## $`R-A`
## [,1] [,2]
## [1,] 0.2783168622143647 0.2128694684488345
## [2,] 0.2128694684488345 0.5171206976822388
##
## $`N-H`
## [,1] [,2]
## [1,] 0.50174386080909639 0.05852822693434581
## [2,] 0.05852822693434581 0.58954391989712829
##
## $`N-B`
## [,1] [,2]
## [1,] 0.46532240931825231 -0.02447299080523012
## [2,] -0.02447299080523012 0.23466479831403567
##
## $`N-C`
## [,1] [,2]
## [1,] 0.4596114119797034 0.1052969490546143
## [2,] 0.1052969490546143 0.5271163324052723
##
## $`N-A`
## [,1] [,2]
## [1,] 0.32144438425674293 0.08691058955164424
## [2,] 0.08691058955164424 0.38639584061984156
##
## $`D-H`
## [,1] [,2]
## [1,] 0.38600291716722673 -0.01103630325958412
## [2,] -0.01103630325958412 0.56563862377136553
##
## $`D-B`
## [,1] [,2]
## [1,] 0.37236156837188084 0.01460643728761303
## [2,] 0.01460643728761303 0.38161243495389818
##
## $`D-C`
## [,1] [,2]
## [1,] 0.4121395885712677 0.1141391780514903
## [2,] 0.1141391780514903 0.6055310759541123
##
## $`D-A`
## [,1] [,2]
## [1,] 0.26661562263238470 0.0956159035877312
## [2,] 0.09561590358773119 0.4787350119987098
##
## $`B-H`
## [,1] [,2]
## [1,] 0.18527233951007541 -0.04730410473965884
## [2,] -0.04730410473965885 0.14054478200087928
##
## $`B-B`
## [,1] [,2]
## [1,] 0.34652332297789007 -0.02406263626412389
## [2,] -0.02406263626412389 0.06809667596834081
##
## $`B-C`
## [,1] [,2]
## [1,] 0.1888027677005812 -0.0229735341207882
## [2,] -0.0229735341207882 0.1146509933412026
##
## $`B-A`
## [,1] [,2]
## [1,] 0.21648134240031180 0.01446063798256255
## [2,] 0.01446063798256255 0.09741284586849415
##
## $`C-H`
## [,1] [,2]
## [1,] 0.12096537887218409 0.02578358779210387
## [2,] 0.02578358779210387 0.53828916877743538
##
## $`C-B`
## [,1] [,2]
## [1,] 0.33263209266415916 0.05946406888262865
## [2,] 0.05946406888262865 0.36075808628426859
##
## $`C-C`
## [,1] [,2]
## [1,] 0.16219937957847888 0.01536999715985726
## [2,] 0.01536999715985726 0.25912864885066017
##
## $`C-A`
## [,1] [,2]
## [1,] 0.4953058545905087 0.5640297790570729
## [2,] 0.5640297790570729 0.9980077520816387
##
## $`Q-H`
## [,1] [,2]
## [1,] 0.7310196225943436 0.1743527574982024
## [2,] 0.1743527574982024 1.2230587045792176
##
## $`Q-B`
## [,1] [,2]
## [1,] 0.5565358566874856 0.1261130212377753
## [2,] 0.1261130212377753 0.2970412458536847
##
## $`Q-C`
## [,1] [,2]
## [1,] 0.3768805409595383 0.1231671629648663
## [2,] 0.1231671629648663 0.3903796759128526
##
## $`Q-A`
## [,1] [,2]
## [1,] 0.3479835779115518 0.2228518508043355
## [2,] 0.2228518508043355 0.4513583290658322
##
## $`E-H`
## [,1] [,2]
## [1,] 0.7617957753926674 0.1395989009564604
## [2,] 0.1395989009564604 1.0458855171598544
##
## $`E-B`
## [,1] [,2]
## [1,] 0.3975509347248869 0.1050039163878713
## [2,] 0.1050039163878713 0.2828103769651661
##
## $`E-C`
## [,1] [,2]
## [1,] 0.3449601931918052 0.1431142276328544
## [2,] 0.1431142276328544 0.4756071358703582
##
## $`E-A`
## [,1] [,2]
## [1,] 0.3486325650575318 0.2453738226482316
## [2,] 0.2453738226482316 0.5029930992957472
##
## $`H-H`
## [,1] [,2]
## [1,] 0.33447675540971161 -0.04457365660574725
## [2,] -0.04457365660574725 0.47507122568889243
##
## $`H-B`
## [,1] [,2]
## [1,] 0.31636669517513610 -0.01235057794213066
## [2,] -0.01235057794213066 0.20338776012354945
##
## $`H-C`
## [,1] [,2]
## [1,] 0.260651846751351279 0.007665211179680645
## [2,] 0.007665211179680645 0.170978781244448985
##
## $`H-A`
## [,1] [,2]
## [1,] 0.1744961550453250 0.03693626011766969
## [2,] 0.0369362601176697 0.20890834496528118
##
## $`I-H`
## [,1] [,2]
## [1,] 0.3467923702101707 -0.1144454417646608
## [2,] -0.1144454417646608 0.7939119697907848
##
## $`I-B`
## [,1] [,2]
## [1,] 0.41380518522445980 0.04593268166006736
## [2,] 0.04593268166006736 0.26017457429338109
##
## $`I-C`
## [,1] [,2]
## [1,] 0.29183372809610691 0.07394998823032814
## [2,] 0.07394998823032815 0.36886655174081656
##
## $`I-A`
## [,1] [,2]
## [1,] 0.17273180251397174 0.09938661632590243
## [2,] 0.09938661632590243 0.32564876457203323
##
## $`L-H`
## [,1] [,2]
## [1,] 0.7014281041486634 0.1973079402120125
## [2,] 0.1973079402120125 0.9625311372031863
##
## $`L-B`
## [,1] [,2]
## [1,] 0.6429097554811781 0.1288515874476844
## [2,] 0.1288515874476844 0.2758243578453125
##
## $`L-C`
## [,1] [,2]
## [1,] 0.35933042406163035 0.07168620584037613
## [2,] 0.07168620584037613 0.38610385393296837
##
## $`L-A`
## [,1] [,2]
## [1,] 0.3330217876473626 0.2060866650936085
## [2,] 0.2060866650936085 0.4361763142161567
##
## $`K-H`
## [,1] [,2]
## [1,] 0.48236704769409006 -0.01213241575519816
## [2,] -0.01213241575519816 1.29162746655277005
##
## $`K-B`
## [,1] [,2]
## [1,] 0.6135256523422328 0.1402952346854244
## [2,] 0.1402952346854245 0.3476981004121050
##
## $`K-C`
## [,1] [,2]
## [1,] 0.3414143825165172 0.1000310108288065
## [2,] 0.1000310108288064 0.3878723975636750
##
## $`K-A`
## [,1] [,2]
## [1,] 0.2899549258917258 0.1688553689019368
## [2,] 0.1688553689019368 0.4363535443356384
##
## $`M-H`
## [,1] [,2]
## [1,] 0.3550914156435880 -0.1450691340575689
## [2,] -0.1450691340575689 0.4221639522390618
##
## $`M-B`
## [,1] [,2]
## [1,] 0.65120895244328003 -0.01270018642066416
## [2,] -0.01270018642066416 0.19093817533547938
##
## $`M-C`
## [,1] [,2]
## [1,] 0.44234526057964491 0.06518725084072853
## [2,] 0.06518725084072853 0.20539314354896351
##
## $`M-A`
## [,1] [,2]
## [1,] 0.22275442238794574 0.05786169286930914
## [2,] 0.05786169286930914 0.20739677676932472
##
## $`F-H`
## [,1] [,2]
## [1,] 0.2815173398062958 -0.0516745164504392
## [2,] -0.0516745164504392 0.5922018511163264
##
## $`F-B`
## [,1] [,2]
## [1,] 0.40613334014284613 0.05989796048815028
## [2,] 0.05989796048815028 0.33912858277682961
##
## $`F-C`
## [,1] [,2]
## [1,] 0.24582241543289249 0.01383772525221255
## [2,] 0.01383772525221254 0.25585495968074040
##
## $`F-A`
## [,1] [,2]
## [1,] 0.18004660210156367 0.0883069815596027
## [2,] 0.08830698155960269 0.2722441798998690
##
## $`P-H`
## [,1] [,2]
## [1,] 0.8914591419426976 0.1982701932784061
## [2,] 0.1982701932784062 1.1521306849440029
##
## $`P-B`
## [,1] [,2]
## [1,] 0.94297331241277049 0.01619229897622479
## [2,] 0.01619229897622479 0.69472249106854733
##
## $`P-C`
## [,1] [,2]
## [1,] 0.63115414638334766 0.03758845687018714
## [2,] 0.03758845687018714 1.11027182581518313
##
## $`P-A`
## [,1] [,2]
## [1,] 0.4824752766635895 0.1148510535385889
## [2,] 0.1148510535385889 0.9885085541485075
##
## $`S-H`
## [,1] [,2]
## [1,] 0.4019535398016106 0.1158767904180865
## [2,] 0.1158767904180865 0.8305993068556718
##
## $`S-B`
## [,1] [,2]
## [1,] 0.5425496168086238 0.1228225159809923
## [2,] 0.1228225159809923 0.4663818468246578
##
## $`S-C`
## [,1] [,2]
## [1,] 0.3966366335707132 0.1807370272851637
## [2,] 0.1807370272851637 0.7023584159844466
##
## $`S-A`
## [,1] [,2]
## [1,] 0.3296319062994950 0.2204581308381371
## [2,] 0.2204581308381371 0.5918870509513731
##
## $`T-H`
## [,1] [,2]
## [1,] 0.2303040428119726 0.2303977189687684
## [2,] 0.2303977189687685 0.9610049842547076
##
## $`T-B`
## [,1] [,2]
## [1,] 0.4631829781407182 0.1863644065554753
## [2,] 0.1863644065554752 0.5135620749254637
##
## $`T-C`
## [,1] [,2]
## [1,] 0.3095046298743416 0.2389029476779659
## [2,] 0.2389029476779659 0.7497294298991272
##
## $`T-A`
## [,1] [,2]
## [1,] 0.2039173270654905 0.1927316134534693
## [2,] 0.1927316134534692 0.6038157485737086
##
## $`Y-H`
## [,1] [,2]
## [1,] 0.32640573914239124 -0.05416470245493292
## [2,] -0.05416470245493293 0.82061067897692641
##
## $`Y-B`
## [,1] [,2]
## [1,] 0.34614096286357493 0.03505556886984786
## [2,] 0.03505556886984786 0.29573434317293767
##
## $`Y-C`
## [,1] [,2]
## [1,] 0.212551168756552694 0.007442127349592653
## [2,] 0.007442127349592653 0.295629193808403523
##
## $`Y-A`
## [,1] [,2]
## [1,] 0.19026225386854595 0.09853908023478672
## [2,] 0.09853908023478672 0.29610857194559709
##
## $`W-H`
## [,1] [,2]
## [1,] 0.3325364786202336 0.08421667858828909
## [2,] 0.0842166785882891 0.53153241523945416
##
## $`W-B`
## [,1] [,2]
## [1,] 0.29823658679909681 0.06653926561219919
## [2,] 0.06653926561219921 0.36086627002690724
##
## $`W-C`
## [,1] [,2]
## [1,] 0.36951665744162199 0.09912325832655604
## [2,] 0.09912325832655602 0.35688454816522874
##
## $`W-A`
## [,1] [,2]
## [1,] 0.2431727938614530 0.1510262754492653
## [2,] 0.1510262754492653 0.3767306898109358
##
## $`V-H`
## [,1] [,2]
## [1,] 0.4549261534107713 0.2856184176071123
## [2,] 0.2856184176071123 2.1083334945396954
##
## $`V-B`
## [,1] [,2]
## [1,] 0.5465864235239208 0.3148459680194052
## [2,] 0.3148459680194052 0.5671458835345615
##
## $`V-C`
## [,1] [,2]
## [1,] 0.2686460717477678 0.1904446587858730
## [2,] 0.1904446587858730 0.6678006885536714
##
## $`V-A`
## [,1] [,2]
## [1,] 0.2175366590247989 0.2528487258154272
## [2,] 0.2528487258154272 0.6482012834462014The fomula for chi-square is (x-\(\mu\))\(\Sigma^{-1}\)(x-\(\mu\))’ ~ \(\chi^2_2\)
from scipy import stats
print(stats.chi2.pdf(3.84 , 2))## 0.0733034810652