{"id":3809,"date":"2023-07-15T09:50:14","date_gmt":"2023-07-15T09:50:14","guid":{"rendered":"https:\/\/statorials.org\/ja\/goldfeld-whent%e3%83%86%e3%82%b9%e3%83%88python\/"},"modified":"2023-07-15T09:50:14","modified_gmt":"2023-07-15T09:50:14","slug":"goldfeld-whent%e3%83%86%e3%82%b9%e3%83%88python","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/goldfeld-whent%e3%83%86%e3%82%b9%e3%83%88python\/","title":{"rendered":"Python \u3067 goldfeld-quandt \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Goldfeld-Quandt \u691c\u5b9a\u306f\u3001<\/strong>\u56de\u5e30\u30e2\u30c7\u30eb\u306b<a href=\"https:\/\/statorials.org\/ja\/\u4e0d\u5747\u4e00\u5206\u6563\u6027\u56de\u5e30\/\" target=\"_blank\" rel=\"noopener\">\u4e0d\u5747\u4e00\u5206\u6563\u6027<\/a>\u304c\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0d\u5747\u4e00\u5206\u6563\u6027\u3068\u306f\u3001\u56de\u5e30\u30e2\u30c7\u30eb\u306e<a href=\"https:\/\/statorials.org\/ja\/\u5909\u6570\u306e\u8aac\u660e\u5fdc\u7b54\/\" target=\"_blank\" rel=\"noopener\">\u5fdc\u7b54\u5909\u6570<\/a>\u306e\u3055\u307e\u3056\u307e\u306a\u30ec\u30d9\u30eb\u3067\u306e<a href=\"https:\/\/statorials.org\/ja\/\u6b8b\u57fa\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\u306e\u4e0d\u5747\u4e00\u306a\u5206\u6563\u3092\u6307\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0d\u5747\u4e00\u5206\u6563\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u5fdc\u7b54\u5909\u6570\u306e\u5404\u30ec\u30d9\u30eb\u3067\u6b8b\u5dee\u304c\u5747\u7b49\u306b\u5206\u6563\u3057\u3066\u3044\u308b\u3068\u3044\u3046<a href=\"https:\/\/statorials.org\/ja\/\u7dda\u5f62\u56de\u5e30\u306e\u4eee\u5b9a\/\" target=\"_blank\" rel=\"noopener\">\u7dda\u5f62\u56de\u5e30\u306e\u91cd\u8981\u306a\u4eee\u5b9a\u306e<\/a>1 \u3064\u306b\u9055\u53cd\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001Python \u3067 Goldfeld-Quandt \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u306e\u30b9\u30c6\u30c3\u30d7\u30d0\u30a4\u30b9\u30c6\u30c3\u30d7\u306e\u4f8b\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/span><\/p>\n<h2><strong>\u30b9\u30c6\u30c3\u30d7 1: \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b<\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4f8b\u3067\u306f\u3001\u30af\u30e9\u30b9\u306e 13 \u4eba\u306e\u751f\u5f92\u304c\u53d6\u5f97\u3057\u305f\u5b66\u7fd2\u6642\u9593\u3001\u53d7\u3051\u305f\u4e88\u5099\u8a66\u9a13\u3001\u304a\u3088\u3073\u6700\u7d42\u8a66\u9a13\u306e\u7d50\u679c\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u542b\u3080\u6b21\u306e\u30d1\u30f3\u30c0 \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u3092\u4f5c\u6210\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6],\n                   ' <span style=\"color: #ff0000;\">exams<\/span> ': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours exam score\n0 1 1 76\n1 2 3 78\n2 2 3 85\n3 4 5 88\n4 2 2 72\n5 1 2 69\n6 5 1 94\n7 4 1 94\n8 2 0 88\n9 4 3 92\n10 4 4 90\n11 3 3 75\n12 6 2 96<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 2: \u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001<strong>\u6642\u9593<\/strong>\u3068<strong>\u8a66\u9a13\u3092<\/strong>\u4e88\u6e2c\u5909\u6570\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001<strong>\u30b9\u30b3\u30a2\u3092<\/strong>\u5fdc\u7b54\u5909\u6570\u3068\u3057\u3066\u4f7f\u7528\u3057\u3066\u91cd\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define predictor and response variables\n<\/span>y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[[' <span style=\"color: #ff0000;\">hours<\/span> ', ' <span style=\"color: #ff0000;\">exams<\/span> ']]\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n\n<span style=\"color: #008080;\">#view model summary\n<\/span><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.718\nModel: OLS Adj. R-squared: 0.661\nMethod: Least Squares F-statistic: 12.70\nDate: Mon, 31 Oct 2022 Prob (F-statistic): 0.00180\nTime: 09:22:56 Log-Likelihood: -38.618\nNo. Observations: 13 AIC: 83.24\nDf Residuals: 10 BIC: 84.93\nModel: 2                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 71.4048 4.001 17.847 0.000 62.490 80.319\nhours 5.1275 1.018 5.038 0.001 2.860 7.395\nexams -1.2121 1.147 -1.057 0.315 -3.768 1.344\n==================================================== ============================\nOmnibus: 1,103 Durbin-Watson: 1,248\nProb(Omnibus): 0.576 Jarque-Bera (JB): 0.803\nSkew: -0.289 Prob(JB): 0.669\nKurtosis: 1.928 Cond. No. 11.7\n==================================================== ============================\n<\/strong><\/span><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 3: Goldfeld-Quandt \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3059\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001 <strong>statsmodels<\/strong> <strong>het_goldfeldquandt()<\/strong>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001Goldfeld-Quandt \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6ce8<\/strong>: Goldfeld-Quandt \u30c6\u30b9\u30c8\u306f\u3001\u30c7\u30fc\u30bf \u30bb\u30c3\u30c8\u306e\u4e2d\u5fc3\u306b\u3042\u308b\u591a\u6570\u306e\u89b3\u6e2c\u5024\u3092\u524a\u9664\u3057\u3001\u6b8b\u5dee\u306e\u5206\u5e03\u304c\u3001\u4e2d\u592e\u306e\u89b3\u6e2c\u5024\u306e\u4e21\u5074\u306b\u7d50\u5408\u3059\u308b 2 \u3064\u306e\u7d50\u679c\u306e\u30c7\u30fc\u30bf \u30bb\u30c3\u30c8\u3068\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u3092\u30c6\u30b9\u30c8\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u901a\u5e38\u3001\u5408\u8a08\u89b3\u6e2c\u5024\u306e\u7d04 20% \u3092\u524a\u9664\u3059\u308b\u3053\u3068\u3092\u9078\u629e\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001 <strong>drop<\/strong>\u5f15\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u89b3\u6e2c\u5024\u306e 20% \u3092\u524a\u9664\u3059\u308b\u3053\u3068\u3092\u6307\u5b9a\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Goldfeld-Quandt test\n<\/span>sm. <span style=\"color: #3366ff;\">stats<\/span> . <span style=\"color: #3366ff;\">diagnosis<\/span> . <span style=\"color: #3366ff;\">het_goldfeldquandt<\/span> (y, x, drop= <span style=\"color: #008000;\">0.2<\/span> )\n\n(1.7574505407790355, 0.38270288684680076, 'increasing')<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u7d50\u679c\u3092\u89e3\u91c8\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u691c\u5b9a\u7d71\u8a08\u91cf\u306f<b>1.757<\/b>\u3067\u3059\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\">\u5bfe\u5fdc\u3059\u308b p \u5024\u306f<strong>0.383<\/strong>\u3067\u3059\u3002<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Goldfeld-Quandt \u691c\u5b9a\u3067\u306f\u3001\u6b21\u306e\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Null (H <sub>0<\/sub> )<\/strong> : \u7b49\u5206\u6563\u6027\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u4ee3\u66ff ( <sub>HA<\/sub> ):<\/strong>\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">p \u5024\u306f 0.05 \u672a\u6e80\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u307e\u305b\u3093\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u554f\u984c\u3067\u3042\u308b\u3068\u4e3b\u5f35\u3059\u308b\u5341\u5206\u306a\u8a3c\u62e0\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n<h2><strong>\u6b21\u306f\u3069\u3046\u3059\u308b<\/strong><\/h2>\n<p><span style=\"color: #000000;\">Goldfeld-Quandt \u691c\u5b9a\u306e\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u306a\u304b\u3063\u305f\u5834\u5408\u3001\u4e0d\u5747\u4e00\u5206\u6563\u6027\u306f\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u3001\u5143\u306e\u56de\u5e30\u306e\u7d50\u679c\u306e\u89e3\u91c8\u306b\u9032\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3060\u3057\u3001\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3057\u305f\u5834\u5408\u306f\u3001\u30c7\u30fc\u30bf\u306b\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u56de\u5e30\u51fa\u529b\u30c6\u30fc\u30d6\u30eb\u306b\u8868\u793a\u3055\u308c\u308b\u6a19\u6e96\u8aa4\u5dee\u306f\u4fe1\u983c\u3067\u304d\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u304c\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u5fdc\u7b54\u5909\u6570\u3092\u5909\u63db\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5fdc\u7b54\u5909\u6570\u306b\u5bfe\u3057\u3066\u5909\u63db\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u5fdc\u7b54\u5909\u6570\u306e<a href=\"https:\/\/statorials.org\/ja\/python\u3066\u3099\u30c6\u3099\u30fc\u30bf\u3092\u5909\u63db\u3059\u308b\/\" target=\"_blank\" rel=\"noopener\">\u5bfe\u6570\u3001\u5e73\u65b9\u6839\u3001\u7acb\u65b9\u6839\u3092<\/a>\u53d6\u5f97\u3057\u307e\u3059\u3002\u4e00\u822c\u306b\u3001\u3053\u308c\u306b\u3088\u308a\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u6d88\u5931\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u91cd\u307f\u4ed8\u3051\u56de\u5e30\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91cd\u307f\u4ed8\u304d\u56de\u5e30\u3067\u306f\u3001\u8fd1\u4f3c\u5024\u306e\u5206\u6563\u306b\u57fa\u3065\u3044\u3066\u5404\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306b\u91cd\u307f\u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u307e\u3059\u3002\u57fa\u672c\u7684\u306b\u3001\u3053\u308c\u306b\u3088\u308a\u3001\u5206\u6563\u304c\u5927\u304d\u3044\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306b\u4f4e\u3044\u91cd\u307f\u304c\u4e0e\u3048\u3089\u308c\u3001\u6b8b\u5dee\u4e8c\u4e57\u304c\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9069\u5207\u306a\u91cd\u307f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u91cd\u307f\u4ed8\u304d\u56de\u5e30\u306b\u3088\u3063\u3066\u4e0d\u5747\u4e00\u5206\u6563\u6027\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001Python \u3067\u4ed6\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/ja\/ols\u56de\u5e30python\/\" target=\"_blank\" rel=\"noopener\">Python \u3067 OLS \u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/python\u6b8b\u5dee\u30af\u3099\u30e9\u30d5\/\" target=\"_blank\" rel=\"noopener\">Python \u3067\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/python\u306e\u30db\u30ef\u30a4\u30c8\u30c6\u30b9\u30c8\/\">Python \u3067 White \u306e\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/\u30d5\u3099\u30eb\u30fc\u30b7\u30e5\u7570\u6559\u306e\u30c6\u30b9\u30c8-python\/\" target=\"_blank\" rel=\"noopener\">Python \u3067 Breusch-Pagan \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Goldfeld-Quandt \u691c\u5b9a\u306f\u3001\u56de\u5e30\u30e2\u30c7\u30eb\u306b\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 \u4e0d\u5747\u4e00\u5206\u6563\u6027\u3068\u306f\u3001\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5fdc\u7b54\u5909\u6570\u306e\u3055\u307e\u3056\u307e\u306a\u30ec\u30d9\u30eb\u3067\u306e\u6b8b\u5dee\u306e\u4e0d\u5747\u4e00\u306a\u5206\u6563\u3092\u6307\u3057\u307e\u3059\u3002 \u4e0d\u5747\u4e00\u5206\u6563\u304c\u5b58 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-3809","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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