除了Pearson相关性之外，我还能做什么？

在检查两个变量是否相关时，我观察到应用Pearson相关得出的数字低至0.1，表明没有相关性。我能做些什么来加强这一主张？

我正在查看的数据集（由于发布限制而被细分）是这样的：

6162.178176 0.049820046
4675.14432  0.145022261
5969.056896 0.47210138
5357.506176 0.052263122
33.796224   16.45154204
6162.178176 0.064262991
6725.448576 0.419005508
3247.656192 0.867394771
5357.506176 0.052263122
3612.97728  0.091337414
6162.178176 0.053065652
867.436416  0.129116092
556.833024  1.01107509
1517.611392 168.1484478
1517.611392 35.11570899
4675.14432  0.053902079
4182.685056 0.070289777
2808.30528  0.071929502
5969.056896 0.47193385
3247.656192 0.896646636
4387.071744 0.056985619
6273.222912 0.046547047
4387.071744 0.034875199
7946.940672 0.074997414
6612.794496 0.062001019
4675.14432  0.083205988
6612.794496 0.03326884
3321.686016 0.090917684
6194.365056 0.041166447
556.833024  1.738402642
2929.00608  0.126664128
5969.056896 0.233872792
3247.656192 0.419995196
3247.656192 0.429232627
807.890688  0.341630377
2336.767488 0.204556081
2969.23968  0.125284598
2929.00608  0.157732687
1517.611392 1666.591338
6725.448576 0.219167537
3247.656192 0.419687282
5357.506176 0.039383996
3719.193984 5.892405746
3070.628352 5.482916872
3070.628352 5.482916872
4675.14432  3.599033281
6612.794496 0.03931772
2336.767488 0.089439793
2929.00608  0.133833795
2969.23968  0.107434911
6725.448576 0.202365684
3247.656192 0.425229741
5357.506176 0.05076989
4182.685056 0.06837713
2484.827136 6.860034548
4675.14432  3.588766218
3070.628352 5.47966021
3247.656192 0.910502783
5357.506176 0.527484226
6009.290496 0.484250179
3247.656192 0.867394771
3247.656192 0.449247061
2969.23968  0.155932175
3564.69696  0.115577847
3247.656192 0.447707489
6009.290496 0.227647507
5969.056896 0.228009219
5357.506176 0.05076989
4182.685056 5.23945736
8445.837312 2.601991867
3247.656192 6.727313086
6273.222912 2.677571041
4675.14432  3.588766218
4675.14432  3.599033281
7946.940672 2.112259383
6194.365056 0.243447066
4182.685056 0.062400108
2969.23968  0.047150118
5357.506176 0.044796962
5969.056896 0.228176749
4387.071744 0.057669447
6823.61856  2.473321135
4675.14432  3.588766218
6162.178176 0.240499375
4274.417664 0.046789999
3627.461376 0.526263357
4675.14432  0.084703268
7946.940672 0.049578827
2929.00608  0.117104571
8445.837312 0.055885519
5969.056896 0.242584386
6471.172224 0.215725985
3247.656192 0.429848456
3247.656192 0.419071453
807.890688  0.313161179
4182.685056 5.231089529
7946.940672 2.753260771
4387.071744 4.981454892
6405.18912  2.622405004
4675.14432  0.097750993
3070.628352 0.092814879
3070.628352 6.443957956
6162.178176 0.046899001
6405.18912  0.196715503
5357.506176 0.104152936
867.436416  4.666624464
4675.14432  0.191651838
589.019904  1.169739758
7946.940672 10.02209571
4675.14432  0.088339519
2803.477248 0.078830674
3310.420608 0.033228406
6009.290496 0.468940552
2518.62336  1.156187164
5357.506176 0.052263122
4387.071744 0.059948871
4182.685056 0.058813895
6823.61856  0.148454957
589.019904  1.745272092
1517.611392 1429.682204
3564.69696  0.095940834
3564.69696  0.115577847
3564.69696  0.109406214
2518.62336  0.506625969
8078.90688  0.180965076
6009.290496 0.232306959
5357.506176 0.254409413
8078.90688  0.174281004
5357.506176 0.046850156
8445.837312 2.606491125
7946.940672 2.744955688
4274.417664 0.055680099
6273.222912 2.686976094
3070.628352 5.46663356
4675.14432  0.030159497
4182.685056 0.375356973
6162.178176 0.254617759
2484.827136 6.755399503
6405.18912  2.600079356
4675.14432  0.021817508
6162.178176 0.239038852
4274.417664 0.090772599
4274.417664 0.02362895
3564.69696  0.051056233
6162.178176 0.051442849
4182.685056 5.23945736
3923.580672 0.060404008
7946.940672 2.109742691
4816.766592 3.487194092
4816.766592 3.493214728
4182.685056 0.339733922
6162.178176 0.25494232
6612.794496 0.063362017
6965.240832 0.275367363
3627.461376 0.537566027
2336.767488 0.06975448
2177.442432 0.129050484
3070.628352 0.085650222
4675.14432  3.588766218
4182.685056 0.344276459
4182.685056 0.040643749
6725.448576 0.164896064
4675.14432  3.590477395
6194.365056 0.258299275
4274.417664 0.067845499
3041.66016  0.635836977
3070.628352 0.085650222
6373.00224  0.032010031
6162.178176 0.044140236
3070.628352 0.074903236
3627.461376 1.892783765
556.833024  6.99850733
589.019904  0.499134236
6162.178176 0.044951638
8078.90688  0.356112534
3247.656192 0.867702686
5357.506176 0.543536471
3247.656192 0.891104178
3247.656192 0.076978592
6725.448576 0.065125767
3564.69696  0.135775917
7946.940672 0.027683609
6725.448576 0.173073957
6725.448576 0.089064691
6725.448576 0.086239601
2484.827136 7.955885427
6823.61856  2.905496523
3070.628352 6.477501579
6162.178176 0.047710402
7946.940672 0.078646617
3321.686016 0.204414263
7946.940672 0.078646617
3299.1552   0.29431777
7946.940672 0.063420632
3041.66016  0.626960245
6162.178176 0.051442849
3070.628352 0.094117544
3564.69696  0.037029796
4885.968384 4.066747559
6273.222912 3.154518862
6162.178176 0.024179762
3321.686016 0.191770082
3321.686016 0.298643519
3627.461376 0.526263357
3627.461376 0.525712007
7946.940672 0.009185925
3070.628352 0.085650222
6373.00224  0.03436371
3564.69696  0.34028138
3564.69696  0.166914609
6725.448576 0.090848959
2808.30528  0.084392534
2336.767488 0.103989807
4675.14432  4.245858233
3564.69696  0.345611426
3564.69696  0.221337188
2808.30528  0.060178643
556.833024  1.828196167
2336.767488 0.087728026
2336.767488 0.093291267
4675.14432  4.250136175
4675.14432  4.239227421
585.801216  1.7736392
3321.686016 0.190565874
3321.686016 0.213746873
3070.628352 0.028007297
3564.69696  0.183465806
589.019904  0.329360687
6273.222912 3.165996216
4675.14432  4.221901753
6373.00224  0.036089741
4387.071744 0.223839512
3321.686016 0.165879616
7946.940672 0.124827911
3321.686016 0.174008018
7946.940672 0.134013836
2336.767488 0.076601545
556.833024  0.441784142
4816.766592 4.125173936
6194.365056 0.037453395
2808.30528  0.35216969
3299.1552   0.167012452
3299.1552   0.279465483
3299.1552   0.168527992
3321.686016 0.29412774
3321.686016 0.141795461
6373.00224  0.045347544
3627.461376 0.321712592
4387.071744 5.00151383
4387.071744 5.005844737
6405.18912  3.097332433
3299.1552   0.193079731
3321.686016 0.286601441
3321.686016 0.077370347
3299.1552   0.180652308
7946.940672 0.126589595
3299.1552   0.081232917
3041.66016  0.395178928
4182.685056 5.254041293
7946.940672 2.73979647
4274.417664 0.062464649
2929.00608  4.474213997
2808.30528  4.58034249
2808.30528  4.553992079
4675.14432  0.041282148
7946.940672 0.078646617
3299.1552   0.215206608
7946.940672 0.078646617
3321.686016 0.329049764
3321.686016 0.11981867
1517.611392 0.125855671
6965.240832 3.154951929
3247.656192 6.768265697
2929.00608  4.343794329
6373.00224  0.044719896
4885.968384 4.056514173
4675.14432  4.239227421
3070.628352 0.090860882
3321.686016 0.191770082
7946.940672 0.12507958
3321.686016 0.06532827
3321.686016 0.167384875
3321.686016 0.324232933
7946.940672 0.053731369
7946.940672 2.753260771
3719.193984 5.894556749
4182.685056 0.059292057
4675.14432  3.590477395
3299.1552   0.07789873
3321.686016 0.185447991
3321.686016 0.324232933
3321.686016 0.089713476
6965.240832 0.169986944
3627.461376 0.337150385
4387.071744 5.00151383
2803.477248 4.763370207
8445.837312 1.506304174
2848.53888  4.464745098
8445.837312 0.046768602
69.201792   7.962221556
4182.685056 0.087981762
5969.056896 0.170211144
1517.611392 0.801259141
2336.767488 0.124103062
8078.90688  1.652946395
5969.056896 2.148245564
8078.90688  1.650470812
5969.056896 2.150758524
3310.420608 0.057394519
69.201792   3.655974689
7946.940672 0.025418587
5357.506176 0.04237046
5357.506176 0.04330373
5357.506176 0.050209928
1733.263488 0.218662657
8078.90688  0.298679021
2177.442432 1.065010935
1757.403648 0.145669437
3070.628352 5.394335654
2929.00608  4.484114966
8445.837312 1.517197115
6471.172224 1.975221731
2929.00608  0.121201524
3310.420608 0.05648829
75.639168   3.344827907
1733.263488 0.133274601
1757.403648 0.169568329
2177.442432 0.118028379
3321.686016 0.164073304
3299.1552   0.296136417
3299.1552   0.14276382
75.639168   2.578029415
3041.66016  0.384000821
2969.23968  4.311878252
2929.00608  4.371107348
2848.53888  4.524775874
2929.00608  0.089791551
5357.506176 0.026878177
8445.837312 0.018470638
2177.442432 0.130887502
6823.61856  0.048507987
6273.222912 0.052923354
2808.30528  4.589600743
2969.23968  0.088574864
8445.837312 0.042624548
5357.506176 0.04237046
7946.940672 0.036366196
6273.222912 0.394534043
1733.263488 0.218662657
6273.222912 0.384650766
5357.506176 0.456929011
1733.263488 0.147698259
1733.263488 0.147698259
6194.365056 0.050691233
4834.469376 0.045920241
2969.23968  4.283251395
2808.30528  0.114303812
72.42048    3.452062179
75.639168   7.284585679
5357.506176 0.052449776
1733.263488 0.188661448
8445.837312 0.020483463
1757.403648 0.106406972
5357.506176 0.478954184
6273.222912 0.012114985
5357.506176 0.041997152
4816.766592 0.052524862
3070.628352 0.08499889
4885.968384 0.059558306
6373.00224  0.036089741
3321.686016 0.086702957
3627.461376 0.321988266
2803.477248 4.761230008
2808.30528  4.686100223
6471.172224 0.068611989
7946.940672 0.036114527
5357.506176 0.018665401
1733.263488 0.107888963
6162.178176 0.050469167
1757.403648 0.194036242
1733.263488 0.171353059
2177.442432 0.084043554
2177.442432 0.109302545
5357.506176 0.474847796
2177.442432 0.152013204
8078.90688  0.019061985
5357.506176 0.056929472
2177.442432 0.116191361
6405.18912  0.051832974
2484.827136 0.117110762
6194.365056 0.041327884
6162.178176 0.032618336
7946.940672 0.059645594
6823.61856  0.066973263
6273.222912 0.074602801
6162.178176 0.047548122
6373.00224  0.047387399
2969.23968  4.33545331
2969.23968  4.33545331
2808.30528  4.638028527
2969.23968  0.093626662
2177.442432 0.104710001
2177.442432 0.136857809
2177.442432 0.124917195
1485.424512 3.495297107
6273.222912 0.405533174
1757.403648 0.195743306
8078.90688  0.011882796
5357.506176 0.04237046
8078.90688  0.303011291
5357.506176 0.028744717
5357.506176 0.036397532
4816.766592 0.052940078
3070.628352 0.065458915
6273.222912 0.073168132
4816.766592 0.097160614
4675.14432  0.08598665
6162.178176 0.05209197
3070.628352 0.073600571
3070.628352 0.142316148
3070.628352 0.142316148
6273.222912 0.052923354
4675.14432  0.073152822
3070.628352 0.085650222
3070.628352 0.034846288
6162.178176 0.02872361
1517.611392 0.3380312
6965.240832 0.981157747
6162.178176 0.02921045
6405.18912  0.064166724
4675.14432  0.047912959
3070.628352 0.021819638
6162.178176 0.031157814
3070.628352 0.088255552
1485.424512 0.34535582
3041.66016  2.255676058
6273.222912 0.055155062
4885.968384 0.066721676
3070.628352 0.139059486
3070.628352 0.111377855
4675.14432  0.078928045
3070.628352 0.071320907
3070.628352 0.112029188
7946.940672 0.013464301
6273.222912 0.040330147
6273.222912 1.089392183
3041.66016  2.268826771
2336.767488 0.034663269
3070.628352 0.103236199
6405.18912  0.069162673
4675.14432  0.08598665
3070.628352 0.103236199
2484.827136 0.148501276
4675.14432  0.073366719
4816.766592 0.064150918
4675.14432  0.054115976
2484.827136 0.059159045
3627.461376 1.902432386
3627.461376 1.864389252
5357.506176 0.049649966
6612.794496 0.054591141
7946.940672 0.045426286
7946.940672 0.036617865
4816.766592 0.06165962
6162.178176 0.054850735
4675.14432  0.08598665
3070.628352 0.087278553
4885.968384 0.033360838
6273.222912 0.069661162
3627.461376 1.892783765
6405.18912  1.066947419
6405.18912  1.064605568
1517.611392 0.03031079
5357.506176 0.425571138
2177.442432 1.042048215
6273.222912 0.023273523
2177.442432 0.130887502
3070.628352 0.08499889
6273.222912 0.056111508
4675.14432  0.072083336
4675.14432  0.067805393
3070.628352 0.073600571
6373.00224  0.057586674
4675.14432  0.08598665
4816.766592 0.068925906
7946.940672 0.039889564
4675.14432  0.061816274
2484.827136 0.043061346
1485.424512 0.34535582
6273.222912 1.089073367
6273.222912 1.094015006
2177.442432 0.14007259
3070.628352 0.108121193
4816.766592 0.068925906
6162.178176 0.048197243
6373.00224  0.038600332
2484.827136 0.150111046
6162.178176 0.059556863
6405.18912  0.073065758
4675.14432  0.073152822
4675.14432  0.067805393
4675.14432  0.073366719
4675.14432  0.022886994
4675.14432  0.054115976
6823.61856  1.001228298
867.436416  47.76834271
5357.506176 0.041623844
5357.506176 0.052823084
1517.611392 1.775157998
75.639168   2.181409505
2929.00608  38.44000215
7946.940672 0.036995369
7946.940672 0.632696305
4675.14432  0.21838898
2177.442432 0.129968993
3310.420608 0.086695932
1517.611392 0.187136181
69.201792   1.835212591
5969.056896 18.86244376
7946.940672 0.035233684
6823.61856  0.150067005
6612.794496 0.04612271
5357.506176 0.041623844
1517.611392 0.198996925
8078.90688  2.260701883
7946.940672 0.007424241
6373.00224  0.048328871
6405.18912  0.149722355
6405.18912  0.159870377
4675.14432  0.212185963
7946.940672 0.103813535
8078.90688  2.260330546
5969.056896 18.85071661
2843.710848 39.53179701
2969.23968  59.65533911
8445.837312 20.85690187
8445.837312 20.86826841
6009.290496 29.34722495
2969.23968  59.37681663
33.796224   294.3819996
3247.656192 0.086523937
1757.403648 2.972566949
3070.628352 0.028007297
3020.738688 0.097327187
114.263424  944.37044
6009.290496 3.027645279
2969.23968  6.110992023
6009.290496 18.71252523
2929.00608  38.43897791
6009.290496 29.34273191
2929.00608  60.36484567
2969.23968  59.39635025
6823.61856  0.271996446
6405.18912  0.294448761
6405.18912  0.290233429
3247.656192 0.034794323
4885.968384 0.044617563
3070.628352 0.0511296
7946.940672 0.734118982
4675.14432  0.12192137
7946.940672 0.130993805
6273.222912 0.148567971
2969.23968  0.067020524
2177.442432 5.664902924
6009.290496 0.034280253
5969.056896 0.02831268
33.796224   173.2146171
6965.240832 1.690537382
6823.61856  0.151825603
4387.071744 0.254383804
1517.611392 48.99805075
1757.403648 0.16103301
1517.611392 1.614379025
5969.056896 3.059779848
3020.738688 0.097327187
867.436416  192.18815
2929.00608  6.235562338
8078.90688  13.93641512
3020.738688 1.112641757
1733.263488 0.397516018
2929.00608  6.2345381
2929.00608  6.218833114
2969.23968  6.110992023
867.436416  345.2783333
5969.056896 3.059779848
5969.056896 18.86244376
3020.738688 0.091037335
1733.263488 83.43047725
8445.837312 2.15668374
6009.290496 3.027645279
6009.290496 3.015663831
2929.00608  6.194934222
114.263424  1242.602357
5969.056896 3.048052702
2969.23968  6.092131976
2808.30528  0.10184078
2808.30528  0.089733834
2969.23968  37.87905731
2929.00608  38.42327292
5969.056896 29.67822272
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2177.442432 0.1621168
5969.056896 1.21861797
3247.656192 0.073283619
3627.461376 3.23035831
4387.071744 0.236148406
3247.656192 0.351638207
4675.14432  0.176465141
2843.710848 6.361406263
2808.30528  0.1039773
6009.290496 18.72450667
8445.837312 13.32680181
6009.290496 18.72217695
2969.23968  59.6455723
2929.00608  60.34811645
2843.710848 62.00841416
6471.172224 27.25703998
5969.056896 29.49527925
3247.656192 2.339841273
114.263424  57.53372138
1757.403648 0.166154202
4675.14432  0.117643427
8445.837312 2.158341361
6009.290496 3.025315553
2848.53888  0.088466407
5969.056896 18.85071661
6471.172224 17.37351381
2929.00608  38.39937403
2969.23968  37.86019726
8078.90688  21.80851972
33.796224   6.272890131
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3020.738688 0.001655224
114.263424  6417.215364
3070.628352 0.097048541
3070.628352 0.060573921
3247.656192 0.580726496
6373.00224  0.042209306
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3321.686016 0.034018869
6373.00224  0.031539295
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3070.628352 0.066110247
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3321.686016 0.567783948
4387.071744 0.0257575
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6373.00224  0.044092249
1733.263488 75.69131924
114.263424  2.608008666
3041.66016  3.841323286
3627.461376 3.241385305
7946.940672 0.122311219
6273.222912 0.185231741
3070.628352 6.947763635
4675.14432  0.112723793
3627.461376 3.124499154
4387.071744 0.25210438
6273.222912 0.174551425
7946.940672 0.131245475
4182.685056 0.676837955
3070.628352 0.896559168
3070.628352 0.921961135
4182.685056 0.665840235
3070.628352 0.881252854
4834.469376 0.056676334
4675.14432  0.031015085
2484.827136 0.226172675
3020.738688 1.086158168
1733.263488 0.171930005
3070.628352 0.053083598
2864.63232  0.669195829
3299.1552   0.565599339
4387.071744 0.0257575
3321.686016 0.019869428
114.263424  1126.89604
6725.448576 1.729252684
6273.222912 0.165146371
8445.837312 0.135688145
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3070.628352 0.881252854
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6162.178176 0.091201517
6373.00224  0.075945368
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2484.827136 0.183916214
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3070.628352 6.476850247
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4675.14432  0.13689417
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4834.469376 0.037439476
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1517.611392 1311.730401
4182.685056 0.085830034
589.019904  1.769040389
556.833024  0.375336934
3564.69696  0.115577847
5357.506176 0.054129662
729.032832  0.73659234
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3247.656192 0.43015637
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3247.656192 0.428924713
5357.506176 0.046850156
3627.461376 0.337150385
3070.628352 5.482916872
6273.222912 2.690323656
2336.767488 0.088155968
8445.837312 0.039901313
6162.178176 0.051442849
3070.628352 0.108121193
6612.794496 0.045517822
6162.178176 0.071403323
3070.628352 0.921961135
585.801216  4.883909288
585.801216  4.883909288
3247.656192 0.866778943
7946.940672 0.066692331
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6273.222912 0.083051409
4675.14432  0.105237393
7946.940672 0.056751399
6162.178176 0.035539381
589.019904  6.453092628
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4387.071744 0.634819798
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6273.222912 0.083689039
3070.628352 0.147852474
4675.14432  0.097750993
3070.628352 0.095745876
6405.18912  3.100767148
7946.940672 2.48988898
3070.628352 6.452750945
556.833024  6.763248295
589.019904  0.483854617
3020.738688 0.420426965
6162.178176 0.022881519
5357.506176 0.09034054
4834.469376 0.108595165
4816.766592 0.105049724
3070.628352 0.160227792
4675.14432  0.093259153
3070.628352 0.090860882
3070.628352 6.477501579

首先查看散点图，发现问题出在第二个变量的一些非常高的值中：

V2上的对数刻度显示出一些微妙的递减关系，因此您可以从此处开始：

编辑：我已经发布了此内容，主要是为了展示如何在这种情况下获得更清晰的散点图...由于V1的分布相当均匀，所以我不想进入日志日志，因此它对于可视化没有用。如果您想适合$V_2=\alpha V_1^{\beta}$，非线性OLS是一个更安全的想法。

我在此上使用@mbq，但建议在两个维度上以logscale进行绘制：

现在，相关系数约为-0.44。

您在@shabbychef的注释中提到，您想查看创建趋势线的代码。这是一个基本的R演示

获取并准备数据：

> # I created a gist on github with the data
> filename <- "https://raw.github.com/gist/1320989/40be602c43b5f29d79af50bf2b63ba6c1a839807/data.txt"
> 
> # downloaded the data using wget because default R doesn't handle https
> # if you don't have wget, just download the file manually
> system(paste("wget -nc", filename))
File 'data.txt' already there; not retrieving.

> # read downloaded data into R
> x <- read.table("data.txt")
> names(x) <- c("x", "y")
> 
> x$logx <- log(x$x)
> x$logy <- log(x$y)

用abline创建图

> png("logplot.png")
> plot(x$logx, x$logy)
> abline(lm(logy~logx, x))
> dev.off()

检查相关性

您可能要检查转换前后的相关性。请注意Spearman相关性如何保持不变。

> cor(x$x, x$y, method="pearson")
[1] -0.1821122
> cor(x$x, x$y, method="spearman")
[1] -0.3322378
> 
> cor(x$logx, x$logy, method="pearson")
[1] -0.4399946
> cor(x$logx, x$logy, method="spearman")
[1] -0.3322378

从多个人那里获取日志的建议是好的。但是，看看例如@jeromy产生的情节。这不是Anscombe四重奏中最糟糕的之一。，但看起来也不是好东西。因此，我将使用Spearman的方法，就像@Jeromy指出的那样，它不会改变。但是我可能根本不想使用任何关联...关联是否捕获了您要捕获的有关该关系的内容？它捕获变量的聚集和零通货膨胀吗？

我将抛出另外三种方法，主要用于反应，因为这些方法是新方法，我对此感到很好奇...

首先，由Reshef等人介绍的MIC（最大信息系数）。（2011）确定非线性相关性。当它在媒体上引起轰动时被描述为“ 21世纪的关联”。

其次，距离相关统计量dCor是Szekely，Rizzo和Bakirov（2007）提出并由Simon＆Tibshirani（2012）提出的标准化布朗协方差，他们对MIC的低功效提出了批评。

第三，Heller，Heller和Gorfine（2012a，b）的HHG测试表明，它们是具有更好功率特性的MIC的替代产品。

# Using @Jeromy Anglim's gist on github with the data
library(RCurl)
writeChar(con="data.txt", getURL("https://raw.github.com/gist/1320989/40be602c43b5f29d79af50bf2b63ba6c1a839807/data.txt", ssl.verifypeer = FALSE))

# read downloaded data into R
x <- read.table("data.txt")
names(x) <- c("x", "y")
x$logx <- log(x$x)
x$logy <- log(x$y)

## maximal information coefficient on untransformed data
library(minerva)
with(x, mine(x, y))
$MIC
    [1] 0.4333141
    # maximal information coefficient on log-log data
    with(x, mine(logx, logy))
    $MIC
[1] 0.4333141

MIC：未转换和对数转换数据之间没有差异。与对数对数数据上的皮尔逊绝对值非常相似。

## distance correlation statistic on untransformed data
library("energy")
with(x, dcor(x, y)) 
[1] 0.2352139
# distance correlation statistic on log-log data
with(x, dcor(logx, logy))
[1] 0.3638021

dCor：值比MIC低，并且对数转换敏感。与Spearman相关性相似。

 ## HHG test
download.file("http://www.math.tau.ac.il/~ruheller/Software/HHG2x2_0.1-1.tar.gz", "HHG2x2_0.1-1.tar.gz")
install.packages("HHG2x2_0.1-1.tar.gz", repos = NULL, type="source")
library(HHG2x2)
writeChar(con="myHHG.R", getURL("https://raw.github.com/andrewdyates/HHG_R/master/R/myHHG.R", ssl.verifypeer = FALSE))
source("myHHG.R")

xs <- x[sample(nrow(x), 50), ] # crashed with the full dataset...
Dx = as.matrix(dist((xs[,1]),diag=TRUE,upper=TRUE))
Dy = as.matrix(dist((xs[,2]),diag=TRUE,upper=TRUE))
myHHG(Dx,Dy); pvHHG(Dx,Dy)
$sum_chisquared
[1] 8374.196

$sum_lr
[1] 3890.457

$max_chisquared
[1] 21.28747

$max_lr
[1] 10.80188

$pv
[1] 9.998e-05

$output_monte
[1] 10001

$A_threshold
[1] 2.985682

$B_threshold

[1] -4.553877

HHG：实际上，我不确定如何从HHG中获得可比的距离指标...

参考文献：

M.Gorfine，R.Heller和Y.Heller（2012a）。评论“检测大数据集中的新型关联”。预印本，可从以下网站获得： http://iew3.technion.ac.il/~gorfinm/files/science6.pdf

Heller，R.，Heller，Y.和Gorfine，M.（2012b）。基于距离等级的一致性多变量关联测试。Biometrika，arXiv预印本arXiv：1201.3522。

Reshef，DN，YA Reshef等。（2011）。“在大数据集中检测新型关联”。科学334（6062）：1518-1524。

Simon，Noah和Robert Tibshirani（2012）。关于在大数据集中检测新颖关联的评论，Reshef等人，《科学》，2011年12月16日。www-stat.stanford.edu/~tibs/reshef/comment.pdf

Szekely，GJ，Rizzo，ML和Bakirov，NK（2007），通过距离的相关性来测量和测试依赖性，《统计年鉴》，第1卷。35 No.6，第2769-2794页。 http://dx.doi.org/10.1214/009053607000000505