{"id":417,"date":"2019-09-09T22:10:07","date_gmt":"2019-09-09T13:10:07","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/pearson-and-spearman-correlation-coefficient-and-partial-correlation-coefficient-in-r\/"},"modified":"2025-02-09T11:56:34","modified_gmt":"2025-02-09T02:56:34","slug":"pearson-and-spearman-correlation-coefficient-and-partial-correlation-coefficient-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/pearson-and-spearman-correlation-coefficient-and-partial-correlation-coefficient-in-r\/","title":{"rendered":"R \u3067\u76f8\u95a2\u4fc2\u6570\u3068\u504f\u76f8\u95a2\u4fc2\u6570\u306e\u9055\u3044\u306b\u3064\u3044\u3066 \u30d4\u30a2\u30bd\u30f3\u3068\u30b9\u30d4\u30a2\u30de\u30f3\u306e\u4e21\u65b9\u306b\u3064\u3044\u3066"},"content":{"rendered":"\n

\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u76f8\u95a2\u95a2\u4fc2\u306e\u5f37\u3055\u3092\u793a\u3059\u6307\u6a19\u3002<\/p>\n\n\n\n

\u4e00\u65b9\u304c\u5927\u304d\u3044\u3068\u304d\u306b\u3082\u3046\u4e00\u65b9\u304c\u5927\u304d\u3051\u308c\u3070\u3001\u6b63\u306e\u76f8\u95a2\u95a2\u4fc2\u3067\u3001\u76f8\u95a2\u4fc2\u6570\u306f1\u306b\u8fd1\u3044\u3002<\/p>\n\n\n\n

\u4e00\u65b9\u304c\u5927\u304d\u3044\u3068\u304d\u306b\u3082\u3046\u4e00\u65b9\u304c\u5c0f\u3055\u3044\u5834\u5408\u306f\u3001\u8ca0\u306e\u76f8\u95a2\u95a2\u4fc2\u3067\u76f8\u95a2\u4fc2\u6570\u306f\uff0d1\u306b\u8fd1\u3044\u3002<\/p>\n\n\n\n

\u3067\u306f\u3001\u504f\u76f8\u95a2\u4fc2\u6570\u3068\u306f\u4f55\u304b\uff1f<\/p>\n\n\n\n

\u9055\u3044\u306f\u4f55\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u504f\u76f8\u95a2\u4fc2\u6570\u3068\u306f\u4f55\u304b\uff1f<\/h2>\n\n\n\n

\u504f\u76f8\u95a2\u4fc2\u6570\u3082\u3001\u76f8\u95a2\u4fc2\u6570\u306e\u4e00\u7a2e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b2\u3064\u306e\u5909\u6570\u3068\u3001\u3068\u3082\u306b\u95a2\u4fc2\u3057\u3066\u3044\u308b\u307b\u304b\u306e\u8981\u56e0\u306e\u5f71\u97ff\u3092\u9664\u3044\u305f\u76f8\u95a2\u95a2\u4fc2\u3092\u898b\u305f\u3044\u5834\u5408\u304c\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u6642\u306b\u3001\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3057\u305f\uff12\u5909\u6570\u3068\u3068\u3082\u306b\u95a2\u9023\u3057\u3066\u3044\u308b\u5225\u306e\u7b2c\uff13\u306e\u5909\u6570\u306e\u305f\u3081\u306b\u3001\u76f8\u95a2\u95a2\u4fc2\u304c\u898b\u3048\u3066\u3044\u305f\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n

\u305d\u306e\u898b\u304b\u3051\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u4f5c\u3063\u3066\u3044\u305f\u7b2c\uff13\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u9664\u3044\u305f\u3001\u771f\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u8abf\u3079\u308b\u306e\u304c\u3001\u504f\u76f8\u95a2\u4fc2\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3067\u306f\u3001\u3069\u3093\u306a\u3075\u3046\u306b\u8a08\u7b97\u3059\u308b\u304b\uff1f<\/p>\n\n\n\n

\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf<\/h2>\n\n\n\n

R\u306b\u7d44\u307f\u8fbc\u307f\u3067\u3064\u3044\u3066\u3044\u308b airquality \u30c7\u30fc\u30bf\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n

\u3053\u308c\u306f\u30011973\u5e74\u306eNew York\u306e\u30aa\u30be\u30f3\u6fc3\u5ea6\u3068\u592a\u967d\u653e\u5c04\u3001\u98a8\u901f\u3001\u6c17\u6e29\u3001\u6708\u3001\u65e5\u306e\u30c7\u30fc\u30bf\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u3046\u3061\u3001\u30aa\u30be\u30f3\u6fc3\u5ea6\u3001\u98a8\u901f\u3001\u6c17\u6e29\u3092\u4f7f\u3046\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n\n\n\n

air1 <-<\/span> airquality[,<\/span>c<\/span>(<\/span>1<\/span>,<\/span>3<\/span>,<\/span>4<\/span>)]<\/span>\npairs<\/span>(<\/span>air1)<\/span>\n<\/code><\/pre>\n\n\n\n
pairs()\u3092\u4f7f\u3046\u3068\u3001\u3044\u3063\u307a\u3093\u306b\u305f\u304f\u3055\u3093\u306e\u5909\u6570\u540c\u58eb\u306e\u6563\u5e03\u56f3\u304c\u63cf\u3051\u308b\u3002<\/p>\n\n\n\n
Ozone \u3068 Wind, Ozone \u3068 Temp\u3001Wind\u3068Temp\u306e\u4e09\u3064\u306e\u6563\u5e03\u56f3\u3092X\u3068Y\u3092\u5909\u3048\u3066\u30012\u30bb\u30c3\u30c8\u63cf\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
pairs<\/span>(<\/span>air1,<\/span>lower.panel=<\/span>NULL<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
lower.panel=NULL \u3082\u3057\u304f\u306f upper.panel=NULL \u3092\u4f7f\u3046\u3068\u3001\u4e0b\u534a\u5206\u307e\u305f\u306f\u4e0a\u534a\u5206\u306e\u30b0\u30e9\u30d5\u3092\u6d88\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u6700\u521d\u306e\u5909\u6570\u3001\u4eca\u56de\u306f\u30aa\u30be\u30f3\u6fc3\u5ea6\u3001\u3068\u306e\u95a2\u4fc2\u3092\u4e2d\u5fc3\u7684\u306b\u898b\u305f\u3044\u306e\u3067\u3001\u4e0b\u534a\u5206\u3092\u6d88\u3057\u3066\u4e0a\u534a\u5206\u3060\u3051\u306b\u3059\u308b\u3068\u898b\u3084\u3059\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u3046\u3084\u3063\u3066\u8a08\u7b97\u3059\u308b\u304b\uff1f<\/h2>\n\n\n\n
R\u306e\u95a2\u6570\u3092\u4f7f\u3046\u5834\u5408<\/h3>\n\n\n\n
R\u3067\u306fcor()\u3092\u4f7f\u3046\u3068\u3001\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u6b20\u640d\u5024 NA \u304c\u3042\u308b\u5834\u5408\u306f\u3001use=\u3067\u8abf\u6574\u3059\u308b\u3002<\/p>\n\n\n\n
\u30da\u30a2\u3067NA\u3092\u524a\u9664\u3057\u3066\u8a08\u7b97\u3059\u308b\u5834\u5408\u306f pairwise.complete.obs \u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
\u3059\u3079\u3066\u306e\u5909\u6570\u3067\u3001NA\u304c\u4e00\u3064\u3067\u3082\u3042\u308b\u30c7\u30fc\u30bf\u884c\u306f\u524a\u9664\u3059\u308b\u5834\u5408\u306f complete.obs \u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
cor<\/span>(<\/span>air1,<\/span>use=<\/span>\"pairwise.complete.obs\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u53f3\u4e0a\u306b\u5411\u304b\u3063\u3066\u3044\u308b\u30d7\u30ed\u30c3\u30c8\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u30d7\u30e9\u30b9\u306e\u5024\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\uff08Ozone\u3068Temp\u306a\u3069\uff09\u3002<\/p>\n\n\n\n
\u53f3\u4e0b\u306b\u5411\u304b\u3063\u3066\u3044\u308b\u30d7\u30ed\u30c3\u30c8\u306e\u5834\u5408\u306f\u30de\u30a4\u30ca\u30b9\u306e\u5024\u3060\uff08Ozone\u3068Wind\u306a\u3069\uff09<\/p>\n\n\n\n
> cor(air1,use=\"pairwise.complete.obs\")\n           Ozone       Wind       Temp\nOzone  1.0000000 -0.6015465  0.6983603\nWind  -0.6015465  1.0000000 -0.4579879\nTemp   0.6983603 -0.4579879  1.0000000<\/code><\/pre>\n\n\n\n
\u76f8\u95a2\u4fc2\u6570\u3092Step by step\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u4e8c\u3064\u306e\u5909\u6570X\u3068Y\u306e\u5171\u5909\u52d5\u3092X\u3068Y\u306e\u5909\u52d5\u306e\u5e73\u65b9\u6839\u3067\u5272\u308b\u3068\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u5909\u52d5\u306f\u5e73\u5747\u3068\u306e\u5dee\u3092\u4e8c\u4e57\u3057\u305f\u3082\u306e\u306e\u5408\u8a08\u3002<\/p>\n\n\n\n
\u5171\u5909\u52d5\u306fX\u306e\u5e73\u5747\u3068\u306e\u5dee\u3068Y\u306e\u5e73\u5747\u3068\u306e\u5dee\u3092\u4e8c\u4e57\u305b\u305a\u306b\u639b\u3051\u5408\u308f\u305b\u305f\u3082\u306e\u306e\u5408\u8a08\u3002<\/p>\n\n\n\n
X\u306e\u5909\u52d5\u3068Y\u306e\u5909\u52d5\u304c\u307e\u3063\u305f\u304f\u540c\u3058\u306a\u3089\u3001\u5171\u5909\u52d5\u3082\u540c\u4e00\u306b\u306a\u308a\u3001\u5272\u308b\u30681\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
X\u3068Y\u304c\u771f\u9006\u306a\u3089\u3001\u5171\u5909\u52d5\u306f\u7b26\u53f7\u304c\u9006\u306b\u306a\u308a\u3001\uff0d1\u3068\u306a\u308b\u3002<\/p>\n\n\n\n
\u901a\u5e38\u306f\u3001\uff0d1\u30681\u306e\u4e2d\u9593\u306b\u306a\u308b\u3002\u3053\u308c\u304c\u76f8\u95a2\u4fc2\u6570\u3060\u3002<\/p>\n\n\n\n
airquality \u30c7\u30fc\u30bf\u306e Wind \u3068 Temp \u306e\u76f8\u95a2\u4fc2\u6570\u3092\u95a2\u6570\u3092\u4f7f\u308f\u305a\u306b\u6c42\u3081\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
Wind <-<\/span> air1$<\/span>Wind\nTemp <-<\/span> air1$<\/span>Temp\nm.Wind <-<\/span> mean<\/span>(<\/span>air1$<\/span>Wind)<\/span>\nm.Temp <-<\/span> mean<\/span>(<\/span>air1$<\/span>Temp)<\/span>\nsum<\/span>((<\/span>Wind-<\/span>m.Wind)<\/span>*<\/span>(<\/span>Temp-<\/span>m.Temp))<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>Wind-<\/span>m.Wind)<\/span>^<\/span>2<\/span>))<\/span>*<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>Temp-<\/span>m.Temp)<\/span>^<\/span>2<\/span>)))<\/span>\n<\/code><\/pre>\n\n\n\n
cor()\u3092\u4f7f\u3063\u305f\u6642\u306e\u7d50\u679c\u884c\u5217\u306b\u304a\u3051\u308b\u3001Wind\u3068Temp\u306e\u4ea4\u70b9\u306e\u5024\u3068\u540c\u3058\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
><\/span> sum<\/span>((<\/span>Wind-<\/span>m.Wind)<\/span>*<\/span>(<\/span>Temp-<\/span>m.Temp))<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>Wind-<\/span>m.Wind)<\/span>^<\/span>2<\/span>))<\/span>*<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>Temp-<\/span>m.Temp)<\/span>^<\/span>2<\/span>)))<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.4579879<\/span>\n<\/code><\/pre>\n\n\n\n
\u504f\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u3046\u3084\u3063\u3066\u8a08\u7b97\u3059\u308b\u304b\uff1f<\/h2>\n\n\n\n
R\u306e\u95a2\u6570\u3092\u4f7f\u3046\u5834\u5408<\/h3>\n\n\n\n
ppcor \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u3002ppcor \u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u6700\u521d\u306e\u4e00\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u3066\u4f7f\u3046\u3002<\/p>\n\n\n\n
install.packages<\/span>(<\/span>\"ppcor\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
library()\u3067\u547c\u3073\u51fa\u3057\u3066\u304b\u3089\u4f7f\u7528\u3059\u308b\u3002<\/p>\n\n\n\n
\u504f\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u4e09\u3064\u306e\u5909\u6570\u3059\u3079\u3066\u6b20\u640d\u5024\u304c\u306a\u3044\u30c7\u30fc\u30bf\u884c\u3060\u3051\u306b\u9650\u3063\u3066\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
\u6b20\u640d\u5024\u304c\u3042\u308b\u3068\u8a08\u7b97\u304c\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>ppcor)<\/span>\nair2 <-<\/span> subset<\/span>(<\/span>air1,<\/span> complete.cases<\/span>(<\/span>air1))<\/span>\ncor<\/span>(<\/span>air2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u6b20\u640d\u5024\u304c\u306a\u3044\u30c7\u30fc\u30bf\u306b\u3059\u308b\u3068\u3001pairwise.complete.obs \u306e\u3068\u304d\u3068\u82e5\u5e72\u5024\u304c\u5909\u308f\u3063\u305f\u3002<\/p>\n\n\n\n
\u5927\u304d\u306a\u9055\u3044\u306f\u306a\u3044\u3002<\/p>\n\n\n\n
> cor(air2)\n           Ozone       Wind       Temp\nOzone  1.0000000 -0.6015465  0.6983603\nWind  -0.6015465  1.0000000 -0.5110750\nTemp   0.6983603 -0.5110750  1.0000000<\/code><\/pre>\n\n\n\n
pcor()\u3067\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
pcor<\/span>(<\/span>air2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
Ozone\u3068Wind\u3001Wind\u3068Temp\u306e\u76f8\u95a2\u4fc2\u6570\uff08$estimate\u306e\u884c\u5217\u3092\u898b\u308b\uff09\u306e\u7d76\u5bfe\u5024\u304c\u76f8\u5bfe\u7684\u306b\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
> pcor(air2)\n$estimate\n           Ozone       Wind       Temp\nOzone  1.0000000 -0.3976400  0.5693387\nWind  -0.3976400  1.0000000 -0.1591191\nTemp   0.5693387 -0.1591191  1.0000000\n\n$p.value\n             Ozone         Wind         Temp\nOzone 0.000000e+00 1.080046e-05 3.149109e-11\nWind  1.080046e-05 0.000000e+00 8.940196e-02\nTemp  3.149109e-11 8.940196e-02 0.000000e+00\n\n$statistic\n          Ozone      Wind      Temp\nOzone  0.000000 -4.606844  7.361793\nWind  -4.606844  0.000000 -1.713287\nTemp   7.361793 -1.713287  0.000000\n\n$n\n[1] 116\n\n$gp\n[1] 1\n\n$method\n[1] \"pearson\"\n<\/code><\/pre>\n\n\n\n
\u504f\u76f8\u95a2\u4fc2\u6570\u3092 Step by step\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
Temp\u3067\u8aac\u660e\u3067\u304d\u308b\u90e8\u5206\u3092\u9664\u3044\u305fOzone\u3068\u3001Temp\u3067\u8aac\u660e\u3067\u304d\u308b\u90e8\u5206\u3092\u9664\u3044\u305fWind\u3068\u306e\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001Temp\u306e\u5f71\u97ff\u3092\u9664\u3044\u305fOzone\u3068Wind\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
Temp2 <-<\/span> air2$<\/span>Temp\nOzone2 <-<\/span> air2$<\/span>Ozone\nWind2 <-<\/span> air2$<\/span>Wind\nrho.yz <-<\/span> cor<\/span>(<\/span>Ozone2,<\/span>Wind2)<\/span>\nrho.xy <-<\/span> cor<\/span>(<\/span>Temp2,<\/span>Ozone2)<\/span>\nrho.xz <-<\/span> cor<\/span>(<\/span>Temp2,<\/span>Wind2)<\/span>\n(<\/span>rho.yz -<\/span> rho.xy*<\/span>rho.xz)<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.xy^<\/span>2<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.xz^<\/span>2<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
Wind\u3068Ozone\u306e\u76f8\u95a2\u4fc2\u6570\u306f\u3082\u3068\u3082\u3068\u30fc0.602\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
Wind\u3082Ozone\u3082Temp\u3068\u76f8\u95a2\u304c\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
Wind\u3068Temp\u306e\u76f8\u95a2\u4fc2\u6570\u306f\u30fc0.511\u3001Ozone\u3068Temp\u306f0.698\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
Temp\u306e\u5f71\u97ff\u3092\u9664\u3044\u305fWind\u3068Ozone\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u306f\u3001\uff0d0.398\u306b\u306a\u308a\u3001\u7d76\u5bfe\u5024\u3067\u8003\u3048\u308c\u3070\u5c0f\u3055\u304f\u306a\u308a\u95a2\u9023\u304c\u5f31\u304f\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
\u6700\u521d\u306e\u30fc0.602\u306f\u898b\u304b\u3051\u306e\u5206\u304c\u542b\u307e\u308c\u3066\u3044\u3066\u3001Temp\u3068\u306e\u76f8\u95a2\u5206\u304c\u4e0a\u4e57\u305b\u3055\u308c\u3066\u3044\u305f\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
><\/span> (<\/span>rho.yz -<\/span> rho.xy*<\/span>rho.xz)<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.xy^<\/span>2<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.xz^<\/span>2<\/span>))<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.39764<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u5c40Ozone\u3068Temp\u304c\u3082\u3063\u3068\u3082\u5f37\u3044\u76f8\u95a2\u95a2\u4fc2\u3067\u3001Wind\u306e\u5f71\u97ff\u3092\u9664\u3044\u305fTemp\u3068Ozone\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u306f0.569\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u3093\u306a\u3068\u304d\u306b\u4f7f\u3046\u304b\uff1f<\/h2>\n\n\n\n
\u901a\u5e38\u3001\u76f8\u95a2\u4fc2\u6570\u3068\u8a00\u3063\u305f\u5834\u5408\u3001Pearson\uff08\u30d4\u30a2\u30bd\u30f3\uff09\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570\u3092\u8a00\u3063\u3066\u3044\u308b\u3002\u9023\u7d9a\u91cf\u3092\u305d\u306e\u307e\u307e\u9023\u7d9a\u91cf\u3068\u3057\u3066\u6271\u3046\u76f8\u95a2\u4fc2\u6570\u3060\u3002<\/p>\n\n\n\n
\u6563\u5e03\u56f3\u3092\u63cf\u3044\u3066\u307f\u305f\u6642\u306b\u3001\u76f4\u7dda\u306e\u95a2\u4fc2\u3067\u306f\u306a\u304f\u3001\u66f2\u7dda\u306e\u95a2\u4fc2\u306b\u898b\u3048\u308b\u3068\u304d\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u4eca\u56de\u306eOzone\u3068Wind\u3001Ozone\u3068Temp\u306e\u5834\u5408\u3082\u3001\u66f2\u7dda\u95a2\u4fc2\u306b\u898b\u3048\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u76f8\u95a2\u95a2\u4fc2\u304c\u76f4\u7dda\u3067\u306f\u306a\u3044\u5834\u5408\u306b\u3001\u3044\u3044\u65b9\u6cd5\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u6570\u5024\u3092\u9806\u5e8f\uff08\u9806\u4f4d\uff09\u306b\u7f6e\u304d\u63db\u3048\u3066\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3060\u3002<\/p>\n\n\n\n
\u9806\u4f4d\u3067\u3042\u308b\u3068\u3001\u76f4\u7dda\u7684\u306a\u95a2\u4fc2\u304b\u3069\u3046\u304b\u306f\u6c17\u306b\u3057\u306a\u304f\u3066\u3088\u3044\u3002<\/p>\n\n\n\n
Spearman\uff08\u30b9\u30d4\u30a2\u30de\u30f3\uff09\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3068\u8a00\u3046\u3002<\/p>\n\n\n\n
\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u4f7f\u3044\u305f\u3044\u5834\u5408\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u304b\uff1f<\/h2>\n\n\n\n
R\u306e\u95a2\u6570\u3092\u4f7f\u3046\u65b9\u6cd5<\/h3>\n\n\n\n
\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u5148\u307b\u3069\u3068\u540c\u3058cor()\u3092\u4f7f\u3048\u308b\u3002cor()\u306b\u3001method=”spearman”\u3092\u8ffd\u52a0\u3059\u308b\u3002<\/p>\n\n\n\n
cor<\/span>(<\/span>air2,<\/span>method=<\/span>\"spearman\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
Ozone\u3068Temp\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u4e0a\u8a18\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570\u306b\u6bd4\u3079\u3066\u9ad8\u3044\u5024\uff080.774\uff09\u3060\u3002<\/p>\n\n\n\n
\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306e\u307b\u3046\u304c\u3088\u308a\u9069\u5207\u306a\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n
> cor(air2,method=\"spearman\")\n           Ozone       Wind       Temp\nOzone  1.0000000 -0.5901551  0.7740430\nWind  -0.5901551  1.0000000 -0.5178411\nTemp   0.7740430 -0.5178411  1.0000000<\/code><\/pre>\n\n\n\n
\u504f\u76f8\u95a2\u4fc2\u6570\u3082\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
pcor()\u306b\u3001method=”spearman”\u3092\u8ffd\u52a0\u3059\u308b\u3002<\/p>\n\n\n\n
pcor<\/span>(<\/span>air2,<\/span> method=<\/span>\"spearman\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u3084\u306f\u308a\u3001Ozone\u3068Temp\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u306f\u3001\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570\u3088\u308a\u3082\u3001\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306e\u307b\u3046\u304c\u9ad8\u3044\uff080.678\uff09\u3002<\/p>\n\n\n\n
\u3053\u308c\u306f\u307e\u3059\u307e\u3059\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306e\u307b\u3046\u304c\u9069\u5207\u306a\u306e\u304b\u3082\u3068\u601d\u3048\u3066\u304d\u305f\u3002<\/p>\n\n\n\n
> pcor(air2, method=\"spearman\")\n$estimate\n           Ozone       Wind       Temp\nOzone  1.0000000 -0.3495442  0.6782860\nWind  -0.3495442  1.0000000 -0.1194151\nTemp   0.6782860 -0.1194151  1.0000000\n\n$p.value\n             Ozone         Wind         Temp\nOzone 0.000000e+00 0.0001286614 8.235308e-17\nWind  1.286614e-04 0.0000000000 2.036758e-01\nTemp  8.235308e-17 0.2036757725 0.000000e+00\n\n$statistic\n          Ozone      Wind      Temp\nOzone  0.000000 -3.965874  9.812601\nWind  -3.965874  0.000000 -1.278549\nTemp   9.812601 -1.278549  0.000000\n\n$n\n[1] 116\n\n$gp\n[1] 1\n\n$method\n[1] \"spearman\"<\/code><\/pre>\n\n\n\n
\u9806\u5e8f\u76f8\u95a2\u4fc2\u6570\u3092 Step by step\u3067\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/h3>\n\n\n\n
\u305d\u308c\u305e\u308c\u306e\u5024\u3092\u9806\u4f4d\u306b\u7f6e\u304d\u63db\u3048\u308b\u305f\u3081rank()\u3092\u4f7f\u3046\u3002\u305d\u3057\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u5e73\u5747\u5024\u3092\u8a08\u7b97\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n\n
r.Ozone <-<\/span> rank<\/span>(<\/span>air2$<\/span>Ozone)<\/span>\nr.Wind <-<\/span> rank<\/span>(<\/span>air2$<\/span>Wind)<\/span>\nr.Temp <-<\/span> rank<\/span>(<\/span>air2$<\/span>Temp)<\/span>\nm.r.Ozone <-<\/span> mean<\/span>(<\/span>r.Ozone)<\/span>\nm.r.Wind <-<\/span> mean<\/span>(<\/span>r.Wind)<\/span>\nm.r.Temp <-<\/span> mean<\/span>(<\/span>r.Temp)<\/span>\n<\/code><\/pre>\n\n\n\n
Ozone\u3068Temp\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
sum<\/span>((<\/span>r.Ozone-<\/span>m.r.Ozone)<\/span>*<\/span>(<\/span>r.Temp-<\/span>m.r.Temp))<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>r.Ozone-<\/span>m.r.Ozone)<\/span>^<\/span>2<\/span>))<\/span>*<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>r.Temp-<\/span>m.r.Temp)<\/span>^<\/span>2<\/span>)))<\/span>\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306fcor()\u306bmethod=”spearman”\u3092\u4f7f\u3063\u305f\u7d50\u679c\u3068\u540c\u3058\u3060\u3002<\/p>\n\n\n\n
><\/span> sum<\/span>((<\/span>r.Ozone-<\/span>m.r.Ozone)<\/span>*<\/span>(<\/span>r.Temp-<\/span>m.r.Temp))<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>r.Ozone-<\/span>m.r.Ozone)<\/span>^<\/span>2<\/span>))<\/span>*<\/span>sqrt<\/span>(<\/span>sum<\/span>((<\/span>r.Temp-<\/span>m.r.Temp)<\/span>^<\/span>2<\/span>)))<\/span>\n[<\/span>1<\/span>]<\/span> 0.774043<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e09\u3064\u306e\u5909\u6570\u305d\u308c\u305e\u308c\u540c\u58eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3057\u305f\u5f8c\u3001\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n
(<\/span>rho.r.WO <-<\/span> cor<\/span>(<\/span>r.Wind,<\/span>r.Ozone))<\/span>\n(<\/span>rho.r.WT <-<\/span> cor<\/span>(<\/span>r.Wind,<\/span>r.Temp))<\/span>\n(<\/span>rho.r.OT <-<\/span> cor<\/span>(<\/span>r.Ozone,<\/span>r.Temp))<\/span>\n<\/code><\/pre>\n\n\n\n
\u9806\u4f4d\u306b\u5909\u63db\u3057\u3066cor()\u3067\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001cor()\u306bmethod=”spearman”\u3092\u4f7f\u3063\u305f\u7d50\u679c\u3068\u540c\u3058\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> (<\/span>rho.r.WO <-<\/span> cor<\/span>(<\/span>r.Wind,<\/span>r.Ozone))<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.5901551<\/span>\n><\/span> (<\/span>rho.r.WT <-<\/span> cor<\/span>(<\/span>r.Wind,<\/span>r.Temp))<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.5178411<\/span>\n><\/span> (<\/span>rho.r.OT <-<\/span> cor<\/span>(<\/span>r.Ozone,<\/span>r.Temp))<\/span>\n[<\/span>1<\/span>]<\/span> 0.774043<\/span>\n<\/code><\/pre>\n\n\n\n
\u4eca\u56de\u306fOzone\u3068Temp\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u6c42\u3081\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
(<\/span>rho.r.OT-<\/span>rho.r.WO*<\/span>rho.r.WT)<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.r.WO^<\/span>2<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.r.WT^<\/span>2<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
pcor()\u306bmethod=”spearman”\u3092\u4f7f\u3063\u305f\u7d50\u679c\u3068\u540c\u3058\u306b\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> (<\/span>rho.r.OT-<\/span>rho.r.WO*<\/span>rho.r.WT)<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.r.WO^<\/span>2<\/span>)<\/span>*<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rho.r.WT^<\/span>2<\/span>))<\/span>\n[<\/span>1<\/span>]<\/span> 0.678286<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u76f8\u95a2\u4fc2\u6570\u3068\u504f\u76f8\u95a2\u4fc2\u6570\u306e\u9055\u3044\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u305f\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001R\u3067\u8a08\u7b97\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
cor()\u3068pcor()\u304c\u3042\u308a\u3001\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u95a2\u6570\u3092\u4f7f\u308f\u305a\u306b\u3001Step by step\u3067\u8a08\u7b97\u3082\u53ef\u80fd\u3060\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u6563\u5e03\u56f3\u3092\u63cf\u3044\u305f\u6642\u306b\u76f4\u7dda\u7684\u3067\u306a\u3044\u76f8\u95a2\u95a2\u4fc2\u306b\u898b\u3048\u305f\u5834\u5408\u306f\u3001\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8003\u616e\u3059\u308b\u3002<\/p>\n\n\n\n
method=”spearman”\u3092\u6307\u5b9a\u3059\u308c\u3070\u3001\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u504f\u76f8\u95a2\u4fc2\u6570\u3082\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
https:\/\/mathtrain.jp\/partialcor<\/a><\/p>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
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