???????????????????(y)?????????????(x)?????????????????????????????????

1
? 16 ?

• ?????????

2
????

• ???????????????????,????1,000????????,????,????
  ?????????????????
• ?????????????????????????????????
• ???????????????????(y)?????????????(x)????????????
  ?????????????????????
• ???????????????????,??????????????????????????????
  ???

3
?16? ?????????

• 16.1 ??????

• 16.2 ??????????

• 16.3 ??????????

• 16.4 ??????

• 16.5 ????

• 16.6 ?????????? ??????

4
16.1 ??????

• ???????(?0, ?1, . . . , ?p)???,??????????? y ? xi
  ???????

• ? p???????????(general linear model)

• ????? zj(j1, 2, ... , p)??x1, x2, ... ,
  xk(????????)????

5
??????

• ??????,????? zj ???????x?????????????????????x???,
  ???????? y?

• ??????z1x1,?(16.1)?????????????????????????

6
?????????

• ????????,??? z1x1?z2 ,

• ??????????????????

7
?????????(??)

• ????????
• ??????????????????????????????????????(??????????)
  ?????
• ?16.1??????15?????????????????,?16.1??????

8
?????????(??)
9
?????????(??)

• ??????????????????????????????????????????????,???
  ????16.2?Minitab????,??????????????????? Sales1
  112.38 Months?? Sales ??????????????? Months
  ????????
• ?16.3????????

10
?????????(??)
11
?????????(??)
12
?????????(??)

• ????????????????????????????(p??0.000)????????????
  ?????78.1(R-sq78.1),???????????,??????????????

13
?????????(??)

• ??????????????,?????16.1????????????(??????????)??
  ?????16.4?????????Minitab??????,????????Sales45.
  36.34 Months-0.0345 MonthsSq?? MonthsSq
  ??????????
• ?16.5??????????,??????16.3????

14
?????????(??)
15
?????????(??)
16
?????????(??)

• ?0.05??????,??????????????( F ??? p
  ??0.000),???????????????????????,???MonthsSq? t
  ??? p ?(0.002)??0.05,????????MonthsSq???Months???
  ???????????R-sq(adj)88.6 ??,??????????????,?????
  ,???????????????????????????

17
????

• ??????? y ??????x1, x2 ????,??????????????????????
  ????????

• ????????,?? z5 x1x2??????????????????

• ????????????(interaction)?

18
????(??)

• ??????????????????????
• ?????,?????????????????????????????3????24??????
  2.00, 2.50, 3.00,??2???????50,000?
  100,000,??????(?????????)?????????????????16.2???

19
????(??)
20
????(??)

• ?16.3??16.2???,????? 2.00,????
  50,000??????461,000????? 2.00,????100,000?????
  ??808,000?????,???? 2.00?,???? 100,000?
  50,000?????????808000-461000347000?
• ??,???? 2.50?,????????????????646000-36400028200
  0????3.00?,????????375000-33200043000?????,????
  ???????????????????????,??????,???????????????????
  ???????????????????

21
????(??)
22
????(??)

• ????????????????,?16.6???6????????????????????????
  ?,???????????????????????????????????????????????
  ???,?????????????y???????,?????????????????y???,??
  ?????????

23
(No Transcript)
24
????

• ???????????,???????????
• ??
• y ???(?)
• x1 ??()
• x2 ????(1,000)

25
????

• ???????????,???????????????????????????z1, z2, z3
• ??
• y Sales ???(?)
• z1 x1 (??) ?????()
• z2 x2 (AdvExp) ????(1000)
• z3 x1x2 (PriceAdv) ?????(??AdvExp)

26
????(??)

• ?16.7?????????????????Minitab?????????????????sal
  es-276175 Price19.7 AdvExp-6.08 PriceAdv
• ?????PriceAdv?t???p??0.000,????????????????????,??
  ?????????,?????????,??????????????????

27
????(??)
28
??????

• ????????????????????????????

• ??????????????10? e2.71828????????

• ???????????????1/y??y???????????????????(reciproca
  l transformation)?

29
??????(??)

• ??????????,????16.4?????,??????12??????????(??????
  ?????)?????????16.8,???????????????

30
??????(??)
31
??????(??)

• ??,????????????????????Minitab??????16.9?????????
  ??? MPG56.1-0.0116 Weight?? MPG
  ??????????? Weight ??(?)
• ???????(F??? p ??0.000) ,??????(R-sq93.5)???,???
  ??16.9???3?????????????

32
??????(??)
33
??????(??)

• ?16.10????????????????????????????????,???????????
  ??????????????? y ??????????,????????????????????
  ?????????????,????????????????????????????

34
??????(??)
35
??????(??)

• ?????????????????????,????????????????????????????
  ??Minitab??????16.11,????????????????????LogeMPG,?
  ????????????16.12?
• ?16.12????????????16.10?????,????????????????????
  ????????????????????,?????????,??????????,????????
  ???????? LogeMPG4.52-0.000501 Weight

36
??????(??)
37
??????(??)
38
??????(??)

• ???????2,500????????,???????????????????????LogeM
  PG4.52-0.000501(2500)3.2675????e?3.2675??,??26.
  2?,?????????????

39
???????????

• ????????(?0, ?1, . . . , ?p )??????????

• ????????,??????????,?????(16.1)???????????????

• ????????????

• ????????????????,??????????????????

40
???????????(??)

• ??,??????? y ?????x(??1,000)???????????? E(y)
  500(1.2)x??,?x1,E(y)500(1.2)1600?x2,E(y)500
  (1.2)2720? x3,E(y)500(1.2)3864???????E(y)????
  ?????????,20,???

41

• ??(16.7)??????,???????????????? log E(y)log ?
  0x log ? 1
• ??y log E(y) , ? 0log ? 0, ? 1log ?
  1,?(16.8)???? y' ? 0 ? 1x

42

• ????,????????????????? ? 0? ? 1??????????b0?b1??
  ,????????????????????x???????y????,????x????(16
  .9)??? ???? ????,??y?????????

43
16.1 ??????????

• ?????x1????????????(?????x1, x2????????????)??????
  F??????????????

• ???F????????x??????????????F????????????????????,?
  ???????n-p-1?

44
??????????(??)

• ?????????????????????
• ??????????????????????????????????????????????????
  x1??????,?????????????????????

45
??????????(??)

• ??15????????????SSE8.029?????????????? --
  ????,?x??,?????????????????????SSE2.299?

46
??????????(??)

• ???SSE(x1)???????x1????????????,SSE(x1,
  x2)???????x1, x2???????????????,??x2??,SSE?????
  ??????F??????????????

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

• F?????????????SSE???????????????,??????x2???,F????
  ??????????????????,???SSE????F?????????????????
  ????????????????,????x1?x2??,?? p2?

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

• ?????F????????????B?4,? a 0.05?,F0.055.59??
  ?F17.45gtF0.055.59,??????????,???,???x1??????????
  ???????x2,???????????????

49
????

• ?????q??????????,??qltp
• ?????? xq1, xq2, . . . , xp?????,?????p?????????

50
????

• ?????? xq1, xq2, . . . , xp???????,?????????
• H0 ßq1 ßq2 ßp 0
• Ha ?????????0
• F ???

51
????

• ????F??Fa??, Fa???????p-q,??????n-p-1?
• ??Fgt Fa ,???????,?????????????????????

52
????(??)

• ?????????30????????????????x1, x2?x3??????????150,
  ???????x1, x2, x3, x4?x5???????????100?????????x4?
  x5??????????????
• ??,???????SST?????30-129,???????????????5(???????
  ???????)???,???????????????29-524???,MSE(????)10
  0/24 4.17???,F????

53
????(??)

• ?????F ???????2,?????24?F????,?0.05??????,??B?4??F
  0.053.40???F6.00gt3.40,?????,??x4,
  x5?????????????????????

54
p ????

• p ?????????????????????????

• ?F????? p ??????????a ???????

• p ????F????????,????????Minitab?Excel???,??????

55
p ????(??)

• ????????????,F????6.00(F6.00?F0.053.40??),??????
  ?x4, x5????????F?(F0.06,?????2,?????24)???p??0.00
  8???p?0.008lta0.05,??????????????????????

56
16.3 ??????????

• ???????????,???8?????25?????????????????????????.?
  ??(David W. Cravens)????????,??????????????

57
(No Transcript)
58
??????????

• ??????

59
??????????

• ???????????????,?16.13???Minitab????????,Sales?Tim
  e????????0.623,Sales?Poten????????0.598,?????

60
??????????

• ????Time?Accounts??????0.758,??,??Accounts????????
  ???????,?????Time???????????
• ?15.4??????????,????????? -- ???????????????????0.
  7,?????????????
• ??,???????,????,???????Time?Accounts???????????Cha
  nge?Rating????????0.549,???????????

61
??????????

• ????Sales??????????????,?????????????????????????S
  ales?Accounts????????0.754,Accounts?Sales?????????
  ?????????,???????????????,??,Accounts????(0.754)(1
  00),?56.85 ?Sales????????????Time,
  Poten?AdvExp??????????0.6?

62
??????????

• ??????????????,??????????????????????????Minitab??
  ????16.14,?8???????????????????88.3?????,?0.05???
  ???,p??(??????? t?????p?)????Poten,
  AdvExp?Share?????????,??,????????????????????????1
  6.15???????????????????,????????????82.7,?????8??
  ?????,??????????

63
(No Transcript)
64
??????????
65
??????????

• ???????,????????????????????????????????????,?????
  ????,??????8???????????????(????????),28??????????
  ?????(?8???????????????????),???????,?????255?????
  ??????????????

66
16.4 ??????

• ????
• ????
• ????

???,?????????? ??,?????????,? ??????????????
??????????,??? ?????????????

• ??????

67
????

• ?????????????????????????,??,????????????F????p??

• ??? a ?????????????????Alpha to remove

• ??????????????,???????????????????

68
????
???? p?lt alpha to enter ?
?????????? ?????F??p?
No
No
Yes
?????p ? ??????? ????
???? p?gt alpha to remove ?
Yes
??
???????? ???F??p?
?????p??? ?????????
???????? ????
69
????

• ?16.16??Minitab???????????????????,Alpha to
  remove?Alpha to enter??????0.05??Minitab??????????
  ??????????????16.16?????,???4?????,
  ????????????881,???454?R-sq???56.85
  ???90.04????????????R-sq??88.05?

70
(No Transcript)
71
????

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

72
????

• ????????????

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

• ????????? p ???Alpha to enter,??????????

73
????
????????
?????????? ?????F??p?
???? p?lt alpha to enter ?
????? p ??? ?????????
Yes
No
??
74
????

• ?Minitab????????????????????,????????,??????(A
  lpha to enter???0.05)????????????????

75
????

• ???????????????????

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

• ?????????p???Alpha to remove,??????????

76
????
????????? ????
?????????? ?????F??p?
???? p? gt alpha to remove ?
????? p ??? ?????????
Yes
No
??
77
????

• ?Minitab????????????????????????(Alpha to
  remove???0.05)???????????????????????,????????
  ????AdvExp, Poten?Share????????????Time,??????????
  ????Accounts?

78
????

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

79
??????

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

• ???????????????????,??????????????????????,?Minita
  b??????,?16.17???????????????????????????

• ?????????????????????,????????????????????????????
  ??????????????????????(R-sq)?

80
(No Transcript)
81
??????

• ??,?????????,Accounts?R-sq56.8,?????????????????
  AdvExp, Accounts?R-sq77.5,????????????????Pote
  n, AdvExp, Share?R-sq84.9,??????????????????????
  ??,?????Time, Poten, AdvExp, Share, Change,
  Accounts?????????????(Adj. R-sq)??,???89.4???,???
  ???(Poten, AdvExp, Share, Accounts)????????????88
  .1 ?89.4 ?????????????,?????????????

82
?????

• ????????????????????????????????????,???????????,?
  ?????????????14???15?????,????????????,???????????
  ???????????????????,??????????????????
• ??????????????????????Accounts, AdvExp, Poten,
  Share???????????????????????????16.7???????????,??
  ??????????????????

83
?????

• ??16.7????,??AdvExp, Accounts???????,??????????75.
  5,??????????????12.6???????????(Poten)????,??Acco
  unts, AdvExp?????????????????????????,????????????
  ?????,???????????????

84
16.5 ????

• ??????????????,????????????

• ????? yt ????? t ?? y ?,yt ??? t ??? y ??????????

• ???????????????(??????)

85
????????

• ??????,?????????,??????????????

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

86
????????
87
????????

• ????????,?????????????????????????

• ????????,?????????????????????????

• ??????????????????

88
????????

• ?? e ??????,?????????

et r et-1 zt
?? ? ??????1???, zt ??????????????,?????0,???? s 2

• ? ? 0,???????,?????0,???? s 2 ???,????????,??????
  ????

• ??-??????????? ? ???0?

89
????????

• ??-???????

? i ??????
90
????????

• ??-???????

• ???????????0?4

• ????????????(?????),??????????

• ?????????????(?????),????????????

• ???2?,??????????

91
????????

• ??????????

???????

• ????????????????

???????
???????
?????????????
92
????????

• ?16.19???????16.8?????????????????A???????????,?dlt
  dL,??????????????????dL d dU,?????????????dgt
  dU,???????????????????

93
????????

• ?B?????????????dgt4-dL,????????????4-dU d
  4-dL,??????????????dUlt4-dU,??????????????????

94
????????

• ?C??????????dltdL?dgt4-dL,???????,??????????dL d
  dU?4-dU d 4-dL,??????????????dUltdlt4-dU,???
  ?????????????

95
16.5 ????????????????

• ???????????????????????????

• ??????????????????????ANOVA???

96
????????????????(??)

• NCP????????????????????????????????????????????,??
  ??????????????6??????,?????????????,??????????????
  ??????????????
• ??NCP????????,?????????????????????????????,??????
  ???k ??????,?????k-1???????NCP???,????x,
  x???????,???????????16.9?

97
????????????????(??)

• ?????????x1, x2?????y????????????,

• E(y) ????????????
• b0 b1x1 b2x2

????? E(y) b0 b1(0) b2(0) b0
???? E(y) b0 b1(1) b2(0) b0 b1
???? E(y) b0 b1(0) b2(1) b0 b2
98
????????????????(??)
???????????????????
??
E(y)????
????? ???? ????
b0 79 b0 b1 79 5 74 b0 b2 79 13
66
99
????????????????(??)
100
????????????????(??)
101
????????????????(??)

• ???????????,?

????????????E(y) ?????????????E(y) 0
????????????E(y) ?????????????E(y) 0
102
????????????????(??)

• ??b0????????E(y) ,??b0 b1???????E(y)
  ,??????(b0 b1) - b0 b1

• ??, b0 b2???????E(y)?????????(b0 b2) - b0 b2

• ??,??????,?? b1 0?b2 0,????????????

103
????????????????(??)

• ????????????????

H0 b1 b2 0

• ???????????????,???MSR/MSE?F??????????
• ??????,??????????2,??????????15?

104
????????????????(??)

• ????,??????MSR?MSE???,F??

105
????????????????(??)

• ANOVA ?

????
???
??
???
p
F
516 430 946
2 15 17
?? ?? ??
258 28.67
9.00
0.003
106
????????????????(??)

• ?0.05??????,?????2,?????15?F???????3.68?

• ??F?????????,??????????H0 ß 1 ß
  20,??????????????????????????

• ?p????,??p?0.003lta0.05,????????H0 ß 1 ß 2 0?

107
End of Chapter 16