hệ hỗ trợ dự đoán chi phí bảo hiểm y tế

✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❍➺ ❤é trñ ❞ü ✤♦→♥ ❝❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ②
t➳
◆❣✉②➵♥ ❚❤à ◆❣➙♥

❱✐➺♥ ❚♦→♥ ù♥❣ ❞ö♥❣ ✈➔ ❚✐♥ ❤å❝✱ ✣❍❇❑ ❍➔ ◆ë✐
❍➔ ◆ë✐✱ t❤→♥❣ ✵✺ ♥➠♠ ✷✵✷✵

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

◆ë✐ ❞✉♥❣
✶

✣➦t ✈➜♥ ✤➲

✷

▼æ t↔ ❞ú ❧✐➺✉

✸

▼æ ❤➻♥❤

✹

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤

✺

❈❤÷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♥❤ ♠æ ❤➻♥❤

✺

❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❈❤✐ ♣❤➼ ❜↔♦ ❤✐➸♠ ❧➔ ❣➻

P❤➼ ❜↔♦ ❤✐➸♠ ✤÷ñ❝ ✤à♥❤ ♥❣❤➽❛ ❧➔ sè t✐➲♥ ♠➔ ❝æ♥❣ t② ❜↔♦ ❤✐➸♠ s➩ t➼♥❤ ❝❤♦ ❜↕♥

t❤❡♦ ❝❤➼♥❤ s→❝❤ ❜↔♦ ❤✐➸♠ ♠➔ ❜↕♥ ✤❛♥❣ ♠✉❛
P❤➼ ❜↔♦ ❤✐➸♠ ❝â t❤➸ ❜❛♦ ❣ç♠ ❦❤♦↔♥ t❤❛♥❤ t♦→♥ ❜↔♦ ❤✐➸♠✱ t❤✉➳ ✈➔ ♣❤➼
❞à❝❤ ✈ö tò② t❤❡♦ ❧✉➟t ❜↔♦ ❤✐➸♠ ✈➔ ♥❤➔ ❝✉♥❣ ❝➜♣ ❤ñ♣ ✤ç♥❣ ❜↔♦ ❤✐➸♠✳
P❤➼ ❜↔♦ ❤✐➸♠ s➩ ✤➢t ❤ì♥ ❤♦➦❝ r➫ ❤ì♥ ✈➔ ❝❤✐ ♣❤➼ ❝â t❤➸ t❤❛② ✤ê✐ tò② t❤✉ë❝
✈➔♦ ❧♦↕✐ ❜↔♦ ❤✐➸♠ ❜↕♥ ✤❛♥❣ t➻♠ ❦✐➳♠✱ ❝ô♥❣ ♥❤÷ ♠ù❝ ✤ë rõ✐ r♦✳

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❚❤ü❝ tr↕♥❣
❚❤à tr÷í♥❣ ❜↔♦ ❤✐➸♠ t❤í✐ ❣✐❛♥ ❣➛♥ ✤➙② r➜t sæ✐ ✤ë♥❣✱ ✤➦❝ ❜✐➺t ❧➔ ❦❤✐ ♥❣➔②
❝➔♥❣ ❝â ♥❤✐➲✉ ❞à❝❤ ❜➺♥❤ ①↔② r❛✱ ❝♦♥ ♥❣÷í✐ q✉❛♥ t➙♠ tî✐ sù❝ ❦❤ä❡ ❝õ❛
♠➻♥❤ ♥❤✐➲✉ ❤ì♥✳ ❱î✐ sè ❧÷ñ♥❣ ❦❤→❝❤ ❤➔♥❣ ♥❣➔② ❝➔♥❣ ❧î♥ 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↔✳
❍➺ t❤è♥❣ ♥➔② ❝❤➾ ❤é trñ ♥❤➔ q✉↔♥ ❧þ ✤÷❛ r❛ q✉②➳t ✤à♥❤ ✈➻ tr➯♥ t❤ü❝ t➳ ❝❤✐
♣❤➼ ❜↔♦ ❤✐➸♠ ❝á♥ ♣❤ö t❤✉ë❝ ✈➔♦ ♣❤➼ ❞à❝❤ ✈ö✱ t❤✉➳ t❤❡♦ q✉② ✤à♥❤ ❝õ❛ ❧✉➟t
❜↔♦ ❤✐➸♠ ✈➔ ❝❤➼♥❤ s→❝❤ ❝õ❛ ❝æ♥❣ t② ❜↔♦ ❤✐➸♠

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

◆ë✐ ❞✉♥❣
✶

✣➦t ✈➜♥ ✤➲

✷

▼æ t↔ ❞ú ❧✐➺✉

✸

▼æ ❤➻♥❤

✹

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤

✺

❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❉ú ❧✐➺✉ ❣ç♠ ✶✸✸✼ ❜↔♥ ❣❤✐
❈→❝ tr÷í♥❣ ❞ú ❧✐➺✉✿
❆❣❡ ✿ t✉ê✐
❙❡①✿ ❣✐î✐ t➼♥❤
❇▼■✿ ❝❤➾ sè ❇▼■
❙♠♦❦❡r✿
❝â ❤ót t❤✉è❝ ❤❛② ❦❤æ♥❣❄
❘❡❣✐♦♥✿ ✈ò♥❣ ♠✐➲♥
❈❤✐❧❞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 ✈➜♥ ✤➲

✷

▼æ t↔ ❞ú ❧✐➺✉

✸

▼æ ❤➻♥❤

✹

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤

✺

❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤

t
ổ t ỳ
ổ
ổ
ữỡ tr

t t rst rs
rst rs ởt tr ỳ tt t ồ õ
st ỡ t ữủ sỷ ử tr ỳ ồ
ị tữ ừ tt t õ ổ ồ ởt tứ t ỳ
ồ ữủ r ồ t t ữủ tỹ
õ ỹ ừ ỳ ợ
ợ ừ ởt ố tữủ ỳ ợ õ t ỹ tứ ợ
ừ õ õ t
r ỗ q tt t ữủ sỷ ử ữợ t
tử



ộ trủ qt


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❈→❝ ✤ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ q✉❛♥ trå♥❣
✣ë ✤♦ ❊✉❝❧✐❞ ✈➔ ✤ë ✤♦ ▼❛♥❤❛tt❛♥

❈❤♦ ❤❛✐ ✤✐➸♠ x = (x1 , x2 , . . . , xm ) ✈➔ y = (y1 , y2 , . . . , ym )✳ ✣ë ✤♦
❦❤♦↔♥❣ ❝→❝❤ ▼✐♥❦♦✇s❦✐ ✤÷ñ❝ ①→❝ ✤à♥❤ t❤❡♦ ❝æ♥❣ t❤ù❝✿
1
r

m

|xi − yi |

d(x, y) =

r

i=1

✣ë ✤♦ ❊✉❝❧✐❞ ❝❤✉➞♥ ✭r❂✷ tù❝ L2 ✲♥♦r♠✮✿
m

(xi − yi )2
i=1

✣ë ✤♦ ❦❤♦↔♥❣ ❝→❝❤ ▼❛♥❤❛tt❛♥ ✭r = 1 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♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❚❤✉➟t t♦→♥

✶

❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ tø ❞ú ❧✐➺✉ ❝➛♥ ❞ü ✤♦→♥ ✤➳♥ ❝→❝ ❞ú ❧✐➺✉ ✤➣ ✤÷ñ❝ ❣➢♥
♥❤➣♥

✷

❙➢♣ ①➳♣ ❞ú ❧✐➺✉ t❤❡♦ ❦❤♦↔♥❣ ❝→❝❤

✸

❚➻♠ ❣✐→ trà tè✐ ÷✉ ❝õ❛ ❑ ✕ sè ❤➔♥❣ ①â♠ ❣➛♥ ♥❤➜t ❞ü❛ ✈➔♦ ❘▼❙❊ ✭❝❤å♥ ❑
ù♥❣ ✈î✐ ❣✐→ 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♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

×✉ ♥❤÷ñ❝ ✤✐➸♠ ❝õ❛ ❑◆◆
×✉ ✤✐➸♠

✣ë ♣❤ù❝ t↕♣ t➼♥❤ t♦→♥ ❝õ❛ q✉→ tr➻♥❤ tr❛✐♥✐♥❣ ❧➔ ❜➡♥❣ ✵✳
❱✐➺❝ ❞ü ✤♦→♥ ❦➳t q✉↔ ❝õ❛ ❞ú ❧✐➺✉ ♠î✐ r➜t ✤ì♥ ❣✐↔♥✳

◆❤÷ñ❝ ✤✐➸♠

❑◆◆ r➜t ♥❤↕② ❝↔♠ ✈î✐ ♥❤✐➵✉ ❦❤✐ ❑ ♥❤ä✳
❑◆◆ ❧➔ ♠ët t❤✉➟t t♦→♥ ♠➔ ♠å✐ t➼♥❤ t♦→♥ ✤➲✉ ♥➡♠ ð ❦❤➙✉ t❡st✳ ❚r♦♥❣ ✤â
✈✐➺❝ t➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ tî✐ tø♥❣ ✤✐➸♠ ❞ú ❧✐➺✉ tr♦♥❣ tr❛✐♥✐♥❣ s❡t s➩ tè♥ r➜t
♥❤✐➲✉ t❤í✐ ❣✐❛♥✱ ✤➦❝ ❜✐➺t ❧➔ ✈î✐ ❝→❝ ❝ì sð ❞ú ❧✐➺✉ ❝â sè ❝❤✐➲✉ ❧î♥ ✈➔ ❝â
♥❤✐➲✉ ✤✐➸♠ ❞ú ❧✐➺✉✳ ❱î✐ ❑ ❝➔♥❣ ❧î♥ t❤➻ ✤ë ♣❤ù❝ t↕♣ ❝ô♥❣ s➩ t➠♥❣ ❧➯♥✳
◆❣♦➔✐ r❛✱ ✈✐➺❝ ❧÷✉ t♦➔♥ ❜ë ❞ú ❧✐➺✉ tr♦♥❣ ❜ë ♥❤î ❝ô♥❣ ↔♥❤ ❤÷ð♥❣ tî✐ ❤✐➺✉
♥➠♥❣ ❝õ❛ ❑◆◆

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❱î✐ ❜➔✐ t♦→♥ ✤➣ ❝❤♦✱ t❛ ❝❤✐❛ t➟♣ ❞ú ❧✐➺✉ t❤➔♥❤ t➟♣ tr❛✐♥ ✈➔ t➟♣ t❡st ✈î✐ t➾
❧➺ ✽✿✷
⑩♣ ❞ö♥❣ ♠æ ❤➻♥❤ ❑◆◆ ✈î✐ sè ❤➔♥❣ ①â♠ k = 15

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

◆ë✐ ❞✉♥❣
✶

✣➦t ✈➜♥ ✤➲

✷

▼æ t↔ ❞ú ❧✐➺✉

✸

▼æ ❤➻♥❤

✹

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤

✺

❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤

✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

ESS
T SS
❊❙❙✿ tê♥❣ ❝→❝ ✤ë ❧➺❝❤ ❜➻♥❤ ♣❤÷ì♥❣ ♣❤➛♥ ❞÷
❚❙❙✿ tê♥❣ ❝→❝ ✤ë ❧➺❝❤ ❜➻♥❤ ♣❤÷ì♥❣ t♦➔♥ ❜ë
R2 = 1 −

2
Radjusted
=1−

n−1
1 − R2
n−k

n ❂ sè ❧÷ñ♥❣ ♠➝✉ q✉❛♥ s→t
k ❂ sè t❤❛♠ sè ❝õ❛ ♠æ ❤➻♥❤✱ ❜➡♥❣ sè ❧÷ñ♥❣ ❜✐➳♥ ✤ë❝ ❧➟♣ ❝ë♥❣ ✶
2
Radjusted
= 0.974 tù❝ ❧➔ ✾✼✪ sü ❜✐➳♥ t❤✐➯♥ ❝õ❛ ❜✐➳♥ ♣❤ö t❤✉ë❝ ✤÷ñ❝ ❣✐↔✐
t❤➼❝❤ ❜ð✐ ❝→❝ ❜✐➳♥ ✤ë❝ ❧➟♣

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❙❛✐ sè t✉②➺t ✤è✐
RM SE =
i

❙❛✐ sè t÷ì♥❣ ✤è✐
RM SE% =

(yi − yi )2
n

RM SE
× 100%
y¯

❱î✐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♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

●✐→ trà F = 12417.23457 ✈î✐ signF = 0 < 0.05 ❝❤ù♥❣ tä ❘ sq✉❛r❡❞ tê♥❣
t❤➸ ❝õ❛ ♠æ ❤➻♥❤ ❦❤→❝ ✵✱ ♥❣❤➽❛ ❧➔ ♠æ ❤➻♥❤ ①➙② ❞ü♥❣ ♣❤ò ❤ñ♣ ✈î✐ tê♥❣ t❤➸
●✐→ trà ❝õ❛ ❝→❝ ♣✲✈❛❧✉❡ t÷ì♥❣ ù♥❣ ✈î✐ ❝→❝ ❜✐➳♥ ✤ë❝ ❧➟♣ < 0.05 ❝❤ù♥❣ tä
❝→❝ ❜✐➳♥ ✤ë❝ ❧➟♣ ✤➲✉ ❝â þ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✤➳♥ ❜✐➳♥ ♣❤ö t❤✉ë❝

◆❣✉②➵♥ ❚❤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 ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

●ñ✐ þ ❝❤♦ ♥❤➔ q✉↔♥ ❧þ

❚➻♥❤ tr↕♥❣ ❤ót t❤✉è❝ ↔♥❤ ❤÷ð♥❣ ♥❤✐➲✉ ♥❤➜t tî✐ ❝❤✐ ♣❤➼ ② t➳ ❝õ❛ ❦❤→❝❤
❤➔♥❣✿ ♥❣÷í✐ ❤ót t❤✉è❝ s➩ ❝â ❝❤✐ ♣❤➼ ② t➳ ❝❛♦ ❤ì♥ ♥❤✐➲✉ s♦ ✈î✐ ♥❣÷í✐
❦❤æ♥❣ ❤ót t❤✉è❝
◆❣÷í✐ ❝â sè t✉ê✐ ❝❛♦ s➩ ❝â ❝❤✐ ♣❤➼ ❝❛♦ ❤ì♥ ♥❣÷í✐ ➼t t✉ê✐
◆❣÷í✐ ❜à ❜➨♦ ♣❤➻ ✭❇▼■ ❃ ✸✵✮ s➩ ❝â ❝❤✐ ♣❤➼ ② t➳ ❝❛♦ ❤ì♥ ♥❣÷í✐ ❜➻♥❤
t❤÷í♥❣✳

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

◆ë✐ ❞✉♥❣
✶

✣➦t ✈➜♥ ✤➲

✷

▼æ t↔ ❞ú ❧✐➺✉

✸

▼æ ❤➻♥❤

✹

❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤

✺

❈❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲

▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❉❡♠♦ ❝❤÷ì♥❣ tr➻♥❤

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤


✣➦t ✈➜♥ ✤➲
▼æ t↔ ❞ú ❧✐➺✉
▼æ ❤➻♥❤
❑✐➸♠ ✤à♥❤ ♠æ ❤➻♥❤
❈❤÷ì♥❣ tr➻♥❤

❚❤❛♥❦ ②♦✉ ❢♦r ②♦✉r ❛tt❡♥t✐♦♥ ❃✳❁

◆❣✉②➵♥ ❚❤à ◆❣➙♥

❍➺ ❤é trñ q✉②➳t ✤à♥❤