Correlation
除了 Pearson 相關性，我還能做什麼？
在檢查兩個變量是否相關時，我觀察到應用 Pearson 相關產生的數字低至 0.1，表明沒有相關性。我能做些什麼來加強這一主張嗎？
我正在查看的數據集（由於發布限製而導致的子集）是：
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 6009.290496 29.32742228 8078.90688 21.81557513 3321.686016 0.55875239 3299.1552 0.571661497 4387.071744 0.418502388 3321.686016 0.034018869 3923.580672 0.051228716 2969.23968 6.091458403 2848.53888 0.100402351 6009.290496 18.72450667 2843.710848 62.00876581 2929.00608 60.23203612 3070.628352 0.066110247 4387.071744 0.423061237 6823.61856 0.016560128 4387.071744 0.054934137 33.796224 12.33865653 3070.628352 0.083370558 6273.222912 0.163233479 5969.056896 3.048052702 6471.172224 2.797020288 2808.30528 0.1039773 2969.23968 37.87905731 8445.837312 13.32514419 2843.710848 39.53144536 2929.00608 60.16272933 5969.056896 29.61255071 6009.290496 29.34456241 5969.056896 0.054112401 33.796224 237.3342063 2177.442432 2.527736173 6273.222912 0.24819778 3247.656192 39.86351767 6373.00224 0.028714881 7946.940672 0.04416794 6162.178176 0.049982326 4675.14432 0.195715883 2929.00608 0.067941136 3247.656192 0.040028868 5969.056896 1.514979696 33.796224 140.1635875 2177.442432 4.328013389 3247.656192 1.878585552 6471.172224 0.775284574 7946.940672 0.11740367 4387.071744 0.649636059 3627.461376 0.777403178 4387.071744 0.642797785 3020.738688 0.087064797 114.263424 1656.94317 4387.071744 0.423061237 6965.240832 0.270773121 3321.686016 0.567783948 2864.63232 0.039446598 3299.1552 0.034251193 4885.968384 0.041138211 5969.056896 21.63038521 33.796224 352.7908917 3627.461376 3.23035831 4834.469376 0.048816112 6405.18912 0.181415408 7946.940672 0.136782196 585.801216 4.832697377 585.801216 4.883909288 3627.461376 0.763619433 4182.685056 0.676837955 585.801216 4.817333804 6162.178176 0.042192873 3247.656192 3.312542758 3041.66016 3.842309589 8445.837312 0.138766585 6965.240832 0.166828402 3247.656192 0.343632433 4182.685056 0.658189647 3070.628352 0.256625 3627.461376 0.777403178 3247.656192 0.856309854 6162.178176 0.02888589 3070.628352 6.975119599 3070.628352 0.172603109 6373.00224 0.082378757 3070.628352 0.16120479 2843.710848 6.36105461 3310.420608 0.086393856 2969.23968 37.85952369 8078.90688 13.93604378 5969.056896 29.6026664 2864.63232 0.658374196 3247.656192 0.57610778 6965.240832 0.016223416 3923.580672 0.058110185 33.796224 3865.550187 6273.222912 0.163074071 6162.178176 0.049170925 6009.290496 1.860119761 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 6823.61856 0.228178053 3020.738688 0.001655224 114.263424 6417.215364 3070.628352 0.097048541 3070.628352 0.060573921 3247.656192 0.580726496 6373.00224 0.042209306 4387.071744 0.429899512 3321.686016 0.034018869 6373.00224 0.031539295 114.263424 91.70038524 114.263424 1235.758522 3070.628352 0.066110247 3321.686016 0.567783948 3321.686016 0.567783948 4387.071744 0.0257575 6405.18912 0.017641946 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 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0.73659234 5357.506176 0.27288816 3247.656192 0.43015637 3247.656192 0.419379368 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 6273.222912 0.083689039 6273.222912 0.083051409 4675.14432 0.105237393 7946.940672 0.056751399 6162.178176 0.035539381 589.019904 6.453092628 3070.628352 0.773131662 4387.071744 0.634819798 4834.469376 0.053366767 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
首先看散點圖顯示問題出在第二個變量的一些非常高的值上：
V2 上的對數刻度顯示了一些微妙的遞減關係，因此您可以從那裡開始：
編輯：我發布這個主要是為了展示如何在這種情況下獲得更清晰的散點圖……我不想進入日誌日誌，因為 V1 分佈非常均勻，所以它對可視化沒有用。如果你想適應這個, 非線性 OLS 是一個更安全的想法。
