{"id":2446,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/ja\/python%e3%81%aesst-ssr-sse\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"python%e3%81%aesst-ssr-sse","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/python%e3%81%aesst-ssr-sse\/","title":{"rendered":"Python \u3067 sst\u3001ssr\u3001sse \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u7dda\u5f62\u56de\u5e30-1\/\" target=\"_blank\" rel=\"noopener\">\u56de\u5e30\u76f4\u7dda\u304c<\/a>\u4e00\u9023\u306e\u30c7\u30fc\u30bf\u306b\u3069\u306e\u7a0b\u5ea6\u9069\u5408\u3059\u308b\u304b\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u79c1\u305f\u3061\u306f\u3088\u304f 3 \u3064\u306e\u7570\u306a\u308b<a href=\"https:\/\/statorials.org\/ja\/sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">\u5e73\u65b9\u548c<\/a>\u5024\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u7dcf\u5e73\u65b9\u548c (SST) \u2013<\/strong>\u500b\u3005\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8 (y <sub>i<\/sub> ) \u3068\u5fdc\u7b54\u5909\u6570\u306e\u5e73\u5747 ( <span style=\"border-top: 1px solid black;\">y<\/span> ) \u306e\u9593\u306e\u5dee\u306e\u5e73\u65b9\u548c\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = \u03a3(y <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. \u4e8c\u4e57\u548c\u56de\u5e30 (SSR)<\/strong> \u2013 \u4e88\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\u70b9 (\u0177 <sub>i<\/sub> ) \u3068\u5fdc\u7b54\u5909\u6570\u306e\u5e73\u5747 ( <span style=\"border-top: 1px solid black;\">y<\/span> ) \u306e\u5dee\u306e\u4e8c\u4e57\u548c\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSR = \u03a3(\u0177 <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. \u4e8c\u4e57\u548c\u8aa4\u5dee (SSE)<\/strong> \u2013 \u4e88\u6e2c\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8 (\u0177 <sub>i<\/sub> ) \u3068\u89b3\u6e2c\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8 (y <sub>i<\/sub> ) \u306e\u5dee\u306e\u4e8c\u4e57\u548c\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>i<\/sub> \u2013 y <sub>i<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u30d0\u30a4\u30b9\u30c6\u30c3\u30d7\u306e\u4f8b\u306f\u3001Python \u3067\u7279\u5b9a\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3053\u308c\u3089\u306e\u5404\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 1: \u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u307e\u305a\u3001\u7279\u5b9a\u306e\u5927\u5b66\u306e 20 \u4eba\u306e\u7570\u306a\u308b\u5b66\u751f\u306e\u5b66\u7fd2\u6642\u9593\u6570\u3068\u53d6\u5f97\u3057\u305f\u8a66\u9a13\u306e\u30b9\u30b3\u30a2\u3092\u542b\u3080\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f5c\u6210\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#create pandas DataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 1, 1, 2, 2, 2, 2, 2, 3, 3,\n                             3, 4, 4, 4, 5, 5, 6, 7, 7, 8],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [68, 76, 74, 80, 76, 78, 81, 84, 86, 83,\n                             88, 85, 89, 94, 93, 94, 96, 89, 92, 97]})\n\n<span style=\"color: #008080;\">#view first five rows of DataFrame\n<\/span>df. <span style=\"color: #3366ff;\">head<\/span> ()\n\n\thours score\n0 1 68\n1 1 76\n2 1 74\n3 2 80\n4 2 76\n<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 2: \u56de\u5e30\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001 <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a>\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<strong>OLS()<\/strong>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u5fdc\u7b54\u5909\u6570\u3068\u3057\u3066\u30b9\u30b3\u30a2\u3001\u4e88\u6e2c\u5909\u6570\u3068\u3057\u3066\u6642\u9593\u3092\u4f7f\u7528\u3059\u308b\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <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 response variable\n<\/span>y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variable\n<\/span>x = df[[' <span style=\"color: #ff0000;\">hours<\/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<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 3: SST\u3001SSR\u3001SSE \u3092\u8a08\u7b97\u3059\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6700\u5f8c\u306b\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u30e2\u30c7\u30eb\u306e SST\u3001SSR\u3001SSE \u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#calculate\n<\/span>sse = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> ) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (sse)\n\n331.07488479262696\n\n<span style=\"color: #008080;\">#calculate ssr\n<\/span>ssr = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> . <span style=\"color: #3366ff;\">mean<\/span> ()) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (ssr)\n\n917.4751152073725\n\n<span style=\"color: #008080;\">#calculate sst\n<\/span>sst = ssr + sse\n<span style=\"color: #008000;\">print<\/span> (sst)\n\n1248.5499999999995\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6307\u6a19\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u7dcf\u4e8c\u4e57\u548c (SST):<\/strong> 1248.55<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u4e8c\u4e57\u548c\u56de\u5e30 (SSR):<\/strong> 917.4751<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u4e8c\u4e57\u548c\u8aa4\u5dee (SSE):<\/strong> 331.0749<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE \u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/li>\n<li> <span style=\"color: #000000;\">1248.55 = 917.4751 + 331.0749<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #000000;\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u4efb\u610f\u306e\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u76f4\u7dda\u306e SST\u3001SSR\u3001\u304a\u3088\u3073 SSE \u3092\u81ea\u52d5\u7684\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li> SST\u8a08\u7b97\u6a5f<\/li>\n<li>RSS\u8a08\u7b97\u6a5f<\/li>\n<li>ESS\u8a08\u7b97\u6a5f<\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001\u4ed6\u306e\u7d71\u8a08\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3067 SST\u3001SSR\u3001\u304a\u3088\u3073 SSE \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/ja\/sst-ssr-sse-in-r\/\" target=\"_blank\" rel=\"noopener\">R \u3067 SST\u3001SSR\u3001SSE \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/ja\/excel\u306esst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">Excel \u3067 SST\u3001SSR\u3001SSE \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u56de\u5e30\u76f4\u7dda\u304c\u4e00\u9023\u306e\u30c7\u30fc\u30bf\u306b\u3069\u306e\u7a0b\u5ea6\u9069\u5408\u3059\u308b\u304b\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u79c1\u305f\u3061\u306f\u3088\u304f 3 \u3064\u306e\u7570\u306a\u308b\u5e73\u65b9\u548c\u5024\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 1. \u7dcf\u5e73\u65b9\u548c (SST) \u2013\u500b\u3005\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8 (y i ) \u3068\u5fdc\u7b54\u5909\u6570\u306e\u5e73\u5747 ( y ) \u306e\u9593\u306e\u5dee\u306e [&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-2446","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO 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