{"id":2449,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"sst-ssr-sse-in-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/","title":{"rendered":"Come calcolare sst, ssr e sse in python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Utilizziamo spesso tre diversi valori <a href=\"https:\/\/statorials.org\/it\/sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">di somma dei quadrati<\/a> per misurare quanto bene una <a href=\"https:\/\/statorials.org\/it\/regressione-lineare-1\/\" target=\"_blank\" rel=\"noopener\">linea di regressione<\/a> si adatta a un insieme di dati:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Somma dei quadrati totali (SST) \u2013<\/strong> La somma dei quadrati delle differenze tra i singoli punti dati (y <sub>i<\/sub> ) e la media della variabile di risposta ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/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. Regressione della somma dei quadrati (SSR)<\/strong> \u2013 La somma dei quadrati delle differenze tra i punti dati previsti (\u0177 <sub>i<\/sub> ) e la media della variabile di risposta ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/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. Errore della somma dei quadrati (SSE)<\/strong> \u2013 La somma dei quadrati delle differenze tra i punti dati previsti (\u0177 <sub>i<\/sub> ) e i punti dati osservati (y <sub>i<\/sub> ).<\/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;\">Il seguente esempio passo passo mostra come calcolare ciascuno di questi parametri per un dato modello di regressione in Python.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Passaggio 1: creare i dati<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Innanzitutto, creiamo un set di dati contenente il numero di ore studiate e i punteggi degli esami ottenuti per 20 studenti diversi in una determinata universit\u00e0:<\/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>Passaggio 2: adattare un modello di regressione<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Successivamente, utilizzeremo la funzione <strong>OLS()<\/strong> della libreria <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> per adattare un semplice modello di regressione lineare utilizzando il punteggio come variabile di risposta e le ore come variabile predittrice:<\/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>Passaggio 3: calcolare SST, SSR e SSE<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Infine, possiamo utilizzare le seguenti formule per calcolare i valori SST, SSR e SSE del modello:<\/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;\">Le metriche risultano essere:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Somma totale dei quadrati (SST):<\/strong> 1248,55<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Regressione della somma dei quadrati (SSR):<\/strong> 917.4751<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Errore somma dei quadrati (SSE):<\/strong> 331.0749<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Possiamo verificare che SST = SSR + SSE:<\/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>Risorse addizionali<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u00c8 possibile utilizzare i seguenti calcolatori per calcolare automaticamente SST, SSR e SSE per qualsiasi linea di regressione lineare semplice:<\/span><\/p>\n<ul>\n<li> Calcolatore SST<\/li>\n<li> Calcolatore RSS<\/li>\n<li> Calcolatore ESS<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">I seguenti tutorial spiegano come calcolare SST, SSR e SSE in altri software statistici:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-r\/\" target=\"_blank\" rel=\"noopener\">Come calcolare SST, SSR e SSE in R<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-excel\/\" target=\"_blank\" rel=\"noopener\">Come calcolare SST, SSR e SSE in Excel<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Utilizziamo spesso tre diversi valori di somma dei quadrati per misurare quanto bene una linea di regressione si adatta a un insieme di dati: 1. Somma dei quadrati totali (SST) \u2013 La somma dei quadrati delle differenze tra i singoli punti dati (y i ) e la media della variabile di risposta ( y ). [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Come calcolare SST, SSR e SSE in Python - Statorials<\/title>\n<meta name=\"description\" content=\"Questo tutorial spiega come calcolare varie somme di quadrati per un modello di regressione in Python, inclusi SST, SSR e SSE.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Come calcolare SST, SSR e SSE in Python - Statorials\" \/>\n<meta property=\"og:description\" content=\"Questo tutorial spiega come calcolare varie somme di quadrati per un modello di regressione in Python, inclusi SST, SSR e SSE.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-22T05:51:57+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuti\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/\",\"url\":\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/\",\"name\":\"Come calcolare SST, SSR e SSE in Python - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/it\/#website\"},\"datePublished\":\"2023-07-22T05:51:57+00:00\",\"dateModified\":\"2023-07-22T05:51:57+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/it\/#\/schema\/person\/0896f191fb9fb019f2cd8623112cb3ae\"},\"description\":\"Questo tutorial spiega come calcolare varie somme di quadrati per un modello di regressione in Python, inclusi SST, SSR e SSE.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/#breadcrumb\"},\"inLanguage\":\"it-IT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/it\/sst-ssr-sse-in-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Casa\",\"item\":\"https:\/\/statorials.org\/it\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Come calcolare sst, ssr e sse in python\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/it\/#website\",\"url\":\"https:\/\/statorials.org\/it\/\",\"name\":\"Statorials\",\"description\":\"La tua guida all&#039;alfabetizzazione statistica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/it\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"it-IT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/it\/#\/schema\/person\/0896f191fb9fb019f2cd8623112cb3ae\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"it-IT\",\"@id\":\"https:\/\/statorials.org\/it\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/it\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/it\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Ciao, sono Benjamin, un professore di statistica in pensione diventato insegnante dedicato di Statorials. 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