??????? y???? x1, x2, . . ., xp??????????????????????????(multiple regression model)

1
? 15 ?

• ???

2
????

• ???????????????????????
• ?????????,?????????,??????????????????????????,
  ??????????,?????????????,?????????????????????
• ?????????????????,????????????????????,?????????
• ???????,?????????????????????????,????????????????
  ????????????????

3
?15? ???

• 15.1 ?????

• 15.2 ?????

• 15.3 ?????

• 15.4 ????

• 15.5 ?????

• 15.6 ????????????? ???

• 15.7 ?????

• 15.8 ????

• 15.9 ?????

4
15.1 ?????

• ??????? y???? x1, x2, . . ., xp??????????????????
  ????????(multiple regression model)

y b0 b1x1 b2x2 . . . bpxp e
?? b0 , b1 , b2 , . . . , bp ???,e ??????
5
?????
?? y ???????? x1 , x2 , . . . ,
xp????????????????(multiple regression equation)?
E(y) ?0 ?1x1 ?2x2 . . . ?pxp
6
????????
???????????????? b0, b1, b2, . . . ,
bp??????????? b0, b1, b2, . . . ,
bp??????????????????????????(estimated multiple
regression equation)
7
????????
????? E(y) ?0 ?1x1 ?2x2 . . . ?pxp
e ?????? E(y) ?0 ?1x1 ?2x2 . . . ?pxp
b0, b1, b2, . . . , bp?????
?b0, b1, b2, . . . , bp ?b0, b1, b2, . . . ,
bp ????
8
15.2 ?????

• ???????

• ?????

?????,?????? b0, b1, b2, . . ., bp
?????????,??,????????,????????????????????????
9
?????(??)

• ?????????
• ?????????,?????????????????????
• ??

10
(No Transcript)
11
?????(??)

• ?15.3???Minitab ????15.1???????????????????

12
?????(??)

• ?????????????????0.05??????,F??
  15.81,p??0.004?????????????????????????,????,??p??
  ?a(a0.05),????????(H0ß10)????,????????t??3.98,?
  ???p??0.004?????,????????????????????????????????
  ????????,??????????????????,?????66.4,??????????
  ?????66.4 ????????????????????,??????????????????
  ?????????????

13
?????(??)

• ??,?????????????????????,???????????????15.2,?????
  ???????(x1)?????(x2)???Minitab??????15.4,?????????
  ?

14
?????(??)
15
?????(??)
16
?????
?????,?????????????,?????????????
?? bi ?????????????,xi ?????,????????
17
?????(??)
b1 0.0611
??????????????????,???????(x2)???,????(x1)??1?,??
???????0.0611???
18
?????(??)
b2 0.923
??????????,??????1?,?????????0.923???
19
15.3 ?????

• SST, SSR ? SSE ???

SST SSR SSE
?? SST ???? SSR ????????
SSE ????????
20
?????(??)

• ??????????????,??????????????15.4?Minitab?????????
  ?????? SST 23.900 , SSR 21.601 , SSE
  2.299??15.3???????????????????SST 23.900 , SSR
  15.871 , SSE 8.029?
• ??????SST????,??SST? ?????????????,?????????S
  SR??,?SSE????????????????????????

21
?????
R2 SSR/SST
????????????????????,SSR21.601? SST
23.900,??,R2 21.601/23.9000.904
??,???? y ????90.4 ??????????????????????????????
15.4????Minitab????????????,???R-sq90.4?
22
?????(??)

• ?15.3??????????????????????R-sq66.4,????????(x1)
  ??????????????66.4 ??????,??????????????????????,
  ????????????66.4 ???90.4?????,??????????????,R??
  ???

23
?????

• ????????,????????,????????????SSRSST-SSE,?SSE???
  ,SSR???,??R2SSR/SST???
• ???????????,?R2??,????????????????????????????????
  ??

24
???????

• n ????????
• P ????????

????????????, n10, p2,????,????????????????0
.88,??15.4?Minitab??????R-sq(adj)87.6,??????????
??????????????
25
15.4 ????
26
????? e ???
??? e ????????????????
?????? x1, x2 , ... , xp??,e ??????? s2?
e ??????
?? e ???? y ??? ?0 ?1x1 ?2x2 ... ?pxp ?
y ??????????????????
27
????
28
15.5 ?????
??????????? t ??? F ?????????,?????????
?????t???F??????????
29
?????F ??
F ??????????????????? ?????????
???F????????(overall significance)????
30
?????F ??
H0 ?1 ?2 . . . ?p 0 Ha ?????????0
????
F MSR/MSE
?????
????
p ??? p ? a ,???H0 ?????F Fa,???H0 ??, Fa
??????? p,??? ???n-p-1?F??,?????
31
?????F ??
32
?????F ??(??)

• ???????????????F????????????,????????? H0 ?1
  ?2 0
• Ha ?1 ? ?2???????0
• ?15.6???????(x1)?????(x2)???????Minitab???????????
  ???????,MSR 10.8? MSE0.328????(15.14)??????????
  F 10.8 / 0.328 32.9???????F??32.88,???????
  ????MSE?MSR???????????

33
?????F ??(??)
34
?????F ??(??)

• ??????????(?15.6)?????,? a 0.01??????,??p?0.000lt
  a0.01,???? H0 ?1 ?2 0?
• ?????? a0.01??????,???B?4??????????2,??????7?,F0.
  019.55???32.88gt9.55,??H0 ?1 ?2 0,???????? y
  ???????????????????????????

35
?????F ??(??)

• ??,??????????? e ???? s2????????15.6???? s2
  ?????MSE0.328?MSE????????????????????14.5????,???
  ?????????????,?s ?????,??????
  ????????????????15.6?Minitab??
  ??

36
?????t ??
??F????????,???t?????? ???????????,?????t??? ?????
(individual significance)????
t ???????????????
t ?????????,?????????? ????????
37
?????t ??
????
?????
????
p???p? a,???H0 ?????t -t?????t t????,
???H0 ??, t??? ??????n-p-1 ? t
?????
38
?????t ??(??)

• ?????????????t ????15.6???????t ????? b1, b2,
  sb1, sb2?????? b1 0.061135 sb1 0.009888 b2
  0.9234 sb2 0.2211
• ??????? ?1 ? ?2???????????? t
  0.061135/0.009888 6.18 t 0.9234/0.2211
  4.18

39
?????t ??(??)

• ?????? t ??Minitab???????,? a 0.01?????n-p-110-2
  -17????,????B?2,t0.0053.499,??6.18gt3.499,??????
  ß10????????,??4.18gt3.499,ß20??????????

40
?????
???????,???????? (multicollinearity)???????????? ?
???
?????????,?????????? ????????????0.7?,????? ??????
??
41
?????
??????????????????
?????????,?????????? ?????????
42
15.6 ????????????????
???????? y ??????? y ??? ??????,????????????? ???
??????x1, x2, . . . , xp????????? ??,??????
???????
43
????????????????
??? y ???????? y ??????? ??,????????????????, ????
????????????
??????x1, x2, . . . , xp?,??????? ?????????????
44
????????????????(??)

• ????????????,????????x1(?????)?x2(????)???????????
  ????
• ????100????2???????????????????????
• ????100????2???????????????????????
• ?x1100?x22????????? ?,???????,?????????????
  ??????7???

45
15.7 ?????
??????,?????????????, ??,??(???)?????(??????? ??)?
??
??, x2 ??????,?? x2 0 ???,? x2 1 ????
????,x2 ???????(dummy Vatianle)??????(indicator
variable)
46
?????(??)

• ?????????
• ??????????????????????????????????????????????????
  ???????,?????????????????????????,????????????????
  ????????,???????????,?????????????????,???????????
  ???????????????????10????????15. 5?

47
?????(??)
48
?????(??)

• ???y????????(??????),x????????????????(?????)???x?
  ?? y ??????????? y ß0 ß1x1e??Minitab?????
  ???????????15.7,??????????? a
  0.05???????,?x1(???????????)??????????????,t
  (?F)???p??0.016,???????x???????????????R-sq
  53.4 ??? x1????y(??????) 53.4 ????

49
?????(??)
50
?????(??)

• ??????????????????,????????????????,???
  x2?????(dummy variable)???????(indicator
  variable)??????????,???????????? y
  ß0ß1x1ß2x2e?15.6???????????????????

51
?????(??)
52
?????(??)

• ??Minitab??15.6???????????????Minitab?????????15.8
  ,?????????????????????0.05???????,F???p??0.001,
  ??????????????????15.8?t?????????????????????????,
  R-sq 85.9?R-sq(adj) 81.9 ???????????????????
  ?????????,?(15.17)?????????????????

53
?????(??)
54
?????
55
????????
???????k???,???k????? ?,??????k-1?????,???? ??????
1??0?
??,??????????????A, B, C ???????????????x1,
x2??? ?????????? A (0, 0), B (1, 0) ? C (0,
1)
??????k????,????????? k-1??????
56
15.8 ????

• ??????????????????????? i ???????????????

57
????(??)

• ?15.7??????????????????????????,?????Minitab??????
  ???????????????????
  ????
• ?15.10?????15.7???????????????????????????????????
  ??????????????-2?2??,??,????????? e
  ?????????,??????,??????????????

58
?????

• ???(outlier)?????????????????
• ?????????????????????
• ????,??????????????,??????????????
• ???????????,??????Student?????(Studentized
  deleted residuals)?????????????????

59
????(??)

• ?????????15.7????????,??????????????????

60
????(??)
61
Student?????????

• ????????? i ??????,??????n-1????????????????
• ? s(i) ???????????
• ??? i ????????,? s(i) lt s
• ????????????????????????????

62
Student?????????(??)

• ???????Student???????????????Minitab?????????Stud
  ent???????15.8?t ????????Student????????????????,?
  ???? p ?????????,n????????,??,?????? i
  ????,????????n-1,????????????(n-1)-p-1?

63
Student?????????(??)

• ???n10 , p2????????,??????????,??????????9-2-1
  6??0.05??????,t???(??B?2)?????6?t0.0252.447????
  i ?Student???????-2.447???2.447,???????? i
  ????????????15.8??Student????????????,????????????
  ???????

64
Student?????????(??)
65
????????

• ?????????????????????????????????????????,????????
  ????? hi ,?????????????????,???????????????? hi ?
• Minitab????????,?hi gt 3( p 1)/n?????????????????
  ???

66
????????(??)

• ??????????,?????p2,?????n10,???????????3(21)/10
  0.9,?????????????????15.9??????????????,???????,?
  ??????,???????????

67
????????(??)
68
???????????????????

• ??????(Cooks distance measure)???? i ?????????
  hi ??? ?????????????

69
???????????????????

• ??????(??)??????,?????????,??????????????????
• ??????,??? i ???????????Digt1,????????????

70
???????????????????(??)

• ???15.10?8???????????????8??????????0.91gt0.75(????
  ????),????????????????????????,???????????????

71
???????????????????(??)

• ??15.10?????????????????????15.11??Minitab????????
  ??????
• ?15.11??????????????????????x15,
  y39???????,?????7????????????????????????????
  y ???????

72
(No Transcript)
73
???????????????????(??)

• ?15.9????????Minitab????????????????????8?????Di
  0.650029??????????,???????Di gt1??????????????????
  ??

74
15.9 ?????

• ???????,y ????????E(y)??????????
• ???????,?????????? E(y) ? x1, x2, . . . , xp
  ??????????????????

75
?????

• ???? y ???0?1,?? (15.27) ?,E(y) ??????????
  y1?,???x1, x2, . . . , xp ????
• E(y) ???????,??????????(logistic regression
  equation)??

76
?????
77
?????(??)

• ?????Simmons????????????????????Simmons???????????
  ???5,000??????????????,????????????? 200???????
  50????
• ??????,??Simmons???????????? 200??????????

78
?????(??)

• ????????Simmons?????????????Simmons????,??????????
  ???????????? 200???????Simmons?????50?Simmons????
  ??50???Simmons?????????????Simmons?????100????????
  ???,Simmons????????(???????????1????0)?
• ?10??????????????15.11????????Simmons?????????,???
  ??????,?1??????Simmons???0??????Simmons?????????,
  1????????? 200??? 50????

79
?????(??)

• ??????15.11???????????????????????????????????????
  ?Simmons?????????,?????????????????????0?1,???????
  ????????????????????????????????????????Simmons???
  ??????????????????

80
?????(??)
81
??????????

• ?????????????????? b0, b1, ... , bp??????? (ß0,
  ß1, ß2,, ßp)?????????????????????????????????????
  ????????????????????? (estimated logistic
  regression equation)????,
  ???????????????,y1???????

82
??????????(??)

• ??Simmons??????????
• ????????????????????

83
??????????(??)

• ??????(??15.11),Minitab????????????????? ß0, ß1?
  ß2?????????15.13,?? b0-2.1464, b10.3416?
  b21.0987,??????????????????
• ????(15.32)????????????????,???????
  2,000???Simmons????????,? x12, x20???(15.32)

84
??????????(??)
85
??????????(??)

• ????????????????0.19????,??????
  2,000???Simmons?????????? x12,
  x21???(15.32)??????????????0.41????????Simmon
  s????????????????????,?????????????

86
?????

• ???????????????????
• ??G?????????,? z ???????????????????????????????
  x??,????? H0ßi0 Haßi ? 0
  ????????,??????????????????????????Minitab???Z???
  ?????? zibi/sbi ??,???p?????p??

87
?????(??)

• ?Simmons????,?????? H0ß1ß20
  Ha?????????0
• ??? a0.05???Simmons?????????????
  x?z??2.66????p??0.008???? a0.05??????,?? H0
  ß10???????,????? H0ß20,????z??2.47?p??0.013????
  a0.05??????,??????????

88
??????

• ??Simmons???????????????0.40????????15.12???????,?
  ???????
• ??Simmons?????????????? 2,000?????
• ??Simmons?????????????? 6,000?????

89
??????

• ?????????????,??Simmons??????????,?????
  5,000????0.3921???,Simmons???????????????
  5,000??Simmons???????????

90
??????????

• ??????????(odds in favor of an event
  occurring)?????????????????????
• ?????????? y ???1????????????,??? y 1???????

91
???

• ??????????????????????????
• ??????????????????? ???
• ????????????????????????????????????????
• ????????????????????,???????????????

92
???(??)

• ?????????????,???? 2,000???Simmons???(x12,
  x21)????? 2,000???Simmons??????(x12,
  x20)???????????x????????????

93
???(??)

• ???????? x12, x21?? y1????0.4099,???? x12,
  x20??y1????0.1880,????????????????????
  ??? 2,000???Simmons??????????????????
  2,000???Simmons???????3??

94
???(??)

• ?Simmons??? x1 ??,x1 ??????????,?? x2
  ???????????????????????????????????????????????
  ,????????????????????????

95
???(??)

• ?Simmons???,?????????? 5,000 (x15)
  ????????????? 2,000 (x12) ?????????????c5-23??
  ????????????????? 5,000???????????????
  2,000???????????2.79??????,????????
  3,000?????2.79?

96
???(??)

• ????,?????????????????????????1,??????????????????
  ??????????????,???????1??????????????????????,?15.
  13?Minitab??????????95 ?????
• ??,x?????????1.41,?95 ??????1.09?1.81????????????
  1,????? x1??????????????,?? x1????95?????1.25?7.1
  7????????????1,????? x2???????????

97
Logit??

• ?? y1?????????????????? e ???????,????

• ??????logit,

98
Logit??

• ? g(x1, x2, ... , xp) ???(15.27)?? ß0 ß1x1
  ß2x2ßpxp,??????????????????????????????,????
  logit??????? g(x1, x2, ... , xp)?????logit(estima
  ted logit)??

99
Logit??

• ??????logit??,??????????

100
Logit??(??)

• ?Simmons????,???logit??????????????????logit
  ?????????????????,?????Simmons?????????

101
End of Chapter 15