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lineare","appliedCssClassNames":"summit-page",":type":"snowflake-site/components/structure/page"}],":type":"snowflake-site/components/breadcrumb"}},":itemsOrder":["breadcrumb"]},":type":"snowflake-site/components/flexible-column-container","isBlogPage":false,"isActiveTOC":false,"appliedCssClassNames":"snowflake-flexible-column-container-gray-10-bg"},"flexible_column_cont_939100716":{"id":"flexible-column-container-3f5fe1f245","propertiesId":"hub-hero","type":"2-column-even","alignColumns":"center","containerMaxWidth":"extra-large","topPadding":"extra-small","bottomPadding":"extra-small","spaceBetween":"small","reverseOnMobile":false,"carouselOnMobile":false,"propertiesCSSClasses":"page-section","backgroundImageOption":"none","flexible_column_content_container_1":{"layout":"SIMPLE","id":"container-d36e333730","appliedCssClassNames":"snowflake-responsive-container-inner-padding-extra-small",":type":"snowflake-site/components/flexible-column-container/flexible-column-content-container",":items":{"title_v2":{"id":"title-v2-9617de7b71","additionalClasses":"hub-hero__headline","type":"heading1","lines":["Regressione lineare: il modello semplice alla base di previsioni più intelligenti"],":type":"snowflake-site/components/title-v2","appliedCssClassNames":"left-alignment"},"text":{"id":"text-1a803ab00e","additionalClasses":"hub-hero__subheadline","text":"\u003Cp\u003EComprendi i fondamenti della regressione lineare, dall’equazione di base ai tipi di modello e alle applicazioni più comuni.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-size-regular text-color-text-05"},"container":{"additionalClasses":"hub-hero__authors","layout":"RESPONSIVE_GRID","columnCount":12,"columnClassNames":{"content_chip":"aem-GridColumn aem-GridColumn--default--12"},"gridClassNames":"aem-Grid aem-Grid--12 aem-Grid--default--12","id":"container-06239f7428","appliedCssClassNames":"snowflake-responsive-container-inner-padding-small",":type":"snowflake-site/components/container",":items":{"content_chip":{"id":"content-chip-599e354738","cta":{"id":"cta","showOutboundIcon":false,"linkTargetContentType":"GENERIC",":type":"snowflake-site/components/button","linkType":"SNOWFLAKE_INTERNAL","text":"Leggi la bio"},"image":{"id":"image","height":"4000","src":"/adobe/dynamicmedia/deliver/dm-aid--8791b148-4d4d-45eb-ab23-aa864d47baf9/will-heany-snowflake.jpg?quality=85&preferwebp=true","lazyEnabled":true,"alt":"Will Heany","isLcpImage":false,"width":"2667",":type":"snowflake-site/components/image"},"headline":{"id":"title","type":"heading5","lines":["Will Heany","Content Manager, Snowflake"],":type":"snowflake-site/components/title-v2"},":type":"snowflake-site/components/content-chip"}},":itemsOrder":["content_chip"]}},":itemsOrder":["title_v2","text","container"]},"flexible_column_content_container_2":{"additionalClasses":"hub-hero__video-column","layout":"SIMPLE","id":"container-7ee4d18a75",":type":"snowflake-site/components/flexible-column-container/flexible-column-content-container",":items":{"youtube":{"id":"embed-86c7e520d1","youtubeVideoId":"JDMEUrwpYlE","layout":"responsive","youtubeAspectRatio":"56.25","youtubeAutoPlay":false,"youtubeLoop":false,"youtubeMute":false,"youtubePlaysInline":false,"youtubeRel":false,"embeddableResourceType":"core/wcm/components/embed/v1/embed/embeddable/youtube","isLcpImage":true,"type":"EMBEDDABLE",":type":"snowflake-site/components/youtube"}},":itemsOrder":["youtube"]},":type":"snowflake-site/components/flexible-column-container","isBlogPage":false,"isActiveTOC":false,"appliedCssClassNames":"snowflake-flexible-column-container-gray-10-bg"},"flexible_column_cont_1398138236":{"id":"flexible-column-container-8cc5fc12a4","propertiesId":"hub-hero-related-topics","type":"1-column","alignColumns":"top","containerMaxWidth":"extra-large","topPadding":"extra-small","bottomPadding":"medium","spaceBetween":"small","reverseOnMobile":false,"carouselOnMobile":false,"propertiesCSSClasses":"page-section","backgroundImageOption":"none","flexible_column_content_container_1":{"additionalClasses":"related-topics-outer-container border-top","layout":"SIMPLE","id":"container-42db8bff5c",":type":"snowflake-site/components/flexible-column-container/flexible-column-content-container",":items":{"text_894059747":{"id":"text-f1c05c861c","additionalClasses":"seo-hub-hero__related-topic-label","text":"\u003Cp\u003EApprofondimenti sul modello ML:\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-size-regular text-color-text-05"},"text":{"id":"text-f12f7f02f2","additionalClasses":"related-topics ","text":"\u003Cul\u003E\n\u003Cli\u003E\u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/decision-tree/\"\u003EAlberi decisionali\u003C/a\u003E\u003C/li\u003E\n\u003Cli\u003E\u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/random-forest/\"\u003EForesta casuale\u003C/a\u003E\u003C/li\u003E\n\u003Cli\u003E\u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/regression/\"\u003EModelli di regressione\u003C/a\u003E\u003C/li\u003E\n\u003Cli\u003E\u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/support-vector-machine/\"\u003EMacchina a vettori di supporto (SVM)\u003C/a\u003E\u003C/li\u003E\n\u003C/ul\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-size-small"}},":itemsOrder":["text_894059747","text"]},":type":"snowflake-site/components/flexible-column-container","isBlogPage":false,"isActiveTOC":false,"appliedCssClassNames":"snowflake-flexible-column-container-gray-10-bg"},"flexible_column_cont_663228916":{"id":"flexible-column-container-83e46f3564","propertiesId":"hub-body","type":"2-column-60-40","alignColumns":"top","containerMaxWidth":"extra-large","topPadding":"medium","bottomPadding":"medium","spaceBetween":"small","reverseOnMobile":false,"carouselOnMobile":false,"propertiesCSSClasses":"page-section","backgroundImageOption":"none","flexible_column_content_container_1":{"additionalClasses":"longform-content","layout":"SIMPLE","id":"hub-body-content","appliedCssClassNames":"snowflake-responsive-container-inner-padding-medium",":type":"snowflake-site/components/flexible-column-container/flexible-column-content-container",":items":{"callout__0":{"id":"text-3ee324f5f1","additionalClasses":"callout callout--general","text":"\u003Cp\u003E\u003Cb\u003EREGRESSIONE LINEARE: LA DEFINIZIONE\u003C/b\u003E\u003C/p\u003E\n\u003Cp\u003ELa regressione lineare è una tecnica per stimare in che modo un insieme di fattori di input determina un risultato numerico, espresso mediante un’unica equazione lineare calibrata sui dati osservati. È apprezzata perché è veloce, facile da spiegare e affidabile quando le relazioni sottostanti sono approssimativamente proporzionali.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-size-regular text-color-text-05"},"text":{"id":"text-4030aa6471","text":"\u003Cp\u003ELa regressione lineare è un metodo statistico fondamentale per modellare le relazioni tra variabili indipendenti e dipendenti. Comprendere come una variabile ne influenzi un’altra consente di prevedere i risultati quando diventano disponibili nuovi dati.\u003C/p\u003E\n\u003Cp\u003EAd esempio, la regressione lineare può determinare l’impatto della superficie di un’abitazione sui prezzi immobiliari o l’influenza del budget pubblicitario di un’azienda sulle vendite di un prodotto. In entrambi i casi, la regressione lineare trasforma gli schemi osservati in passato in previsioni pratiche per il futuro. Di conseguenza, rappresenta un \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/\"\u003Emodello di machine learning\u003C/a\u003E fondamentale e svolge un ruolo chiave nell’analisi predittiva e nei processi decisionali basati sui dati.\u003C/p\u003E\n\u003Cp\u003EQuesta guida illustra i principi fondamentali della regressione lineare, i vantaggi e i limiti di questo metodo statistico e le modalità per applicarlo in diversi ambiti accademici e aziendali.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_what-is-linear-regression":{"id":"title-v2-0a79098f9b","additionalClasses":"anchor-title anchor-title--what-is-linear-regression","type":"heading2","lines":["Che cos’è la regressione lineare?"],":type":"snowflake-site/components/title-v2"},"text_what-is-linear-regression_0":{"id":"text-e9fd9d5075","text":"\u003Cp\u003ELa regressione lineare è un metodo statistico che determina la relazione tra una o più variabili indipendenti (predittori) e una variabile dipendente (risultato), adattando una retta ai data point. Riducendo al minimo la distanza tra la retta e tutti i data point, si ottiene la retta che rappresenta meglio gli schemi presenti nei dati. Questa “retta di migliore adattamento” può quindi essere utilizzata per prevedere risultati futuri man mano che vengono introdotti nuovi dati. È il modello di apprendimento supervisionato più semplice e costituisce il riferimento rispetto al quale vengono valutati gli altri approcci di regressione.\u003C/p\u003E\n\u003Cp\u003ECome suggerisce il nome, la regressione lineare presuppone una relazione lineare tra predittori e risultati. Quando la relazione tra le variabili è meno lineare, per formulare previsioni si utilizzano altre forme di analisi di regressione: \u003C/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELa \u003Cb\u003Eregressione polinomiale\u003C/b\u003E utilizza linee curve per rappresentare relazioni più complesse tra le variabili, ad esempio quando l’efficienza del carburante di un veicolo in movimento raggiunge il massimo a velocità moderate, ma diminuisce a velocità inferiori o superiori. \u003C/li\u003E\n\u003Cli\u003ELa \u003Cb\u003Eregressione logistica \u003C/b\u003Eserve a prevedere risultati binari, ad esempio se un paziente svilupperà il diabete o se una persona richiedente andrà in default sul proprio prestito. \u003C/li\u003E\n\u003Cli\u003ELa \u003Cb\u003Eregressione non lineare \u003C/b\u003Eriguarda relazioni che non possono essere approssimate mediante rette, come la crescita esponenziale dei batteri in una piastra di Petri o la velocità di decadimento dei materiali radioattivi.\u003C/li\u003E\n\u003C/ul\u003E\n\u003Cp\u003ETutti questi metodi appartengono alla più ampia famiglia dei \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/regression/\"\u003Emodelli di regressione\u003C/a\u003E, di cui la regressione lineare è l’esempio fondamentale.\u003C/p\u003E\n\u003Cp\u003ELa regressione lineare continua a essere diffusa sia nella ricerca accademica sia nelle applicazioni aziendali perché è facile da interpretare, richiede una potenza di elaborazione minima e risolve efficacemente numerosi problemi concreti, dalla \u003Ca href=\"https://www.snowflake.com/en/fundamentals/sales-forecasting/\"\u003Eprevisione delle vendite\u003C/a\u003E alla valutazione del rischio.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_understanding-the-line-of-best-fit-in-linear-regression":{"id":"title-v2-82387dfdf0","additionalClasses":"anchor-title anchor-title--understanding-the-line-of-best-fit-in-linear-regression","type":"heading2","lines":["La retta di migliore adattamento nella regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_understanding-the-line-of-best-fit-in-linear-regression_0":{"id":"text-37368f7252","text":"\u003Cp\u003ELa retta di migliore adattamento (o linea di regressione) è la retta che si avvicina maggiormente a tutti i data point. Una volta individuata, fornisce i valori della pendenza (l’angolo della retta) e dell’intercetta (il punto in cui la retta interseca l’asse y) che rappresentano con maggiore precisione le relazioni tra le variabili dei dati.\u003C/p\u003E\n\u003Cp\u003ELa retta di migliore adattamento viene generata mediante il metodo dei “minimi quadrati”. Innanzitutto, un algoritmo misura la distanza verticale tra una retta proposta e ciascun data point. Ognuno di questi valori numerici viene elevato al quadrato per eliminare i numeri negativi che potrebbero distorcere i risultati e per contribuire ad attribuire un peso maggiore ai data point più lontani dalla retta. Tutti i valori al quadrato vengono quindi sommati.\u003C/p\u003E\n\u003Cp\u003EL’algoritmo verifica più rette in questo modo finché non ne trova una che produce la somma dei quadrati più bassa, ossia il “migliore adattamento” per ridurre al minimo la differenza tra le previsioni del modello e i valori effettivi.\u003C/p\u003E\n\u003Cp\u003ENella pratica, raramente il software valuta le rette candidate una alla volta. Per i set di dati più piccoli, i coefficienti ottimali possono essere calcolati direttamente in un unico passaggio. Per quelli più grandi, la ricerca viene eseguita tramite la \u003Ca href=\"https://www.snowflake.com/en/artificial-intelligence/machine-learning/model-training/gradient-descent/\"\u003Ediscesa del gradiente\u003C/a\u003E, che segue la pendenza della superficie di errore verso la somma più bassa anziché campionare rette in modo casuale.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_how-linear-regression-is-used":{"id":"title-v2-27d664eba4","additionalClasses":"anchor-title anchor-title--how-linear-regression-is-used","type":"heading2","lines":["Come si usa la regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_how-linear-regression-is-used_0":{"id":"text-ce1b1c5988","text":"\u003Cp\u003ELa regressione lineare trova decine di applicazioni pratiche nel mondo aziendale. Ecco alcuni dei casi d’uso più comuni:\u003C/p\u003E\r\n\u003Ch3\u003EFinance: valutare il rischio\u003C/h3\u003E\r\n\u003Cp\u003ELe banche utilizzano la regressione lineare per prevedere il rischio di default sui prestiti analizzando fattori come il reddito, la storia creditizia, il rapporto debito-reddito e la stabilità lavorativa. Questo consente agli istituti di credito di determinare tassi di interesse adeguati e prendere decisioni informate sull’approvazione dei prestiti.\u003C/p\u003E\r\n\u003Ch3\u003ESanità: prevedere gli esiti di salute per i pazienti\u003C/h3\u003E\r\n\u003Cp\u003EGli ospedali utilizzano la regressione lineare per prevedere i tempi di recupero dei pazienti o l’efficacia dei trattamenti in base a variabili come età, patologie preesistenti e dosaggi dei farmaci. Ciò consente di definire \u003Ca href=\"https://www.snowflake.com/en/customers/all-customers/case-study/nyc-health/\"\u003Epiani terapeutici personalizzati\u003C/a\u003E e allocare con maggiore precisione le risorse per l’assistenza ai pazienti.\u003C/p\u003E\r\n\u003Ch3\u003EMarketing: prevedere le vendite\u003C/h3\u003E\r\n\u003Cp\u003ELe aziende prevedono le vendite future analizzando i dati storici insieme a fattori come la spesa pubblicitaria, la stagionalità, le variazioni dei prezzi e le condizioni economiche. Queste previsioni orientano la gestione dell’inventario, l’allocazione del budget e la pianificazione strategica nei diversi trimestri.\u003C/p\u003E\r\n\u003Ch3\u003EOperations: ottimizzare la supply chain\u003C/h3\u003E\r\n\u003Cp\u003ELe aziende manifatturiere utilizzano la regressione lineare per prevedere la domanda in base ai modelli storici di vendita, alle tendenze stagionali e agli indicatori economici. Ciò consente di mantenere livelli ottimali di inventario, riducendo i costi di mantenimento e prevenendo le rotture di stock.\u003C/p\u003E\r\n\u003Ch3\u003ESettore immobiliare: determinare il valore degli immobili\u003C/h3\u003E\r\n\u003Cp\u003ELe piattaforme immobiliari prevedono i prezzi delle abitazioni mediante modelli di regressione lineare che includono superficie, numero di camere da letto e bagni, posizione, età dell’immobile e condizioni del mercato locale. In questo modo, acquirenti, venditori e istituti di credito ricevono indicazioni sui prezzi basate sui dati.\u003C/p\u003E\r\n\u003Ch3\u003ERisorse umane: confrontare le retribuzioni\u003C/h3\u003E\r\n\u003Cp\u003ELe organizzazioni determinano retribuzioni competitive modellando la relazione tra lo stipendio e fattori come gli anni di esperienza, il livello di istruzione, il ruolo professionale, la posizione geografica e le dimensioni dell’azienda. Questo favorisce strutture retributive eque, capaci di attrarre e trattenere talenti rispettando al contempo i vincoli di budget.\u003C/p\u003E\r\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_why-is-linear-regression-important-to-machine-learning":{"id":"title-v2-6949f13067","additionalClasses":"anchor-title anchor-title--why-is-linear-regression-important-to-machine-learning","type":"heading2","lines":["Perché la regressione lineare è importante per il machine learning?"],":type":"snowflake-site/components/title-v2"},"text_why-is-linear-regression-important-to-machine-learning_0":{"id":"text-83106730e9","text":"\u003Cp\u003ELa regressione lineare occupa una posizione strategica unica nel \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/\"\u003Emachine learning\u003C/a\u003E. È al tempo stesso uno strumento pratico per risolvere problemi quotidiani e una base concettuale per comprendere algoritmi più sofisticati.\u003C/p\u003E\n\u003Cp\u003EUno dei maggiori vantaggi strategici del metodo è la capacità di quantificare le relazioni nei dati, mostrando con precisione in che modo ciascuna variabile influenza il risultato. Ciò lo rende indispensabile per le organizzazioni che devono prendere con sicurezza decisioni basate sui dati o soddisfare requisiti normativi di trasparenza.\u003C/p\u003E\n\u003Cp\u003ELa regressione lineare è particolarmente efficace nelle previsioni perché fornisce non solo il valore previsto, ma anche un livello di confidenza per ciascuna previsione, essenziale per la gestione del rischio e la pianificazione strategica. Consente alle organizzazioni di modellare gli scenari migliori e peggiori, stabilire obiettivi realistici e predisporre piani di emergenza.\u003C/p\u003E\n\u003Cp\u003ENonostante la sua semplicità, la regressione lineare offre solide prestazioni predittive per molti problemi concreti, pur rimanendo efficiente dal punto di vista computazionale e facile da implementare. Costituisce inoltre la base concettuale di tecniche avanzate come la regressione regolarizzata e le \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/neural-network/\"\u003Ereti neurali\u003C/a\u003E, risultando essenziale per sviluppare competenze nel machine learning.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_the-linear-regression-equation-and-hypothesis-function":{"id":"title-v2-2474050122","additionalClasses":"anchor-title anchor-title--the-linear-regression-equation-and-hypothesis-function","type":"heading2","lines":["L’equazione della regressione lineare e la funzione di ipotesi"],":type":"snowflake-site/components/title-v2"},"text_the-linear-regression-equation-and-hypothesis-function_0":{"id":"text-269ddb6e80","text":"\u003Cp\u003EOgni equazione di regressione lineare parte da un risultato da prevedere e da un’ipotesi sulle variabili che consentiranno di ottenerlo. Un algoritmo determina quindi il peso ottimale, o coefficiente, da assegnare a ciascuna variabile per produrre previsioni coerenti con i dati osservati. Ciò riduce al minimo gli errori di previsione e mostra quanto ogni variabile contribuisce al risultato.\u003C/p\u003E\n\u003Cp\u003EAd esempio, per creare un’equazione che preveda il prezzo di vendita di un’abitazione, le variabili potrebbero includere la superficie, il numero di camere da letto e la posizione. L’algoritmo analizza i dati storici delle vendite e determina l’influenza di ciascuna variabile sul prezzo delle abitazioni.\u003C/p\u003E\n\u003Cp\u003ETuttavia, se il modello non produce previsioni accurate, potrebbe essere necessario rivedere l’ipotesi e addestrarlo utilizzando variabili aggiuntive, come l’imposta immobiliare o il tasso di criminalità del quartiere. In alternativa, si potrebbe scoprire che la relazione tra le variabili non è lineare e che occorre applicare una diversa forma di analisi di regressione.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_key-assumptions-of-linear-regression-models":{"id":"title-v2-6232cab869","additionalClasses":"anchor-title anchor-title--key-assumptions-of-linear-regression-models","type":"heading2","lines":["Principali ipotesi dei modelli di regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_key-assumptions-of-linear-regression-models_0":{"id":"text-c1d173b4ae","text":"\u003Cp\u003EOgni modello di regressione lineare si basa su alcune ipotesi fondamentali:\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003ELinearità:\u003C/b\u003E la relazione tra le variabili indipendenti e dipendenti deve essere lineare, ossia rappresentabile mediante una retta. Se la relazione effettiva è curva o non lineare, i modelli produrranno previsioni imprecise e non riusciranno a rappresentare lo schema reale presente nei dati.\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003EIndipendenza delle osservazioni:\u003C/b\u003E ogni data point deve essere indipendente, vale a dire che un’osservazione non deve influenzarne un’altra. Quando i campioni di dati sono raggruppati, ad esempio pazienti trattati nello stesso ospedale o famiglie che vivono nella stessa zona, possono condividere fattori comuni che introducono bias nei risultati, facendo apparire il modello più accurato di quanto sia in realtà.\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003EOmoschedasticità (varianza costante):\u003C/b\u003E l’accuratezza del modello dovrebbe essere uniforme per tutte le previsioni: il modello non dovrebbe funzionare bene per alcuni valori e male per altri. Ad esempio, se il modello prevede con precisione il prezzo di vendita delle abitazioni economiche, ma è estremamente impreciso per quelle costose, non sarà possibile considerare affidabili i test statistici che utilizza per determinare il livello di confidenza delle previsioni.\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003ENormalità dei residui:\u003C/b\u003E gli errori di previsione (residui) devono seguire una distribuzione normale: a volte troppo alti, a volte troppo bassi, ma perlopiù contenuti. Se i residui di un modello non seguono questo andamento, ad esempio se le previsioni sono sistematicamente troppo basse a un estremo dell’intervallo e troppo alte all’altro, i test statistici e gli intervalli di confidenza del modello diventano inaffidabili. Questo problema è spesso particolarmente grave quando si utilizzano campioni di dati ridotti.\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003EAssenza di multicollinearità:\u003C/b\u003E le variabili indipendenti non devono sovrapporsi eccessivamente né misurare sostanzialmente lo stesso fenomeno. Se il modello per i prezzi delle abitazioni include sia la superficie sia il numero di stanze, potrebbe non riuscire a stabilire quale variabile incida maggiormente sul prezzo, generando coefficienti instabili e interpretazioni inaffidabili.\u003C/p\u003E\n\u003Cp\u003E\u003Cb\u003EAssenza di bias da variabili omesse:\u003C/b\u003E il modello dovrebbe includere tutte le variabili rilevanti che influenzano il risultato. Se si prevedono i prezzi delle abitazioni senza includere la posizione, il modello attribuirà erroneamente un peso eccessivo ad altre variabili, come la superficie o il numero di camere da letto. Sembrerà quindi che le dimensioni contino più di quanto accada realmente, mentre era la posizione, esclusa dal modello, a determinare quei prezzi più elevati.\u003C/p\u003E\n\u003Cp\u003ELa verifica di queste ipotesi fa parte della \u003Ca href=\"https://www.snowflake.com/en/artificial-intelligence/machine-learning/model-evaluation/\"\u003Evalutazione del modello\u003C/a\u003E. I grafici dei residui, i controlli della varianza e le matrici di correlazione sono gli strumenti standard per stabilire se un modello addestrato fornisce effettivamente le garanzie statistiche che sembra offrire.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_common-types-of-linear-regression-models":{"id":"title-v2-77450c614b","additionalClasses":"anchor-title anchor-title--common-types-of-linear-regression-models","type":"heading2","lines":["Tipi comuni di modelli di regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_common-types-of-linear-regression-models_0":{"id":"text-c4a42b315a","text":"\u003Cp\u003EEsistono diversi tipi di modelli di regressione, sviluppati nel corso degli anni per affrontare i vari problemi che emergono nell’uso delle tecniche di regressione lineare. Ecco quelli più utilizzati:\u003C/p\u003E\n\u003Ch3\u003ERegressione lineare semplice\u003C/h3\u003E\n\u003Cp\u003ELa forma più elementare di regressione utilizza una sola variabile indipendente per prevedere una variabile dipendente. È ideale per comprendere relazioni semplici e definire modelli di riferimento, ma spesso non riesce a rappresentare schemi complessi del mondo reale che coinvolgono più fattori.\u003C/p\u003E\n\u003Ch3\u003ERegressione lineare multipla\u003C/h3\u003E\n\u003Cp\u003EQuesto modello utilizza più variabili indipendenti per prevedere un singolo risultato, consentendo di considerare contemporaneamente diversi fattori. È più flessibile della regressione semplice, ma risente della multicollinearità quando le variabili predittive sono fortemente correlate tra loro.\u003C/p\u003E\n\u003Ch3\u003ERegressione Ridge\u003C/h3\u003E\n\u003Cp\u003ELa regressione Ridge affronta la multicollinearità e l’overfitting aggiungendo una penalità che riduce i valori dei coefficienti e rende il modello più prudente nelle previsioni. In questo modo, nessuna singola variabile prevale sulle altre, il modello generalizza meglio sui nuovi dati e conserva tutte le variabili del modello originale.\u003C/p\u003E\n\u003Ch3\u003ERegressione Lasso\u003C/h3\u003E\n\u003Cp\u003ELa regressione Lasso (Least Absolute Shrinkage and Selection Operator) affronta i problemi dell’overfitting e delle feature sparse, ossia meno rilevanti, aggiungendo una penalità che può ridurre a zero alcuni coefficienti ed eliminare di fatto dal modello le variabili meno importanti. La regressione Lasso è particolarmente utile quando sono presenti molte feature e si presume che solo alcune siano davvero rilevanti per le previsioni.\u003C/p\u003E\n\u003Ch3\u003ERegressione Elastic net\u003C/h3\u003E\n\u003Cp\u003EElastic Net combina i punti di forza delle regressioni Ridge e Lasso applicando contemporaneamente entrambi i tipi di penalità, così da bilanciare la riduzione dei coefficienti e l’eliminazione delle variabili irrilevanti. Questo approccio ibrido gestisce bene la multicollinearità ed esegue anche la selezione delle feature, offrendo flessibilità con set di dati complessi nei quali non è chiaro quali variabili siano più importanti.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_key-advantages-of-linear-regression":{"id":"title-v2-e15d084917","additionalClasses":"anchor-title anchor-title--key-advantages-of-linear-regression","type":"heading2","lines":["Principali vantaggi della regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_key-advantages-of-linear-regression_0":{"id":"text-c92f142776","text":"\u003Cp\u003EPer i problemi adatti, la regressione lineare offre un metodo relativamente semplice ed economico per analizzare i dati e formulare previsioni. Ecco i vantaggi principali:\u003C/p\u003E\n\u003Ch3\u003EFacile da implementare e interpretare\u003C/h3\u003E\n\u003Cp\u003ELa regressione lineare è semplice da sviluppare e comprendere. È possibile spiegare i risultati a stakeholder senza competenze tecniche con affermazioni semplici come: “Per ogni aumento di 1.000 dollari della spesa pubblicitaria, le vendite aumentano di 50.000 dollari”. Questa trasparenza la rende preziosa nei settori regolamentati e nei contesti aziendali in cui chi prende le decisioni deve comprendere la logica del modello e potersene fidare.\u003C/p\u003E\n\u003Ch3\u003EFunziona bene con dati correlati linearmente\u003C/h3\u003E\n\u003Cp\u003EPer i problemi aziendali reali caratterizzati da relazioni semplici tra le variabili, come la previsione delle vendite, l’ottimizzazione dei prezzi e l’allocazione delle risorse, la regressione lineare approssima la realtà con precisione sufficiente a fornire previsioni affidabili.\u003C/p\u003E\n\u003Ch3\u003ETraining rapido e costi di elaborazione ridotti\u003C/h3\u003E\n\u003Cp\u003ELa regressione lineare richiede una potenza di elaborazione minima e completa il training quasi istantaneamente, anche su set di dati di grandi dimensioni. Questo la rende pratica per applicazioni in tempo reale, prototipazione rapida e scenari in cui le risorse di elaborazione sono limitate o costose.\u003C/p\u003E\n\u003Ch3\u003EUtile per le previsioni e l’analisi delle tendenze\u003C/h3\u003E\n\u003Cp\u003EIl modello eccelle nell’identificare e proiettare le tendenze sulla base dei dati storici, risultando ideale per task come la pianificazione della domanda e le proiezioni della capacità. È possibile estendere facilmente le previsioni nel futuro e comprendere in che modo le variazioni delle variabili principali influiranno sui risultati.\u003C/p\u003E\n\u003Ch3\u003ESupporta l’inferenza statistica e la verifica delle ipotesi\u003C/h3\u003E\n\u003Cp\u003ELa regressione lineare fornisce informazioni statistiche dettagliate che aiutano a determinare se le relazioni tra le variabili siano statisticamente significative o probabilmente casuali. Questa capacità è essenziale per la ricerca, la convalida e le decisioni basate sui dati con livelli di confidenza quantificati.\u003C/p\u003E\n\u003Ch3\u003EFondamento delle tecniche avanzate\u003C/h3\u003E\n\u003Cp\u003EPadroneggiare la regressione lineare fornisce il fondamento concettuale e matematico necessario per comprendere algoritmi di machine learning più complessi, come la regressione regolarizzata, i modelli lineari generalizzati e le reti neurali. È quindi uno strumento di apprendimento essenziale, che permette di sviluppare competenze trasferibili a numerosi ambiti analitici.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_major-limitations-of-linear-regression":{"id":"title-v2-7639db05b5","additionalClasses":"anchor-title anchor-title--major-limitations-of-linear-regression","type":"heading2","lines":["Principali limiti della regressione lineare"],":type":"snowflake-site/components/title-v2"},"text_major-limitations-of-linear-regression_0":{"id":"text-3d0562ee9c","text":"\u003Cp\u003ECome indicato in precedenza, la regressione lineare non è sempre la scelta adatta per ogni modello predittivo. Ecco alcuni dei suoi principali limiti e i relativi metodi per superarli:\u003C/p\u003E\n\u003Ch3\u003EPresuppone relazioni lineari\u003C/h3\u003E\n\u003Cp\u003ELa regressione lineare può modellare solo relazioni rappresentabili con una linea retta. Di conseguenza, può non rilevare curve, picchi o crescite esponenziali presenti nei dati reali. Se i dati presentano schemi non lineari, è possibile passare alla regressione polinomiale o a modelli non lineari, come gli \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/decision-tree/\"\u003Ealberi decisionali\u003C/a\u003E e le reti neurali, in grado di rappresentare relazioni più complesse.\u003C/p\u003E\n\u003Ch3\u003ESensibile agli outlier e al rumore\u003C/h3\u003E\n\u003Cp\u003EValori estremi o data point errati possono influenzare in modo sproporzionato la retta di migliore adattamento, allontanandola dall’andamento reale e alterando coefficienti e previsioni. È possibile affrontare il problema pulendo i dati per correggere gli outlier o applicando metodi di regolarizzazione, come la regressione Ridge o Lasso, che riducono l’impatto delle osservazioni anomale.\u003C/p\u003E\n\u003Ch3\u003ERichiede residui con distribuzione normale\u003C/h3\u003E\n\u003Cp\u003EQuando gli errori di previsione non seguono una curva di distribuzione normale, i test statistici e gli intervalli di confidenza diventano inaffidabili, compromettendo la capacità di valutare l’affidabilità e la significatività del modello. Se gli errori non seguono una distribuzione normale, è possibile utilizzare trasformazioni logaritmiche o basate sulla radice quadrata per comprimere i valori elevati in numeri più piccoli e ridurne l’impatto sui calcoli statistici. È inoltre possibile adottare un tipo di modello che non richieda una distribuzione normale, come gli alberi decisionali o le \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/support-vector-machine/\"\u003Emacchine a vettori di supporto\u003C/a\u003E.\u003C/p\u003E\n\u003Ch3\u003EPuò offrire prestazioni inferiori con dati complessi o non lineari\u003C/h3\u003E\n\u003Cp\u003ELa regressione lineare incontra difficoltà quando le relazioni sono complesse, ad esempio quando due variabili interagiscono in modi imprevisti o quando una variabile produce un effetto solo dopo aver raggiunto una determinata soglia. Per i dati complessi è possibile utilizzare modelli più sofisticati, come le \u003Ca href=\"https://www.snowflake.com/it/artificial-intelligence/machine-learning/models/random-forest/\"\u003Eforeste casuali\u003C/a\u003E o le reti neurali, che gestiscono naturalmente questi schemi. In alternativa, si possono creare manualmente nuove variabili, ad esempio combinando o elevando al quadrato quelle esistenti, per consentire alla regressione lineare di rappresentare la complessità.\u003C/p\u003E\n\u003Ch3\u003EMulticollinearità tra i predittori\u003C/h3\u003E\n\u003Cp\u003EQuando le variabili predittive sono troppo simili tra loro, il modello non riesce a determinare quale sia davvero rilevante e produce risultati inaffidabili. È possibile risolvere il problema rimuovendo le variabili duplicate, combinando quelle simili o utilizzando tecniche di regressione specializzate, come Ridge o Elastic Net, che gestiscono meglio le variabili correlate.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_when-should-you-use-linear-regression":{"id":"title-v2-605850d4ba","additionalClasses":"anchor-title anchor-title--when-should-you-use-linear-regression","type":"heading2","lines":["Quando usare la regressione lineare?"],":type":"snowflake-site/components/title-v2"},"text_when-should-you-use-linear-regression_0":{"id":"text-457931e950","text":"\u003Cp\u003ELa regressione lineare è lo strumento adatto più spesso di quanto la sua semplicità possa suggerire, ma la scelta dipende da alcuni controlli da effettuare prima di adattare il modello ai dati.\u003C/p\u003E\n\u003Cp\u003EÈ indicata quando la relazione da modellare è plausibilmente rappresentabile con una linea retta e quando spiegare il risultato è importante quanto produrlo. La trasparenza la rende preziosa nei settori regolamentati e nei contesti aziendali in cui chi prende le decisioni deve comprendere la logica del modello e potersene fidare. Un modello più accurato, ma che nessuno riesce a interpretare, è spesso la scelta peggiore. \u003Cbr\u003E\n\u003Cbr\u003E\nLa regressione lineare è una buona scelta anche quando serve un’inferenza statistica, non solo una previsione, perché indica se una relazione è significativa o probabilmente casuale. È utile anche quando la velocità è importante, perché completa il training quasi istantaneamente persino su set di dati di grandi dimensioni.\u003C/p\u003E\n\u003Cp\u003EÈ invece opportuno considerare un metodo diverso quando l’andamento è curvilineo, dipende da soglie o deriva dall’interazione imprevista tra due variabili. In questi casi, le foreste casuali o le reti neurali gestiscono i dati in modo più naturale. \u003C/p\u003E\n\u003Cp\u003ELo stesso vale quando prevalgono outlier che non è possibile correggere, quando i residui non seguono una distribuzione normale o quando i predittori misurano sostanzialmente lo stesso fenomeno. Per molti di questi problemi esistono soluzioni intermedie che evitano di cambiare completamente metodo: Ridge ed Elastic Net gestiscono i predittori correlati, mentre le trasformazioni logaritmiche o basate sulla radice quadrata possono correggere gli errori con distribuzione non normale.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"title_v2":{"id":"title-v2-d296fcc5f5","additionalClasses":"anchor-title anchor-title--why-linear-regression-remains-essential-to-data-science","type":"heading2","lines":["Perché la regressione lineare resta essenziale per la data science"],":type":"snowflake-site/components/title-v2","appliedCssClassNames":"left-alignment"},"callout_when-should-you-use-linear-regression_0":{"id":"text-b69133f993","text":"\u003Cp\u003EPoiché la regressione lineare è il modello di riferimento con cui si confrontano gli altri approcci di regressione, vale la pena svilupparla anche quando si prevede di aver bisogno di un modello più potente. Indica quanta parte del segnale è semplicemente lineare e, di conseguenza, quale aumento effettivo di accuratezza offre un modello più complesso.\u003C/p\u003E\n\u003Cp\u003ELa regressione lineare rimane uno degli strumenti più importanti della data science perché unisce semplicità ed efficacia: è facile da comprendere e implementare e risolve problemi reali in numerosi settori. La sua trasparenza la rende preziosa per processi decisionali spiegabili, soprattutto nei settori regolamentati, dove gli stakeholder devono comprendere il ragionamento alla base delle previsioni.\u003C/p\u003E\n\u003Cp\u003ELe organizzazioni di successo utilizzano la regressione lineare in modo strategico, scegliendo i modelli più adatti ai propri dati e obiettivi aziendali.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-color-text-05"},"callout_when-should-you-use-linear-regression_1":{"id":"text-66663024ce","additionalClasses":"callout callout--general","text":"\u003Cp\u003E\u003Cb\u003EIN SINTESI\u003C/b\u003E\u003C/p\u003E\n\u003Cp\u003ELa regressione lineare è il modello di riferimento rapido e trasparente con cui vengono confrontati tutti gli altri modelli di regressione: mostra quanta parte del segnale presente nei dati è semplicemente lineare e quale contributo effettivo offrirebbe un modello più complesso. È indicata quando le relazioni sono approssimativamente lineari e l’interpretabilità è importante. Occorre invece passare a metodi come le foreste casuali o le reti neurali quando gli schemi diventano curvilinei, dipendono da soglie o sono interdipendenti.\u003C/p\u003E\n","richText":true,":type":"snowflake-site/components/text","appliedCssClassNames":"text-size-regular text-color-text-05"},"card_v2_when-should-you-use-linear-regression_0":{"id":"card-v2-7cafc57e49","additionalClasses":"seo-customer","configurationStatus":{"configured":true,"message":""},"button":{"id":"button","showOutboundIcon":false,"buttonLink":{"valid":true,"url":"/en/customers/all-customers/case-study/whoop/"},"linkTargetContentType":"DOCUMENT",":type":"snowflake-site/components/button","linkType":"SNOWFLAKE_INTERNAL","text":"Leggi il case study"},":type":"snowflake-site/components/card-v2","title":{"id":"title","type":"heading4","lines":["WHOOP"],":type":"snowflake-site/components/title-v2"},"image":{"id":"image","height":"351","src":"/adobe/dynamicmedia/deliver/dm-aid--f2810fbd-fb51-47bc-b4b4-a9a56d6426fa/whoop%25403x.png?quality=85&preferwebp=true","lazyEnabled":true,"alt":"Whoop logo","isLcpImage":false,"width":"624",":type":"snowflake-site/components/image"},"type":"content-card","text":{"id":"text","text":"\u003Cp\u003EWHOOP migliora le previsioni finanziarie tramite AI/ML e ottimizza l’esperienza degli utenti Con Snowflake e Apache Iceberg, WHOOP dispone di un accesso centralizzato ai dati, riduce la complessità, abbassa i costi e migliora i processi critici.\u003C/p\u003E\r\n","richText":true,":type":"snowflake-site/components/text"},"layoutStyle":"horizontal"}},":itemsOrder":["callout__0","text","title_what-is-linear-regression","text_what-is-linear-regression_0","title_understanding-the-line-of-best-fit-in-linear-regression","text_understanding-the-line-of-best-fit-in-linear-regression_0","title_how-linear-regression-is-used","text_how-linear-regression-is-used_0","title_why-is-linear-regression-important-to-machine-learning","text_why-is-linear-regression-important-to-machine-learning_0","title_the-linear-regression-equation-and-hypothesis-function","text_the-linear-regression-equation-and-hypothesis-function_0","title_key-assumptions-of-linear-regression-models","text_key-assumptions-of-linear-regression-models_0","title_common-types-of-linear-regression-models","text_common-types-of-linear-regression-models_0","title_key-advantages-of-linear-regression","text_key-advantages-of-linear-regression_0","title_major-limitations-of-linear-regression","text_major-limitations-of-linear-regression_0","title_when-should-you-use-linear-regression","text_when-should-you-use-linear-regression_0","title_v2","callout_when-should-you-use-linear-regression_0","callout_when-should-you-use-linear-regression_1","card_v2_when-should-you-use-linear-regression_0"]},"flexible_column_content_container_2":{"additionalClasses":"hub-sidebar","layout":"SIMPLE","id":"hub-body-aside","appliedCssClassNames":"snowflake-responsive-container-inner-padding-small",":type":"snowflake-site/components/flexible-column-container/flexible-column-content-container",":items":{"container":{"additionalClasses":"sticky-sidebar","layout":"RESPONSIVE_GRID","columnCount":12,"columnClassNames":{"text_943981956_copy_":"aem-GridColumn 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