✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❍➺ ❤é trđ ❞ü ✤♦→♥ ❝❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ② t➳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❱✐➺♥ ❚♦→♥ ù♥❣ ❞ö♥❣ ✈➔ ❚✐♥ ❤å❝✱ ✣❍❇❑ ❍➔ ◆ë✐ ❍➔ ◆ë✐✱ t❤→♥❣ ✵✺ ♥➠♠ ✷✵✷✵ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼æ t↔ ❞ú ❧✐➺✉ ✸ ▼ỉ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼æ t↔ ❞ú ❧✐➺✉ ✸ ▼æ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❈❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ❧➔ ❣➻ P❤➼ ❜↔♦ ❤✐➸♠ ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ ❧➔ sè t✐➲♥ ♠➔ ❝æ♥❣ t② ❜↔♦ ❤✐➸♠ s➩ t➼♥❤ ❝❤♦ ❜↕♥ t❤❡♦ ❝❤➼♥❤ s→❝❤ ❜↔♦ ❤✐➸♠ ♠➔ ❜↕♥ ✤❛♥❣ P õ t ỗ t t♦→♥ ❜↔♦ ❤✐➸♠✱ t❤✉➳ ✈➔ ♣❤➼ ❞à❝❤ ✈ư tị② t❤❡♦ t ủ ỗ ❤✐➸♠✳ P❤➼ ❜↔♦ ❤✐➸♠ s➩ ✤➢t ❤ì♥ ❤♦➦❝ r➫ ❤ì♥ ✈➔ ❝❤✐ ♣❤➼ ❝â t❤➸ t❤❛② ✤ê✐ tò② t❤✉ë❝ ✈➔♦ ❧♦↕✐ ❜↔♦ ❤✐➸♠ ❜↕♥ ✤❛♥❣ t➻♠ ❦✐➳♠✱ ❝ơ♥❣ ♥❤÷ ♠ù❝ ✤ë rõ✐ r♦✳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❚❤ü❝ tr↕♥❣ ❚❤à tr÷í♥❣ ❜↔♦ ❤✐➸♠ t❤í✐ ❣✐❛♥ ❣➛♥ ✤➙② r➜t sỉ✐ ✤ë♥❣✱ ✤➦❝ ❜✐➺t ❧➔ ❦❤✐ ♥❣➔② ❝➔♥❣ ❝â ♥❤✐➲✉ ❞à❝❤ ❜➺♥❤ ①↔② r ữớ q t tợ ọ ỡ ợ số ữủ ợ t❤➻ ❝→❝ ❝æ♥❣ t② ❜↔♦ ❤✐➸♠ ❝➛♥ ❝â ♠ët ❤➺ ❤é trñ ❞ü ✤♦→♥ ❝❤✐ ♣❤➼ ❦❤→♠ ❝❤ú❛ ❜➺♥❤ ❝õ❛ ❦❤→❝❤ ❤➔♥❣ ❞ü❛ tr➯♥ ❝→❝ sè ❧✐➺✉ ❝→ ♥❤➙♥ ❝õ❛ ❤å ✈➲ t✉ê✐ t→❝✱ ❝❤➾ sè ❇▼■✱ t➻♥❤ tr↕♥❣ ❤ót t❤✉è❝✱ sè ❝♦♥ ✳ ✳ ✳ ✳ tø ✤â ❝â t❤➸ ♥❤❛♥❤ ❝❤â♥❣ ✤÷❛ r❛ q✉②➳t ✤à♥❤ ✈➲ ❝❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ② t➳ ♠➔ ❦❤→❝❤ ❤➔♥❣ ❝➛♥ ❝❤✐ tr↔✳ tố ộ trủ q ỵ ữ r❛ q✉②➳t ✤à♥❤ ✈➻ tr➯♥ t❤ü❝ t➳ ❝❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ❝á♥ ♣❤ö t❤✉ë❝ ✈➔♦ ♣❤➼ ❞à❝❤ ✈ö✱ t❤✉➳ t❤❡♦ q✉② ✤à♥❤ ❝õ❛ ❧✉➟t ❜↔♦ ❤✐➸♠ ✈➔ ❝❤➼♥❤ s→❝❤ ❝õ❛ ❝ỉ♥❣ t② ❜↔♦ ❤✐➸♠ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼æ t↔ ❞ú ❧✐➺✉ ✸ ▼æ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ữỡ tr ỳ ỗ trữớ ❞ú ❧✐➺✉✿ ❆❣❡ ✿ t✉ê✐ ❙❡①✿ ❣✐ỵ✐ t➼♥❤ ❇▼■✿ ❝❤➾ sè ❇▼■ ❙♠♦❦❡r✿ ❝â ❤ót t❤✉è❝ ❤❛② ❦❤ỉ♥❣❄ ❘❡❣✐♦♥✿ ✈ị♥❣ ♠✐➲♥ ❈❤✐❧❞r❡♥✿ sè ❝♦♥ ❊①♣❡♥s❡s✿ ❝❤✐ ♣❤➼ ② t➳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼ỉ t↔ ❞ú ❧✐➺✉ ✸ ▼æ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❚❤✉➟t t♦→♥ ❑◆◆ ✲ ❑ ♥❡❛r❡st ♥❡✐❣❤❜♦rs ❑◆◆ ✭❑✲◆❡❛r❡st ◆❡✐❣❤❜♦rs✮ ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ t❤✉➟t t♦→♥ ❤å❝ ❝â ❣✐→♠ s→t ✤ì♥ ❣✐↔♥ ♥❤➜t ✤÷đ❝ sû ❞ư♥❣ ♥❤✐➲✉ tr♦♥❣ ❦❤❛✐ ♣❤→ ❞ú ❧✐➺✉ ✈➔ ị tữ tt t õ ❦❤æ♥❣ ❤å❝ ♠ët ✤✐➲✉ ❣➻ tø t➟♣ ❞ú ❧✐➺✉ ❤å❝ ✭♥➯♥ ❑◆◆ ✤÷đ❝ ①➳♣ ✈➔♦ ❧♦↕✐ ❧❛③② ❧❡❛r♥✐♥❣✮✱ ♠å✐ t➼♥❤ t♦→♥ ✤÷đ❝ t❤ü❝ ❤✐➺♥ ❦❤✐ ♥â ❝➛♥ ❞ü ✤♦→♥ ♥❤➣♥ ỳ ợ ợ ởt ố tữủ ❞ú ❧✐➺✉ ♠ỵ✐ ❝â t❤➸ ❞ü ✤♦→♥ tø ❝→❝ ❧ỵ♣ õ õ t r ỗ q tt t ữủ sỷ ữợ t ❝→❝ ❜✐➳♥ ❧✐➯♥ tư❝✳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❈→❝ ✤ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ q✉❛♥ trå♥❣ ✣ë ✤♦ ❊✉❝❧✐❞ ✈➔ ✤ë ✤♦ ▼❛♥❤❛tt❛♥ ❈❤♦ ❤❛✐ ✤✐➸♠ x = (x1 , x2 , , xm ) ✈➔ y = (y1 , y2 , , ym )✳ ✣ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ ▼✐♥❦♦✇s❦✐ ✤÷đ❝ ①→❝ ✤à♥❤ t❤❡♦ ❝ỉ♥❣ t❤ù❝✿ r m |xi − yi | d(x, y) = r i=1 ✣ë ✤♦ ❊✉❝❧✐❞ ❝❤✉➞♥ ✭r❂✷ tù❝ L2 ✲♥♦r♠✮✿ m (xi − yi )2 i=1 ✣ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ ▼❛♥❤❛tt❛♥ ✭r = tù❝ L1 ✲♥♦r♠✮✿ m |xi − yi | d(x, y) = i=1 ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❚❤✉➟t t♦→♥ ✶ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ tø ❞ú ❧✐➺✉ ❝➛♥ ❞ü ✤♦→♥ ✤➳♥ ❝→❝ ❞ú ❧✐➺✉ ✤➣ ✤÷đ❝ ❣➢♥ ♥❤➣♥ ✷ ❙➢♣ ①➳♣ ❞ú ❧✐➺✉ t❤❡♦ ❦❤♦↔♥❣ ❝→❝❤ ✸ ❚➻♠ ❣✐→ trà tè✐ ÷✉ ❝õ❛ ❑ ✕ sè ❤➔♥❣ ①â♠ ❣➛♥ ♥❤➜t ❞ü❛ ✈➔♦ ❘▼❙❊ ✭❝❤å♥ ❑ ù♥❣ ✈ỵ✐ ❣✐→ trà ❘▼❙❊ ♥❤ä ♥❤➜t✮ ✹ ❚➼♥❤ ❣✐→ trà ❜✐➳♥ ✤➛✉ r❛ ❜➡♥❣ tr✉♥❣ ❜➻♥❤ ❣✐→ trà ❝õ❛ ❑✲❤➔♥❣ ①â♠ ❣➛♥ ♥â ♥❤➜t ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ổ ữỡ tr ì ữủ ì ✤✐➸♠ ✣ë ♣❤ù❝ t↕♣ t➼♥❤ t♦→♥ ❝õ❛ q✉→ tr➻♥❤ tr❛✐♥✐♥❣ ❧➔ ❜➡♥❣ ✵✳ ❱✐➺❝ ❞ü ✤♦→♥ ❦➳t q✉↔ ❝õ❛ ❞ú ợ rt ỡ ữủ rt ❝↔♠ ✈ỵ✐ ♥❤✐➵✉ ❦❤✐ ❑ ♥❤ä✳ ❑◆◆ ❧➔ ♠ët t❤✉➟t t♦→♥ ♠➔ ♠å✐ t➼♥❤ t♦→♥ ✤➲✉ ♥➡♠ ð ❦❤➙✉ t❡st✳ ❚r♦♥❣ ✤â ✈✐➺❝ t➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ tỵ✐ tø♥❣ ✤✐➸♠ ❞ú ❧✐➺✉ tr♦♥❣ tr❛✐♥✐♥❣ s❡t s➩ tè♥ r➜t ♥❤✐➲✉ t❤í✐ ❣✐❛♥✱ ✤➦❝ ❜✐➺t ❧➔ ✈ỵ✐ ❝→❝ ❝ì sð ❞ú ❧✐➺✉ ❝â sè ❝❤✐➲✉ ❧ỵ♥ ✈➔ ❝â ♥❤✐➲✉ ✤✐➸♠ ❞ú ❧✐➺✉✳ ❱ỵ✐ ❑ ❝➔♥❣ ❧ỵ♥ t❤➻ ✤ë ♣❤ù❝ t↕♣ ❝ơ♥❣ s➩ t➠♥❣ ❧➯♥✳ ◆❣♦➔✐ r❛✱ ✈✐➺❝ ❧÷✉ t♦➔♥ ❜ë ❞ú ❧✐➺✉ tr♦♥❣ ợ ụ ữ tợ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ữỡ tr ợ t t t➟♣ ❞ú ❧✐➺✉ t❤➔♥❤ t➟♣ tr❛✐♥ ✈➔ t➟♣ t❡st ✈ỵ✐ t➾ ❧➺ ✽✿✷ ⑩♣ ❞ư♥❣ ♠ỉ ❤➻♥❤ ❑◆◆ ✈ỵ✐ sè ❤➔♥❣ ①â♠ k = 15 ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼æ t↔ ❞ú ❧✐➺✉ ✸ ▼ỉ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ESS T SS ❊❙❙✿ tê♥❣ ❝→❝ ✤ë ❧➺❝❤ ❜➻♥❤ ♣❤÷ì♥❣ ♣❤➛♥ ❞÷ ❚❙❙✿ tê♥❣ ❝→❝ ✤ë ❧➺❝❤ ❜➻♥❤ ♣❤÷ì♥❣ t♦➔♥ ❜ë R2 = − Radjusted =1− n−1 − R2 n−k n ❂ sè ❧÷đ♥❣ ♠➝✉ q✉❛♥ s→t k ❂ sè t❤❛♠ sè ❝õ❛ ♠ỉ ❤➻♥❤✱ ❜➡♥❣ sè ❧÷đ♥❣ ❜✐➳♥ ✤ë❝ ❧➟♣ ❝ë♥❣ ✶ Radjusted = 0.974 tù❝ ❧➔ ✾✼✪ sü ❜✐➳♥ t❤✐➯♥ ❝õ❛ ❜✐➳♥ ♣❤ư t❤✉ë❝ ✤÷đ❝ ❣✐↔✐ t❤➼❝❤ ❜ð✐ ❝→❝ ❜✐➳♥ ✤ë❝ ❧➟♣ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❙❛✐ sè t✉②➺t ✤è✐ RM SE = i ❙❛✐ sè t÷ì♥❣ ✤è✐ RM SE% = (yi − yi )2 n RM SE × 100% y¯ ❱ỵ✐yi ❧➔ ❦➳t q✉↔ ❞ü ✤♦→♥ yi ❧➔ ❞ú ❧✐➺✉ t❤ü❝ t➳ y ❧➔ tr✉♥❣ ❜➻♥❤ ❝õ❛ ❞ú ❧✐➺✉ t❤ü❝ t➳ Ð ✤➙② RM SE%train = 9.6% RM SE%test = 10.46% ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ●✐→ trà F = 12417.23457 ✈ỵ✐ signF = < 0.05 ❝❤ù♥❣ tä ❘ sq✉❛r❡❞ tê♥❣ t❤➸ ❝õ❛ ♠æ ❤➻♥❤ ❦❤→❝ ✵✱ ♥❣❤➽❛ ❧➔ ♠ỉ ❤➻♥❤ ①➙② ❞ü♥❣ ♣❤ị ❤đ♣ ✈ỵ✐ tê♥❣ t❤➸ ●✐→ tr tữỡ ự ợ ❧➟♣ < 0.05 ❝❤ù♥❣ tä ❝→❝ ❜✐➳♥ ✤ë❝ ❧➟♣ ✤➲✉ õ ỵ tố tở ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◗✉② tr➻♥❤ ❣✐↔✐ q✉②➳t ❜➔✐ t♦→♥ ■♥♣✉t✿ ❉ú ❧✐➺✉ ❦❤→❝❤ ❤➔♥❣ ❖✉t♣✉t✿ ❑➳t q✉↔ ❞ü ✤♦→♥ ❝❤✐ ♣❤➼ ② t➳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ổ ữỡ tr ủ ỵ q ỵ tr út tố ữ t tợ ❝❤✐ ♣❤➼ ② t➳ ❝õ❛ ❦❤→❝❤ ❤➔♥❣✿ ♥❣÷í✐ ❤ót t❤✉è❝ s➩ ❝â ❝❤✐ ♣❤➼ ② t➳ ❝❛♦ ❤ì♥ ♥❤✐➲✉ s♦ ợ ữớ ổ út tố ữớ õ số tờ s➩ ❝â ❝❤✐ ♣❤➼ ❝❛♦ ❤ì♥ ♥❣÷í✐ ➼t t✉ê✐ ◆❣÷í✐ ❜à ❜➨♦ ♣❤➻ ✭❇▼■ ❃ ✸✵✮ s➩ ❝â ❝❤✐ ♣❤➼ ② t➳ ❝❛♦ ❤ì♥ ♥❣÷í✐ ❜➻♥❤ t❤÷í♥❣✳ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ◆ë✐ ❞✉♥❣ ✶ ✣➦t ✈➜♥ ✤➲ ✷ ▼æ t↔ ❞ú ❧✐➺✉ ✸ ▼æ ❤➻♥❤ ✹ ❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤ ✺ ❈❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❉❡♠♦ ❝❤÷ì♥❣ tr➻♥❤ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trđ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼ỉ t↔ ❞ú ❧✐➺✉ ▼ỉ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ ❤➻♥❤ ❈❤÷ì♥❣ tr➻♥❤ ❚❤❛♥❦ ②♦✉ ❢♦r ②♦✉r ❛tt❡♥t✐♦♥ ❃✳❁ ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ... , , xm ) ✈➔ y = (y1 , y2 , , ym )✳ ✣ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ ▼✐♥❦♦✇s❦✐ ✤÷đ❝ ①→❝ ✤à♥❤ t❤❡♦ ❝ỉ♥❣ t❤ù❝✿ r m |xi − yi | d(x, y) = r i=1 ✣ë ✤♦ ❊✉❝❧✐❞ ❝❤✉➞♥ ✭r❂✷ tù❝ L2 ✲♥♦r♠✮✿ m (xi − yi )2 i=1 ✣ë ✤♦... tr➻♥❤ ❙❛✐ sè t✉②➺t ✤è✐ RM SE = i ❙❛✐ sè t÷ì♥❣ ✤è✐ RM SE% = (yi yi )2 n RM SE ì 100% y ợyi ❧➔ ❦➳t q✉↔ ❞ü ✤♦→♥ yi ❧➔ ❞ú ❧✐➺✉ t❤ü❝ t➳ y ❧➔ tr✉♥❣ ❜➻♥❤ ❝õ❛ ❞ú ❧✐➺✉ t❤ü❝ t➳ Ð ✤➙② RM SE%train = 9.6%... ✭r❂✷ tù❝ L2 ✲♥♦r♠✮✿ m (xi − yi )2 i=1 ✣ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ ▼❛♥❤❛tt❛♥ ✭r = tù❝ L1 ✲♥♦r♠✮✿ m |xi − yi | d(x, y) = i=1 ◆❣✉②➵♥ ❚❤à ◆❣➙♥ ❍➺ ❤é trñ q✉②➳t ✤à♥❤ ✣➦t ✈➜♥ ✤➲ ▼æ t↔ ❞ú ❧✐➺✉ ▼æ ❤➻♥❤ ❑✐➸♠ ✤à♥❤ ♠ỉ