Bài giảng Thống kê Tác giả: TS. Cao Hào Thi, Trường Đại học Bách khoa, ĐHQG Tp.HCM, 2010

Trng HBK Tp.HCM Thng K - Chng 1

TS. Cao Ho Thi 1

CHNG 1CHNG 1

D LIU D LIU

1

vv

THNG KTHNG K

NI DUNG CHNHNI DUNG CHNH

Thng k v cc ng dng trong kinh doanh v

kinh t

D li

2

D liu

Ngun d liu

Thng k m t

Thng k suy din

THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH T

Thng k l mt Ngh thut v Khoa hc v:

Thu thp

3

Phn tch

Trnh by

V gii thch D LIU

www.daykemquynhon.ucoz.com


TS. Cao Ho Thi 2


ng dng trong kinh doanh v kinh t:

Cc ng dng ca thng k rt hin nhin trong nhiu

4

lnh vc

Thng k c s dng :

Thng bo cho cng chng

D bo cho vic lp k hoch v ra quyt nh


ng dng trong kinh doanh v kinh t:

Cc lnh vc kinh doanh v kinh t da trn cc k thut v thng tin thng k:

5

k thut v thng tin thng k:

K ton

Ti chnh

Tip th

Sn xut

Kinh t


Cc phn mm thng k so vi Excel

Cc phn mm thng k thng l Hp en MINITABMINITAB: l mt phn mm thng k c ngun gc

6

c thit k ti i hc Penn State c bit dnh cho sinh vin.

SAS: SAS: Statistical Analysis System H thng phn tch thng k

SPSS: SPSS: Statistical Package for the Social Science Phn mm thng k cho khoa hc x hi



TS. Cao Ho Thi 3

THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH TCc phn mm thng k so vi Excel

S dng Excel phn tch thng k bi v: Excel sn c cc vn phng

Excel mnh gii quyt cc vn thng k thng

7

Excel mnh gii quyt cc vn thng k thng gp

Ngi s dng c th hiu c ngha ca cc vn thng k

Cc nh qun l v ra quyt nh thnh cng l nhng ngi c th hiu v s dng cc thng tin mt cch hiu qu nht

D LIUD LIU

D liu D liu l cc s kin v con s c thu thp, phn

tch v tng kt trnh by v gii thch

8

Tp d liu l tt c cc d liu c thu thp cho mt nghin cu c th

Thang o D liu nh tnh so vi nh lng D liu cho so vi chui thi gian

D LIUD LIU

Cc phn t, cc bin v cc quan st Phn t l tan b thc th da vo d liu c thu

thp

9

Bin l cc c tnh c quan tm i vi cc phn t

Quan st l tp cc i lng o lng c thu thp

i vi mt phn t c th



TS. Cao Ho Thi 4

D LIUD LIU

VariablesVariablesStockStock Annual Earn/Annual Earn/

CompanyCompany Exchange Sales($M) Sh.($)Exchange Sales($M) Sh.($)

DataramDataram AMEXAMEX 73.1073.10 0.860.86

10

ElementsElements Data SetData Set DatumDatum

EnergySouthEnergySouth OTCOTC 74.0074.00 1.671.67KeystoneKeystone NYSENYSE 365.70365.70 0.86 0.86 LandCareLandCare NYSENYSE 111.40111.40 0.330.33PsychemedicsPsychemedics AMEXAMEX 17.6017.60 0.130.13

Cu hi?Cu hi?

Tham kho Bng 1.1:B D LIU CA 5 LAI CHNG KHAN:

11

C bao nhiu phn t trong b d liu ny ? C bao nhiu bin trong b d liu ny? C bao nhiu quan st trong b d liu ny? C bao nhiu s lng d liu trong b d liu

ny?

D LIUD LIU

Thang o Xc nh lng thng tin c trong d liu v ch ra s tng kt d liu v phn tch thng k no l thch hp nht

12

Thang o ch danh

Thang o th t

Thang o khong

Thang o t l



TS. Cao Ho Thi 5

D LIUD LIU Thang o ch danh

S dng nhn hiu hoc tn nhn dng mt thuc tnh ca phn t bng s hoc khng bng s

Thang o th tC c tnh ca thang o ch danh v c th dng sp hng hoc th t d liu bng s hoc khng bng sTh kh

13

Thang o khongC c tnh ca thang o th t v khong cch gia cc quan st c din t di dng cc n v o lng c nh lun lun bng s

Thang o t lC c tnh ca thang o khong v t l ca 2 gi tr l c ngha lun lun bng s(Cha gi tr Zero C ngha l khng c g)

D LIUD LIU

D liu nh tnh so vi nh lng

D liu nh tnh

D liu nh tnh l cc nhn hiu hay tn c dng

14

D liu nh tnh l cc nhn hiu hay tn c dng

nhn dng v c trng cho mi phn t

BIn nh tnh l bin vi d liu nh tnh

D liu nh tnh s dng thang o ch danh hoc thang

o th t; c th o bng s hoc khng bng s

D LIUD LIU


D liu nh lng

15

D liu nh lng l d liu cho bit s lng bao nhiu

ca mt i lng no

Bin nh lng l bin vi d liu nh lng

D liu nh tnh s dng thang o khong hoc thang o

t l; lun o bng s



TS. Cao Ho Thi 6

D LIUD LIU


S khc nhau gia d liu nh lng v nh

16

tnh Cc php tnh s hc thng thng ch c ngha i vi

d liu nh lng

Tuy nhin, khi d liu nh tnh c ghi nhn nh cc gi tr bng s th cc php tnh s hc s cho ra cc kt qu khng c ngha

Cu hi ?Cu hi ?

Hy pht biu xem cc bin sau y bin no l bin nh tnh, bin no l bin nh lung v hy ch ra thang o thch hp cho mi bin.

T i

17

Tui Gii tnh Th hng trong lp Nhit Thu nhp

D LIUD LIU

D liu cho v d liu chui thi gian

D liu cho l cc d liu c thu thp trong cng

18

p g g

hay gn cng mt thi im

D liu chui thi gian l cc d liu c thu thp

trong cc thi im lin tip nhau



TS. Cao Ho Thi 7

NGUN D LIU NGUN D LIU

Ngun d liu c th thu thp t:

Cc ngun hin c:

19

Internet tr thnh mt ngun d liu quan trng

Cc nghin cu thng k:

Nghin cu th nghim

Nghin cu quan st

NGUN D LIUNGUN D LIU

Cc sai s ca thu thp d liu Mt sai s trong thu thp d liu xy ra khi gi tr ca d

liu thu thp c khng bng vi gi ng/thc c

20

c t mt qui trnh thu thp ng

S dng d liu sai c th xu hn khng s dng bt k d liu no

GIGO Garbage In Garbage Out Rc vo Rc Ra

THNG K M TTHNG K M T

Thng k m t: Thu thp, Tng kt v M t d liu

Cc phng php c s dng tng kt d liu:

Lp Bng

21

Lp Bng

Th

Bng s



TS. Cao Ho Thi 8

THNG K M TTHNG K M T

Thng k m t:

Cc tham s thng k

22

g

Tn s

Phn phi xc sut

THNG K SUY DINTHNG K SUY DIN

Tng th l tp tt c cc phn t cn quantm trong mt nghin cu c th

Mu l mt tp con ca tng th

23

p g

Thng k suy din: l qu trnh s dng dliu thu thp c t mu c lng hockim nh cc gi thuyt thng k v cc ctrng ca tng th

THNG K SUY DINTHNG K SUY DIN

Ly MuLy Mu

24

Tng thTng thNN

MuMunn

c Lngc LngKim nh gi thuytKim nh gi thuyt



TS. Cao Ho Thi 9

CHNG 2CHNG 2

TRNH BY TRNH BY

25

BNG BNG v BIU BNG BNG v BIU


Tng kt d liu nh tnh

Tng kt d liu nh lng

26

Phn tch d liu khm ph: Trnh by dng

cnh v l

th phn tn im v bng cho

TNG KT D LIU NH TNH TNG KT D LIU NH TNH

Phn phi tn sPhn phi tn s l mt bng tng kt mt tp d

liu trong trnh by tn s (hay s) ca cc gi tr

27

g y ( y ) g

quan st c trong mi lp ca cc lp khng trng

ln nhau



TS. Cao Ho Thi 10

TNG KT D LIU NH TNHTNG KT D LIU NH TNHD LIU T MT MU GM 50 LON NC GII KHT

Coke Classic Sprite Pepsi-ColaDiet Coke Coke Classic Coke ClassicPepsi-Cola Diet Coke Coke ClassicDiet Coke Coke Classic Coke ClassicCoke Classic Diet Coke Pepsi-ColaCoke Classic Coke Classic Dr Pepper

28

Coke Classic Coke Classic Dr.PepperDr.Pepper Sprite Coke ClassicDiet Coke Pepsi-Cola Diet CokePepsi-Cola Coke Classic Pepsi-ColaPepsi-Cola Coke Classic Pepsi-ColaCoke Classic Coke Classic Pepsi-ColaDr.Pepper Pepsi-Cola Pepsi-ColaSprite Coke Classic Coke ClassicCoke Classic Sprite Dr.PepperDiet Coke Dr.Pepper Pepsi-ColaCoke Classic Pepsi-Cola SpriteCoke Classic Diet Coke

TNG KT D LIU NH TNHTNG KT D LIU NH TNH

PHN PHI TN SCA LON NC GII KHT

Nc gii kht Tn s

29

Nc gii kht Tn sCoke Classic 19Diet Coke 8Dr.Pepper 5Pepsi-Cola 13Sprite 5Tng 50


Phn phi tn s tng i v tn s phn trm Phn phi tn s tng i: Mt bng tng kt tp

t d li t t h b t t i h

30

mt d liu trong trnh by tn s tng i ngha l, t s ca tng s cc gi tr quan st c trong mi lp ca cc lp khng trng ln nhau

Tn s tng i ca 1 lp = Tn s ca 1 lp / n

Tn s phn trm = Tn s tng i* 100



TS. Cao Ho Thi 11


Phn phi tn s tng i v tn s phn trm

31

Phn phi tn s tng i: Mt bng tng kt tp

mt d liu trong trnh by phn trm ca tng s

cc gi tr quan st c trong mi lp ca cc lp

khng trng ln nhau


PHN PHI TN S TNG I v PHN TRMCA LON NC GII KHT

Nc gii kht Tn s tng i Tn s phn trm

32

Nc gii kht Tn s tng i Tn s phn trmCoke Classic .38 38Diet Coke .16 16Dr.Pepper .10 10Peppsi-Cola .26 26Sprite .10 10

Tng 1.00 100

TNG KT D LIU NH TNHTNG KT D LIU NH TNHBiu hnh thanh v biu hnh trnBIU HNH THANH CA NC GII KHT

1820

33

02468

1012141618

CokeClassic

Diet Coke Dr. Pepper Pepsi- Cola Sprite

Nc gii kht

Tn

s



TS. Cao Ho Thi 12


Biu hnh thanh v biu hnh trn

BIU HNH TRN CA NC GII KHT

34

Coke Classic

38%

Diet Coke16%

Dr. Pepper10%

Pepsi- Cola26%

Sprite10%

TNG KT D LIU NH LNGTNG KT D LIU NH LNG

Phn phi tn sPhn phi tn s l mt bng tng kt mt tp d

liu trong trnh by tn s (hay s) ca cc gi tr

35

g y ( y ) g

quan st c trong mi lp ca cc lp khng trng

ln nhau


Phn phi tn s Xy dng mt phn phi tn s

Thu thp d liu mu

36

Xc nh s lp khng trng lp

Xc nh chiu rng ca mi lp

Xc nh cc gii hn ca mi lp

m s cc gi tr d liu c trong mi lp

Tng kt cc tn s ca lp vo trong mt bng phn phi tn s



TS. Cao Ho Thi 13

TNG KT D LIU NH LNGTNG KT D LIU NH LNGPhn phi tn s S lp (K): 5 K 20 Chiu rng lp

Chiu rng lp = (Gi tr ln nht Gi tr nh nht) / K

37

Cc gii hn ca lpCc gii hn ca lp l s ln nht v nh nht thuc v lp

Gii hn di ca lp = S nh nht

Gii hn trn ca lp = S ln nht

S khc bit gia gii hn di ca cc lp lin nhau s cho ta chiu rng ca lp


Phn phi tn s Cc bin gii ca lp

Cc bin ca lp l cc ng phn chia gia cc

38

Cc bin ca lp l cc ng phn chia gia cc

lp

im gia ca lp

im gia ca lp l gi tr nm gia cc gii

hn di v gii hn trn ca lp


CC THI GIAN KIM TON CUI NM(Tnh theo s ngy)

39

12 14 19 1815 15 18 1720 27 22 2322 21 33 2814 18 16 13



TS. Cao Ho Thi 14


PHN PHI TN S I VI D LIU THI GIAN KIM TAN

Thi gian kim tan Tn s

40

g(ngy)10-14 415-19 820-24 525-29 230-34 1Tng 20


Phn phi tn s tng i v tn s phn trm

41

Tn s tng i ca 1 lp = Tn s ca 1 lp / n

Tn s phn trm = Tn s tng i* 100


PHN PHI TN S TNG I V TN S PHN TRM

I VI D LIU THI GIAN KIM TAN

Thi i T t i T h t

42

Thi gian Tn s tng i Tn s phn trm(ngy)10-14 .20 2015-19 .40 4020-24 .25 2525-29 .10 1030-34 .05 5Tng 1.00 100



TS. Cao Ho Thi 15


Biu im

Trc honh trnh by min cc gi tr ca d liu.

43

Mi gi tr c biu th bng mt im nm trn trc

01234

10 15 20 25 30 35

Thi gian kim tan tnh theo ngy


Biu tn s

Mt biu tn s c xy dng bng t cc

44

bin quan tm trn trc honh v tn s, tn s

tng i, tn s phn trm trn trc tung

Biu tn s m t dng ca tp d liu


6789

45

0

1

2

3

4

0 5 10 15 20 25 30 35

012345

5 10 15 20 25 30 35Thi gian kim tan tnh theo ngy



TS. Cao Ho Thi 16


Cc phn phi tch ly

Phn phi tn s tch ly trnh by s cc quan

46

st c gi tr nh hn hoc bng gii hn trn

ca lp ca mi lp


CC PHN PHI TN S TCH LY, TN S TNG I TCH LY V TN S PHN TRM TCH LY

I VI D LIU THI GIAN KIM TAN

Thi gian (ngy) Tn s Tn s tng i Tn s %Tch ly Tch ly Tch ly

47

Tch ly Tch ly Tch ly

Nh hn hoc bng 14 4 .20 20Nh hn hoc bng 19 12 .60 60Nh hn hoc bng 24 17 .85 85Nh hn hoc bng 29 19 .95 95Nh hn hoc bng 34 20 1.00 100


OgiveOgive l th ca phn phi tch ly

25

48

0

5

10

15

20

5 10 15 20 25 30 35

Thi gian kim tan tnh theo ngy



TS. Cao Ho Thi 17

PHN TCH D LIU KHM PH: PHN TCH D LIU KHM PH: TRNH BY DNG CNH V LTRNH BY DNG CNH V L

Trnh by dng cnh v l: Mt k thut phn

tch khm ph theo sp hng cc th t ca

49

tch khm ph theo sp hng cc th t ca

d liu nh lng v cho thy su sc v dng

ca phn phi cng mt lc


S CU HI C TR LI NG K THI NNG KHIU

112 72 69 97 10773 92 76 86 73

50

126 128 118 127 12482 104 132 134 8392 108 96 100 92115 76 91 102 8195 141 81 80 10684 119 113 98 7538 98 115 106 95100 85 94 106 119


6 8 9

7 2 3 3 5 6 6

8 0 1 1 2 3 4 5 6

9 1 2 2 2 4 5 5 6 7 8 8

51

9 1 2 2 2 4 5 5 6 7 8 8

10 0 0 2 4 6 6 6 7 8

11 2 3 5 5 8 9 9

12 4 6 7 8

13 2 4

14 1



TS. Cao Ho Thi 18

TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

Bng cho Bng cho l mt tng kt di dng bng ca d

liu gm 2 bin. Cc gi tr ca mt bin c trnh

52

liu gm 2 bin. Cc gi tr ca mt bin c trnh

by theo cc hng. Cc gi tr ca mt bin khc

c trnh by theo cc ct

Bng cho c s dng rng ri trong vic xem xt

mi quan h gia hai bin


BNG CHO V NH GI CHT LNG V GI CA CC BA N TI 300 NH HNG LOS-ANGELES

Gi ba n

53

Gi ba nCht lng $10-19 $20-29 $30-39 $40-49 TngTt 42 40 2 0 84Rt tt 34 64 46 6 150Xut sc 2 14 28 22 66Tng 78 118 76 28 300


PHN TRM TNH THEO HNG I VI MI LOI CHT LUNG

Gi ba nCht lng $10 19 $20 29 $30 39 $40 49 Tng

54

Cht lng $10-19 $20-29 $30-39 $40-49 TngTt 50.0 47.6 2.4 0.0 100Rt tt 22.7 42.7 30.6 4.0 100Xut sc 3.0 21.2 42.4 33.4 100



TS. Cao Ho Thi 19


th phn tn im v ng xu hng

Mt th phn tn im l mt trnh by di dng th i h h i bi Mt bi

55

th v mi quan h ca hai bin. Mt bin c trnh by trn trc honh v bin khc c trnh by trn trc tung

Mt ng xu hng l mt ng cho thy mt cch gn ng mi quan h gia hai bin


D LIU MU I VI CA HNG THIT B STEREO V M THANHTun S thng v Doanhs ($100s)

x y1 2 50

56

1 2 502 5 573 1 414 3 545 4 546 1 387 5 638 3 489 4 5910 2 46


th phn tn im th phn tn im i vi ca hn thit b Stereo v m thanh

60

65

57

35

40

45

50

55

60

0 1 2 3 4 5 6

Sales ($100s)

Number of commercials



TS. Cao Ho Thi 20


th phn tn im Cc loi quan h c miu t bng th phn tn im

58

Quan h ng bin Dng nh khng quan h Quan h nghch bin

CC QUI TRNH BNG BIU V TH CC QUI TRNH BNG BIU V TH I VI TNG KT D LIU I VI TNG KT D LIU

D LIU

D liu nh tnh

D liu nh lng

59

Phng php Bng

Phng php th

Phng php Bng

Phng php th

Phn phi tn s

Phn phi tn s tng i

Phn phi tn s phn trm

Bng cho

Biu hnh thanh

Biu hnh trn

Phn phi tn s

Phn phi tn s tng i

Phn phi tn s tch ly

Phn phi tn s tng i tch ly

Cnh v l - Bng cho

Biu im

Biu tn s

Biu tn s tch ly (Ogive)

th phn tn im

CHNG 3CHNG 3

CC I LNGCC I LNG

60

CC I LNGCC I LNG

BNG SBNG S



TS. Cao Ho Thi 21

CC NI DUNG CHNHCC NI DUNG CHNH

Gii thiu i lng v v tr i lng v s bin thin

61

i lng v dng phn phi, v tr tng i v nhn dng cc im c bit

Phn tch d liu khm ph i lng v s lin h gia 2 bin Trung bnh c trng s v x l d liu nhm

GII THIUGII THIU

Mt i lng m t l mt con s n gin

c tnh ton t d liu mu cung cp thng

62

tin v d liu tng th

C hai loi i lng m t:

i lng v v tr

i lng v s bin thin

GII THIUGII THIU

Tham s ca tng th (population parameter) l mt gi tr bng s c dng nh mt i lng tng kt i vi mt d liu ca tng th

63

lng tng kt i vi mt d liu ca tng th

Cc tr thng k ca mu (sample statistics) c dng nh mt i lng tng kt i vi mt mu



TS. Cao Ho Thi 22

CC I LNG V V TR CC I LNG V V TR (measure of location)(measure of location)

Mt s cc i lng v v tr l: S trung bnh (Mean)

S trung v (Median)

64

S trung v (Median)

S yu v (Mode)

S phn v (Percentiles)

S t phn (Quartiles)

CC I LNG V V TRCC I LNG V V TR

S trung bnh S trung bnh c s dng ph bin nht o

lng v tr

65

Trung bnh ca tng th:

Trung bnh ca mu:

Nx

nx

x


S yu v (Md)

S trung v l gi tr gia tp d liu c sp xp

66

theo th t

n l s l, Md l gi tr gia tp d liu

n l s chn, Md l trung bnh ca hai gi tr gia

tp d liu



TS. Cao Ho Thi 23


S yu v (Mo)

S yu v l gi tr d liu xut hin vi tn s

67

ln nht

Bimodal c hai s yu v

Multimodal > two hai s yu v


S phn v

S phn v pth l gi tr c t nht p % s hng ca

68

tp d liu c gi tr nh hn hoc bng gi tr ny,

v c t nht (100-p) % s hng ca tp d liu c

gi tr ln hn hoc bng gi tr ny

Phn v 50th l s trung v


S phn vXc nh phn v pth

Bc 1: Sp xp tp d liu theo th t tng dn

69

Bc 1: Sp xp tp d liu theo th t tng dn

Bc 2: tnh ch s i:

Bc 3: Nu i khng l s nguyn lm trn ln trn. S

nguyn k tip > i s ch v tr ca phn v pth.

Nu i l s nguyn, phn v pth l trung bnh ca 2 gi tr d liu v tr i v i + 1

n*i 100p



TS. Cao Ho Thi 24


S t phn

S t phn ch n thun l cc s phn v c th, s

70

chia tp d liu ra lm 4 phn, c gi tn l:

Q1 = s t phn th nht = P25%

Q2 = s t phn th hai = P50% = Median

Q3 = s t phn th ba = P75%

CC I LNG V S BIN THINCC I LNG V S BIN THIN

i lng v s bin thin c s dng m t xu hng ca cc gi tr d liu phn tnxung quanh gi tr trung bnh.Mt i l bi thi

71

Mt s i lng v s bin thin: Khong bin thin (Range) Khong bin thin ni t phn (Interquartile Range) Phng sai (Variance) lch chun (Standard Deviation) H s bin thin (Coefficient of variation)


Khong bin thin Range = Gi tr ln nht Gi tr nh nht

hay Range = Max Min

72

Range Max Min

Khong bin thin ni t phn (IQR) IQR = Q3 Q1



TS. Cao Ho Thi 25


Phng sai

Phng sai ca tng th:

Nx 2i2

73

Phng sai ca mu:

N

1n

xxs

2i2


lch chun lch chun l cn bc hai ca phng sai. lch chun v phng sai c s dng ph bin o lng s bin thin

74

lng s bin thin

H s bin thin

22 ss

100*XS100*

MeanDeviation StandardCV

CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

Dng phn phi lch (Skewness) l i lng v dng ca phn

phi ca tp d liu

75

phi ca tp d liu i vi d liu lch v bn tri, lch s m i vi d liu lch v bn phi, lch s dng Nu d liu i xng, lch s bng 0

i vi phn phi i xng, s trung bnh v s trung v s bng nhau



TS. Cao Ho Thi 26


Tr thng k Z (Z-Scores)Tr thng k Z thng c gi l gi tr chun ha

xxiZ

76

Zi: l s lch chun m Xi cch xa gi tr trungbnh

si

iZ


nh l Chebyshev

nh l Chebyshev c s dng pht biu v phn

77

trm ca cc s hng s nm trong mt con s c th

ca lch chun tnh t gi trung bnh


nh l Chebyshev

Ti thiu (1-1/Z2) ca cc s hng c trong mi tp

78

( ) g g

d liu s phi nm trong Z lch chun tnh t

s trung bnh, khi Z > 1.

hay

Prob 2z11zsxxzsx



TS. Cao Ho Thi 27


nh l Chebyshev

i vi mi tp d liu

79

p

Prob

Prob

Prob

%75 s2xx2s-x

%89 s3xx3s-x

%94 s4xx4s-x


Qui tc kinh nghim

i vi mi tp d liu c phn phi dng hnh chung:

80

Prob

Prob

Prob

%68 s1xx1s-x

%95 s2xx2s-x

%7.99 s3xx3s-x


MT PHN PHI DNG HNH CHUNG I XNG

81



TS. Cao Ho Thi 28


Nhn dng cc im c bit (outliers)

Cc im c bit l cc gi tr thi cc (ln khc

82

thng hoc nh khc thng)

S dng Z nhn dng im c bit: mi gi tr

d liu vi Z nh hn 3 hoc ln hn +3 l im

c bit

PHN TCH D LIU KHM PHPHN TCH D LIU KHM PH

M hnh 5-im Gi tr nh nht = Min

S t phn th nht = Q1

83

1

S t phn th hai = Q2 = Median

S t phn th ba = Q3 Gi tr ln nht = Max

Mt cch gn ng, 25% ca cc gi tr d liu gia cc s k nhau trong m hnh 5-im


Biu hp (Box plot):

Biu hp l tng kt d liu bng th

84

Biu hp l tng kt d liu bng th

Outliers

Whiskers



TS. Cao Ho Thi 29


Upper Limit Lower Limit Median Q1 Q3

85

0

1

2

3

4

1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

*

Outlier

IQR1.5(IQR) 1.5(IQR)

I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

ng phng sai (Covariance) ng phong sai o lng s lin h tuyn tnh gia 2

bin.

86

ng phng sai ca tng th:

ng phng sai ca mu:

N

yx yixixy

1nyyxx

s iixy


ng phng sai

sxy > 0 Quan h ng bin

87

sxy < 0 Quan h nghch bin

Gi tr ca ng phng sai ph thuc n v o

lng ca x v y



TS. Cao Ho Thi 30


60

65

III . .0s) = 3x

TH PHN TN IM C PHN CHIA

I VI C HNG THIT B STEREO V M THANH

88

35

4045

50

55

0 1 2 3 4 5 6

IVIII

....

...

S thng v

Doa

nh s

($10

0

= 51y


. .yGII THCH V NG PHNG SAI CA MU

89

....

....

.

.

Sxy dng:(x v y c quan h tuyn

tnh ng bin ) x


.Sxy gn bng 0:(x v y khng c quan h yGII THCH V NG PHNG SAI CA MU

90

. .. ..

. .

. ..

..

. . . .

(x v y khng c quan h tuyn tnh )

x



TS. Cao Ho Thi 31


y

GII THCH V NG PHNG SAI CA MU

....Sxy m:(x v y c quan h tuyn

91

x

....

. ..

.

(x v y c quan h tuyn tnh nghch bin )


H s tng quan (Correlation Coefficient) Mt i lng bng s o lng mi quan h

tuyn tnh gia 2 bin H s tng quan Pearson

92

H s tng quan Pearson

Tng th: Mu: yx

xyxy

yx

xyxy ss

sr

2i

2i

iixy

yyxx

yyxxrr


H s tng quanCc tnh cht quan trng ca r: -1 r 1

93

r cng ln th mi quan h tuyn tnh cng mnh.

r = 0 -> khng c quan h tuyn tnh gia X vY

r = 1 hoc r = -1 X v Y tng quan tuyn tnh hon ton

Du ca r cho thy mi quan h gia X v Y l ng bin hay nghch bin



TS. Cao Ho Thi 32


25

30

35

dred

s)

..

. .y

25

30

35

dred

s)

..

. .y

94

0

5

10

15

20

25

10 20 30 40 50 60 70

Income (thousand)

Squa

re fo

otag

e (h

und

. ..

. ..

.

x0

5

10

15

20

25

10 20 30 40 50 60 70

Income (thousand)

Squa

re fo

otag

e (h

und

. ..

. ..

.

x


. ..... .

..

. .

y y y

th phn tn im i vi cc gi tr r khc nhau

95

.

.

... . .

.... .. .

..

.. . . .

. .x x xr = 0 r = 1 r = -1


yy y

th phn tn im i vi cc gi tr r khc nhau

96

... .

. .. . . .

. ... .

... ..

... .

.

.. .

... .

. . .....

. .

y

x

y

x

y

xr = .5r = -.8r = 0.9



TS. Cao Ho Thi 33

TRUNG BNH C TRNG S V TRUNG BNH C TRNG S V X L D LIU NHMX L D LIU NHM

Trung bnh c trng s (The weighted Mean)

Trung bnh ca tp d liu c c bng cch

97

gn mi gi tr d liu mt trng s phn nh

tm quan trng ca n trong tp d liu

i

ii

wx*w

x


D liu nhm (Grouped data)

D liu c sn trong cc lp c tng kt bng

98

D liu c sn trong cc lp c tng kt bng

phn phi tn s. Cc gi tr ring ca tp d liu gc

s khng c ghi nhn


D liu nhm

Trung bnh ca d liu nhm

99

Tng th

Mu

NM*f ii

nM*f

x ii



TS. Cao Ho Thi 34


D liu nhm

Phng sai ca d liu nhm

100

Tng th

Mu

NM*f 2ii2

1n

xM*fs

2ii2

CHNG 4CHNG 4

GII THIU GII THIU

101

vvXC SUTXC SUT


Th nghim, qui tc m v xc nh xc sut Bin c v xc sut ca bin c Mt s mi quan h cn bn ca xc sut

102

Xc sut c iu kin nh l Bayes



TS. Cao Ho Thi 35

TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

Th nghim (Experiment) Th nghim l mi qu trnh to ra kt qu c nh ngha r rng

103

Khng gian mu (Sample space) im ca mu l mt kt qu c th ca mt th

nghim

Khng gian mu l tp hp ca tt c cc im c th c ca mu (cc kt qu ca th nghim)


Qui tc m S cy l mt phng tin th rt hu ch trong

vic xc nh cc im ca mu ca mt th nghim c lin quan n nhiu bc.

104

Qui tc m i vi th nghim nhiu bc

S kt qu ca th nghim = (n1)x(n2)x.. x(nk) Qui tc m i vi t hp

S t hp ca N phn t c chn n trong mt ln l:

!nN!n!N

nN


Yu cu cn bn ca xc sutGi Ei l kt qu ca th nghim 0 P(Ei) 1

105

P(Ei) = 1

Cc phng php xc nh xc sut Phng php c in Phng php tn s tng i Phng php ch quan



TS. Cao Ho Thi 36


Phng php c in

Mt phng php xc nh xc sut thch hp khi tt c cc

kt qu ca th nghim c cng kh nng xy ra

106

Phng php tn s tng i

Mt phng php xc nh xc sut thch hp khi c sn

d liu (d liu lch s) c lng t l ca s ln kt

qu th nghim s xy ra nu th nghim c lp li vi

mt s ln ln


Phng php ch quan

Mt phng php xc nh xc sut da trn c s

h

107

phn on

Mt xc sut ch quan l mt mc tin tng ca c

nhn i vi vic xy ra mt kt qu ca th nghim

BIN C v BIN C v XC SUT CA BIN CXC SUT CA BIN C

Bin cMt bin c l mt tp hp ca cc kt qu ca th nghim

108

g

Xc sut ca bin cXc sut ca mt bin c bt k s bng vi tngcc xc sut ca cc kt qu ca th nghim



TS. Cao Ho Thi 37

MT S MI QUAN H CN BN MT S MI QUAN H CN BN CA XC SUTCA XC SUT

Phn b/ph ca bin c

Phn ph ca bin c A l bin c cha tt c kt

qu ca mu m khng thuc v A

109

qu ca mu m khng thuc v A

P(A) = 1 P(Ac)

Bin c Bin c AA AAcc

Khng gian mu SKhng gian mu S


BIn c HI ca 2 bin c: A BA B l bin c cha tt c cc kt qu ca th nghim thuc A hoc B, hoc c hai

110

Bin c Bin c AA Bin cBin cBB



Bin c GIAO ca 2 bin c: A B A B l bin c cha tt c cc kt qu ca th nghim thuc A v B


111

Phn giaoPhn giao

Bin c Bin c AA Bin c Bin c BB




TS. Cao Ho Thi 38


Php cng xc sut P(A B) = P(A) + P(B) P(A B) BIn c cch bit

112

Hai bin c dc gi l cch bit nu hai bin c khng c cc im phn giao.

A v B l hai bin c cch bit: P(A B) = 0

Php cng xc sut i vi hai bin c cch bit

P(A B) = P(A) + P(B)

XC SUT C IU KINXC SUT C IU KIN

Xc sut c iu kin

hay

)B(PBAP)B\A(P

BAP

113

Cc bin c c lpNu A v B l hai bin c c lp th:

P(A\B) = P(A) hay P(B\A) = P(B)

)A(PBAP)A\B(P

XC SUT C IU KINXC SUT C IU KIN

Php nhn xc sut

P(A B) = P(B). P(A\B) = P(A). P(B\A)

114

Php nhn xc sut i vi hai bin c c lp

P(A B) = P(A). P(B)



TS. Cao Ho Thi 39

NH L BAYESNH L BAYES

Cc xc sut tin nghim: Cc c lng ban u v xc sut ca cc bin c

Xc sut hu nghim: Cc xc sut c sa li

115

g ca cc bin c da trn cc thng tin b sung

nh l Bayes

)B(P)BA(P

)A\B(P)A(P)A\B(P)A(P)A\B(P)A(P)B\A(P 1

2211

111

CHNG 5CHNG 5

PHN PHI XC SUTPHN PHI XC SUT

116

PHN PHI XC SUTPHN PHI XC SUTRI RCRI RC


Cc bin ngu nhin

Cc phn phi xc sut ri rc

117

Gi tr k vng v phng sai ca bin ri rc

Phn phi xc sut nh thc

Phn phi xc sut Poisson



TS. Cao Ho Thi 40

BIN NGU NHINBIN NGU NHIN

Bin ngu nhin

Mt bin ngu nhin l mt m t bng s ca kt qu ca th nghim

118

q g

Bin ngu nhin ri rc

Mt bin ngu nhin ri rc c th nhn mt s m c ca cc gi tr trong mt khong

BIN NGU NHINBIN NGU NHIN

Bin ngu nhin lin tc

Mt bin ngu nhin lin tc c gi nh c th nhn mi gi tr trong mt khong

119

th nhn mi gi tr trong mt khong

Mi gi tr c th c trong khong ny

2 3 4 5 6 7 8 X

X: height, in feet

PHN PHI XC SUT RI RCPHN PHI XC SUT RI RC

Phn phi xc sut i vi mt bin ngu nhin s m t lm th no cc xc sut c phn phi theo cc gi tr ca bin ngu nhin

120

Mt phn phi xc sut i vi mt bin ngu nhin ri rc X l mt danh sch cc gi tr c th c ca bin X v cc xc sut tng ng



TS. Cao Ho Thi 41


Mt phn phi xc sut c th c trnh by di dng: Bng th ( th t )

121

th ( th tn s) Cng thc (Hm s)

x 1 2 3 4 5 6P (x) 1/6 1/6 1/6 1/6 1/6 1/6

1 2 3 4 5 6

1/6X

c sut


Hm xc sut ri rc f(x) l mt hm xc nh xc sut i vi mi gi tr ca bin X

f(x) = Prob (X=x)

122

Cc iu kin yu cu i vi hm xc sut ri rc

0 f(x) 1

f(x) = 1


Hm phn phi xc sut ri rc u

f(x) = 1/n

123

n = s cc gi tr c th c ca bin ngu nhin ri rc



TS. Cao Ho Thi 42

GI TR K VNG v PHNG SAI GI TR K VNG v PHNG SAI ca BIN NGU NHIN RI RCca BIN NGU NHIN RI RC

Gi tr k vngE (x) = = x * f(x)

Phng sai

124

Var (x) = 2 = (x - )2 * f(x)or

2 = x2 * f(x) - 2

lch chun

2

PHN PHI XC SUT NH THCPHN PHI XC SUT NH THC

Mt th nghim nh thcMt th nghim nh thc c 4 tnh cht:

Th nghim gm c mt chui n ln th tng t

125

Hai kt qu c th c cho mi ln th: thnh cng v tht bi

Xc sut ca thnh cng, p, khng thay i ln th ny sang ln th khc. V vy, xc sut ca tht bi, 1-p, khng thay i ln th ny sang ln th khc

Cc ln th c lp vi nhau

PHN PHI XC SUT NH THCPHN PHI XC SUT NH THC

Hm xc sut nh thc

xnx p1pxn

)x(f

126

Gi tr k vng v phng sai ca phn phi xc sut nh thc

Gi tr k vng: E(x) = = np

Phng sai: 2 = np (1-p)



TS. Cao Ho Thi 43

PHN PHI XC SUT POISSONPHN PHI XC SUT POISSON

Cc tnh cht ca Th nghim Poisson

Xc sut ca mt s kin s ging nhau cho bt k

2 kh di

127

2 khong c cng di

Vic xy ra hay khng xy ra trong 1 khong bt k

s c lp vi vic xy ra hay khng xy ra trong 1

khong bt k khc

PHN PHI XC SUT POISSONPHN PHI XC SUT POISSON

Hm xc sut Poisson

= Gi tr k vng hay s trung bnh ca s kin trong

!xe)x(f

x

128

g y g gmt khong.

Gi tr k vng v phng sai ca phn phi xc sut Poisson Gi tr k vng: E(x) =

Phng sai: Var(x) =

CHNG 6CHNG 6

PHN PHI XC SUTPHN PHI XC SUT

129

PHN PHI XC SUTPHN PHI XC SUTLIN TCLIN TC



TS. Cao Ho Thi 44


Gii thiu

Phn phi xc sut u

130

Phn phi xc sut chun

Tnh gn ng phn phi chun cho phn phi

nh thc

GII THIUGII THIU

Mt bin ngu nhin lin tc l mt gi tr ngu nhin c th nhn bt k gi tr no trong mt khong hay tp hp cc khong

131

Mt Phn phi xc sut i vi mt bin ngu nhin lin tc c c trng bi mt Hm mt xc sut (Probability Density Function PDF)

GII THIUGII THIU

Cc din tch di ng cong mt xc sut l cc xc sut f(x)

ty

132

a bx

SDen

si

b

a

dx)x(fS)bXa(P



TS. Cao Ho Thi 45

GII THIUGII THIU

Mt s cc phn phi xc sut ph bin i vi

bin lin tc:

Phn phi u (Uniform Distribution)

133

Phn phi u (Uniform Distribution)

Phn phi chun (Normal Distribution)

PHN PHI XC SUT UPHN PHI XC SUT U

Hm mt xc sut ca phn phi u

elsewhere0

bxa forab

1)x(f

f(x)

134

elsewhere0( )

x

Den

sity

h

a b

PHN PHI XC SUT UPHN PHI XC SUT U

Gi tr k vng v phng sai ca phn phi u

bab

135

12

abdx)x(fx)x(Var

2badx)x(f.x)x(E

2b

a

22

a



TS. Cao Ho Thi 46

PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

Hm mt xc sut ca phn phi chun

2

2

2x

e21)x(f

136

Vi = Trung bnh = lch chun = 3.14159e = 2.71828X N (, 2)

2


ng cong chun

Dng ca f(x) i xng, ging dng hnh chung

137

ng cong chun c 2 tham s, v . Chng

xc nh v tr v dng ca phn phi


1 2 3

138

1 2 3



TS. Cao Ho Thi 47


1

139

X

2

1 < 2

PHN PHI XC SUT CHUNPHN PHI XC SUT CHUNf(x)

S

140

a b x

S

P( a < X < b) = S

P ( - < X < + ) = 68.26%

P ( - 2 < X < + 2) = 95.44%

P ( - 3 < X < + 3) = 99.72%


Phn phi xc sut chun chun ha

Phn phi xc sut chun chun ha l mt phn phi chun

c trung bnh bng 0 v phng sai bng 1

141

Mt bin ngu nhin chun chun ha Z l mt bin tun

theo phn phi xc sut chun chun ha

Z N (0,12)



TS. Cao Ho Thi 48


Mt bin chun chun ha Nu X N (, 2) th bin chun chun ha Z c trung bnh bng 0, phng sai bng 1 v Z N (0, 12)

142

XZ

a b x

f(x)

S

- 3 - 2 - + +2 +3

PHN PHI XC SUT CHUNPHN PHI XC SUT CHUNf(x)

143

Z

S

-3 -2 -1 Za 0 1 Zb 2 3


X N(, 2) Z N (0, 12)

XZ

144

P (a < X < b) = P (Za < Z < Zb) = S

aZa

bZb



TS. Cao Ho Thi 49


S dng bng din tch ca ng cong chun tm gi tr ca S f(x)

145

Z S or S Z

z

S

-3 -2 -1 0 1 2 3

Using table Using table

TNH GN NG PHN PHI CHUN TNH GN NG PHN PHI CHUN CHO PHN PHI NH THCCHO PHN PHI NH THC

Khi chng ta gp mt vn ca phn phi nh thc vi s ln th ln, chng ta c th mun tnh gn ng xc sut ca phn phi nh thc

146

n > 20

np 5

n(1-p) 5

Vi n cho trc, tnh gn ng phn phi chun cho phn phi nh thc s tt nht khi p= 0.5


Khi s dng phn phi chun tnh gn ng cho phn phi nh thc, chng ta t

= np

147

Vo trong nh ngha ca ng cong chun

)p1(np



TS. Cao Ho Thi 50


Nhn t iu chnh lin tc l gi tr 0.5, ngha l

cng hoc tr vo gi tr ca X khi s dng

148

phn phi xc sut chun lin tc tnh gn

ng cho phn phi xc sut nh thc ri rc

CHNG 7CHNG 7

LY MULY MU

149

LY MULY MUvv

PHN PHI MUPHN PHI MU


Gii thiu vn ly mu Ly mu ngu nhin n gin c lng im

150

Gii thiu phn phi mu Phn phi mu ca trung bnh mu Phn phi mu ca t l mu Cc tnh cht ca c lng im Cc phng php ly mu khc



TS. Cao Ho Thi 51

GII THIU VN LY MUGII THIU VN LY MU

Mt Tng th l tp hp tt c cc phn t cn

quan tm trong mt nghin cu.

151

Mt Mu l mt tp hp con ca tng th.

Mc ch ca thng k suy din l thu thp

thng tin v tng th t cc thng tin c trong

mu.


Ly mu ngu nhin

Tng thN (C) Mu

152

c lngKim nh Gi thuyt

N (C) (Trung bnh) ( lch chun)p (T l)

Mun

s x

p


Cc tr thng k mu: Mt c trng ca mu,

nh l trung bnh mu , lch chun mu s, x

153

t l mu .Gi tr ca tr thng k mu c

dng c lng gi tr tham s ca tng th

p



TS. Cao Ho Thi 52

LY MU NGU NHIN N GINLY MU NGU NHIN N GIN

nh ngha ca mu ngu nhin n gin v qu trnh la chn mt the mu ngu nhin n gin ty thc vo tng th l hu hn hay v hn.

154

Tng th hu hn thng c nh ngha bng mt danh sch.

Tng th v hn thng c nh ngha l mt qu trnh ang din ra. Cc phn t ca tng th v hn c th khng lit k c


Ly mu t tng th hu hn Mt mu ngu nhin n gin c mu n t tng th

hu hn c N l mt mu c chn sao cho mi mu c th vi c mu n u c cng xc sut c

155

mu c th vi c mu n u c cng xc sut c chn

S mu ngu nhin n gin c mu n khc nhau t tng th hu hn c N l:

)!nN(!n!N


Ly mu t tng th hu hn Ly mu khng thay th: Khi mt phn t c

chn vo mu th n c ly ra khi tng th v khng th c chn ln th hai

156

khng th c chn ln th hai

Ly mu c thay th : Khi mt phn t c chn vo mu th n c b tr li tng th. Mt phn t c la chn ln trc th n c th c la chn ln na v v vy phn t c th xut hin trong mu hn mt ln



TS. Cao Ho Thi 53


Ly mu t tng th v hnMt mu ngu nhin n gin t mt tng th

v hn l mt mt c chn phi tha mn

157

v hn l mt mt c chn phi tha mn

cc iu kin sau:

Mi phn t c chn phi n t cng mt tng

th

Mi phn t c chn mt cch c lp

C LNG IMC LNG IM

Trong c lng im chng ta s dng d liu t mu tnh mt gi tr ca tr thng k mu v da vo cung cp mt c lng v mt tham s ca tng th

158

ca tng th c lng im l mt tr thng k mu, nh l ,

s hay cung cp c lng im v tham s ca tng th, , v p.

xp

GII THIU PHN PHI MUGII THIU PHN PHI MU

Phn phi xc sut ca bt k tr thng k mu c th c gi l phn phi mu ca tr thng k.

Phn phi xc sut ca c gi l phn phi mu ca .Kin thc v phn phi mu ny v

xx

159

mu ca .Kin thc v phn phi mu ny v cc tnh cht ca n s cho php chng ta pht biu v xc sut cho trung bnh ca mu gn bng vi trung bnh ca tng th .

Trong thc t, chng ta ch chn mt mu ngu nhin n gin t tng th

x

x



TS. Cao Ho Thi 54

PHN PHI MU CAPHN PHI MU CA

Phn phi mu ca

Phn phi mu ca l phn phi xc sut ca

xx

x

160

tt c cc gi tr c th ca trung bnh mu

Gi tr k vng ca

E( ) =

x

x

x

PHN PHI MU CAPHN PHI MU CA x

Tng th vi trung

Mt mu ngu nhin n gin vi n phn t c

h t t th

161

gbnh = ? chn t tng th

Tng kt ca d liu mu cung cp mt gi tr trung bnh mu X

Gi tr c dng suy din v gi tr

X


lch chun ca Tng th v hn hay khng bit N

xx

nX

162

Tng th hu hn hay bit N

Vi l nhn t iu chnh tng th hu hn

1NnN

nx

1NnN



TS. Cao Ho Thi 55

lch chun ca B qua nhn t iu chnh tng th hu hn khi

n/N 0.05Sai s chun l lch chun ca mt c lng

PHN PHI MU CAPHN PHI MU CA xx

163

Sai s chun l lch chun ca mt c lng im

xbar c xem nh sai s chun ca trung bnh

Phn phi ca Cu hi: Phn phi xc sut ca l g?

PHN PHI MU CAPHN PHI MU CA xx

x

164

nh l gii hn trung tm Phn phi ca tng th c bit l phn phi

chunX N (, 2) N (, 2/n) x

nh l gii hn trung tm Trong vic chn cc mu ngu nhin n gin c

mu n t mt tng th, phn phi mu ca trung bnh mu c th gn ng tun theo phn phi

PHN PHI MU CAPHN PHI MU CA x

x

165

bnh mu c th gn ng tun theo phn phi chun khi c mu ln.

X ~ Bt k phn phi no Khng bit phn phi

xc sut tng th C mu ln

(N>30)

x

N (, 2/n)X



TS. Cao Ho Thi 56

N (, 2/n) Z N (0,12)vi

PHN PHI MU CAPHN PHI MU CA xX

x

166

n/x


Phn phi mu ca

Phn phi mu ca l phn phi xc sut

pp

p

167

ca tt c cc gi tr c th ca t l mu

Gi tr k vng ca

E( ) = p

p

p

p

PHN PHI MU CAPHN PHI MU CA p

Tng th vi t l p

= ?

Mt mu ngu nhin n gin vi n phn t c

chn t tng th

168

Tng kt ca d liu mu cung cp mt gi tr trung bnh mu p

Gi tr c dng suy din v gi tr

p

p



TS. Cao Ho Thi 57

lch chun ca Tng th v hn:

PHN PHI MU CAPHN PHI MU CA pp

n)p1(p

p

169

Tng th hu hn:

B qua nhn t iu chnh tng th hu hn

khi n/N < 0.05

1NnN

n)p1(p

p

1NnN

Dng phn phi mu ca

Phn phi mu ca c th gn ng tun

PHN PHI MU CAPHN PHI MU CA p

p

p

170

theo phn phi xc sut chun khi c mu ln np 5 n(1 p) 5

TNH CHT CA C LNG IMTNH CHT CA C LNG IM

Gi = tham s tng th c quan tm

= tr thng k mu hay c lng im ca Kh thi l h

171

Khng thin lchTr thng k mu l mt c lng khng thin lch ca tham s tng th nu

E( ) = thin lch (Bias)

Bias ( ) = E( ) -



TS. Cao Ho Thi 58

TNH CHT CA C LNG IMTNH CHT CA C LNG IM

hu hiuCho hai c lng im khng thin lch ca tham s tng th, c lng im vi lch chun nh hn c xem l hiu qu hn nu:

12

172

qVar ( ) < Var ( )

nht qunMt tnh cht ca c lng im c trnh by khi cc c mu ln hn s cung cp cc c lng im gn vi tham s ca tng th

2

21

CC PHNG PHP LY MU KHCCC PHNG PHP LY MU KHC

Ly mu h thngMt phng php ly mu xc sut theo chng ta s chn mt cch ngu nhin mt trong k phn t u tin v sau chn mi phn t th k k tip

173

v sau chn mi phn t th k k tip

Ly mu thun tinMt phng php ly mu phi xc sut theo cc phn t c chn vo mu da trn c s thun tin

CC PHNG PHP LY MU KHCCC PHNG PHP LY MU KHC

Ly mu phn onMt phng php ly mu phi xc sut theo cc phn t c chn vo mu da trn s phn on ca ngi thc hin nghin cu

174

ngi thc hin nghin cu



TS. Cao Ho Thi 59

CHNG 8CHNG 8

C G O GC G O G

175

C LNG KHONGC LNG KHONG


c lng khong ca trung bnh tng th: bit c lng khong ca trung bnh tng th: khng

176

bit Xc nh c mu c lng khong ca t l tng th

C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

c lng khong l mt c lng ca mt

tham s ca tng th theo cung cp mt

177

khong c tin l s cha gi tr ca tham s

Trng hp c mu ln: n 30

Trng hp c mu nh: n < 30



TS. Cao Ho Thi 60


Dng tng qut ca c lng khong l:

c lng im Bin ca sai s

178

Bin ca sai s l gi tr cng v tr vo c lng im to ra mt khong tin cy

to ra mt khong tin cy ca , th c v s phi c s dng tnh bin ca sai s

f(x)

S /21-


179

P( Z > Z/2) = /2P( Z < -Z/2) = /2P( -Z/2 < Z < Z/2) = 1-

Z/2: l gi tr ca bin phn phi chun chun ha tng ng vi mt din tch /2 di ui pha trn ca phn phi

-z/2 z/2x

S /2


1Z

n/xZP

22

180

1n

Zxn

ZxP

n/

22



TS. Cao Ho Thi 61

Tnh c lng khong: bit

Vi


Zx2

181

Vi: (1-) l tin cy x l c lng im ca

l bin ca sai s

C mu ln (n 30) dng cng thc ny

n2

nZ

2

CC GI TR CA Z/2 I VI CC MC TIN CY C S DNG PH BIN NHT

M ti

/2

Z


182

Mc tin cy /2 Z/2 90% 95% 99%

.10

.05

.01

.050 .0.25 .005

1.645 1.960 2.576

Tnh c lng khong: bit Bin ca sai s l gi tr cng v tr vo c lng im to ra mt khong tin cy


183

Khong tin cy: Mt khong tin cy 100(1 - )% i vi trung bnh ca phn phi chun l

n

Zx,n

Zx22



TS. Cao Ho Thi 62

C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: KHNG BIT TRUNG BNH TNG TH: KHNG BIT

Nu khng bit , lch chun ca mu s c dng c lng lch chun ca tng th v khong tin cy thch hp s da trn mt phn phi xc sut c gi l phn

184

trn mt phn phi xc sut c gi l phn phi t

Tr thng k t:

n/sxt

Tr thng k t s tun theo mt Phn phi Students t, vi t do df

df = n - 1


185

Phn phi t thng c c dng vi phn phi c mu nh ca

If n N then t # Z

x

Phn phi chun chun ha Z

ng cong t vi bc t do l 20


186

t

t do l 20ng cong t vi bc t do l 10

Phn phi t



TS. Cao Ho Thi 63

c lng khong ca mt trung bnh tng th: khng bit


stx

187

C mu nh (n < 30) v tng th tun theo mt phn phi chun hoc gn chun cng dng cng thc ny

ntx

2

TNG KT CC TH TC C LNG KHONG I VI TNG KT CC TH TC C LNG KHONG I VI TRUNG BNH TNG THTRUNG BNH TNG TH

C th gi s lch chun ca tng th

bit?C Khng

Dng lch chun ca mu s c

188

lng

nstx 2/

Dng

Trng hp khng bit

x zn

/2

Dng

Trng hp bit

XC NH C MUXC NH C MU

Gi E = bin ca sai s k vng

nZE

2

189

C mu i vi c lng khong ca mt trung bnh ca tng th

C mu i vi khng bit

2

22

EZ

n 2

2

22

EsZ

n 2



TS. Cao Ho Thi 64

C LNG KHONG CA C LNG KHONG CA T L TNG THT L TNG TH

n/)p1(p

p)p(E

p

190

c lng khong ca t l tng th

hayp2

Zp

n/)p1(pZp2

Xc nh c muGi E = bin ca sai s k vng

C LNG KHONG CA C LNG KHONG CA T L TNG THT L TNG TH

n/)p1(pZE

191

2

2

E)p1(pZ

n

n/)p1(pZE

2

2

CHNG 9CHNG 9

KIM NH GI THUYT

192

KIM NH GI THUYT



TS. Cao Ho Thi 65


Pht trin gi thuyt khng v gi thuyt khc Cc sai lm loi I v loi II

193

Kim nh mt-pha v trung bnh ca tng th: bit Kim nh hai-pha v trung bnh ca tng th: bit Kim nh v trung bnh ca tng th: khng bit Kim nh v t l ca tng th

PHT TRIN GI THUYT PHT TRIN GI THUYT KHNG v GI THUYT KHCKHNG v GI THUYT KHC

Gi thuyt

Gi thuyt l mt gi s hay pht biu v cc tham s ca tng th; N c th ng hoc sai

194

Gi thuyt Khng (H0)

H0 l mt pht biu (ng thc hoc bt ng thc) lin quan n tham s ca tng th

H0 l mt gi nh ng trong th tc kim nh gi thuyt

Mt tuyn b ca nh sn xut thng b nghi ng v c pht biu trong H0

PHT TRIN GI THUYT KHNG PHT TRIN GI THUYT KHNG v GI THUYT KHCv GI THUYT KHC

Gi thuyt khc (Ha)Ha l pht biu ngc vi H0Ha c kt lun l ng nu H0 b bc b

195

a g 0

Nh nghin cu mong mun ng h Ha v nghi ng H0

Tng kt cc dng ca gi thuyt Khng v gi thuyt khc H0 : = 0 or H0 : 0 or H0 : 0 Ha : 0 Ha : 0 Ha : 0

Nhim v ca tt c kim nh gi thuyt hoc l bc b H0 hay khng bc bH0 ( Accept H0 )



TS. Cao Ho Thi 66

CC SAI LM LOI I V LOI IICC SAI LM LOI I V LOI II

Sai lm loi I l sai lm ca vic bc b H0 khi n ngSai lm loi II l sai lm ca vic khng bc b H0 khi n sai

196

CC KT LUN NG V SAI TRONG KIM NH GI

THUYT

iu kin ca tng th

H0 ng H0 sai

CC SAI LM LOI I V LOI IICC SAI LM LOI I V LOI II

l xc sut ca sai lm loi I = P( Bc b H0 / H0 ng ) = P(Sai lm loi I ) c gi l mc ngha ca kim nh, 0.01 < < 0.1

197

Thng chn = 0.05

l xc sut ca sai lm loi II = P( Khng bc b H0 / H0 sai ) = Sai lm loi II )(1-) = P(Bc b H0 / H0 sai) = Nng lc ca kim nh cng nh th cng ln

MIN BC BMIN BC B

Mt min bc b R nh r cc gi tr ca tr thng ks ch dn cho chng ta bc b H0

198

Kim dnh 2-pha

H0 : = 0Ha : 0

Khng bc b

H0Bc b H0 Bc b H0

-Z/2

Z

Z/2

/2 /2

f(x)



TS. Cao Ho Thi 67

MIN BC BMIN BC B

Kim nh 1-phaH0 : 0 H0 : 0Ha : 0 Ha : 0

199

Bc b H0 Khng bc b H0

-Z

Z

Bc b H0

Z

Z

Khng bc b H0

KIM NH 1KIM NH 1--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

Gi thuytTrng hp 1 Trng hp2H : H :

200

H0 : 0 H0 : 0Ha : 0 Ha : 0

Tr thng k

n/

XZ 0


Phng php p-valuep-value

201

p-value l xc sut, c tnh t tr thng k, o lng mc ng h (hay khng ng h) cung cp bi mu i vi gi thuyt H0

Tiu ch p-value i vi kim nh gi thuyt

Bc b H0 nu p-value <



TS. Cao Ho Thi 68


Phng php gi tr ti hn(Qui tc bc b)Bc b H0 nu Z < -Z Bc b H0 nu Z >Z

202

Bc b H0 nu Z < Z Bc b H0 nu Z >Z

Bc b H0 Khng bc b H0

-Z

Z

Bc b H0

Z

Z

Khng bc b H0


Gi thuyt:H0 : = 0Ha : 0

203

a 0

Tr thng k:

n/X

Z 0


p-value i vi kim nh 2-phaTrong kim nh 2-pha, p-value c tnh bng cch nhn i din tch phn ui ca phn phi

204

i din tch phn ui ca phn phi

V din tch c nhn i nn p-value c th so snh trc tip vi v qui tc bc b vn ging nh trc




TS. Cao Ho Thi 69


Phng php gi tr ti hn(Qui tc bc b)

205

Bc b Ho nu Z < -Z/2 Bc b Ho nu Z > Z/2

/2 /2

f(x)

- Z/2 Z/2

Khng bc b H0Bc b H0Bc b H0

Z


Mi lin h gia c lng khong v kim nh gi thuytMt phng php khong tin cy kim nh gi thuyt di dng:

H0 : = 0

206

0 0Ha : 0

Chn mt mu ngu nhin n gin t tng th v dng gi tr ca trung bnh ca mu pht trin khong tin cy i vi .

Nu khong tin cy cha gi tr c gi thuyt 0, th khng bc b H0. Nu khng cha th bc b H0

nZX /2

CC BC KIM NH GI THUYT CC BC KIM NH GI THUYT

Bc 1: Pht trin H0 v HaBc 2: nh mc ngha Bc 3: Thu thp d liu mu v tnh tr thng k kim nh

207

Phng php p-valueBc 4: Dng gi tr ca tr thng k kim nh tnh p-valueBc 5: Bc b H0 nu p-value < Phng php gi tr ti hnBc 4: Dng xc nh gi tr ti hn v qui tc bc bBc 5: Dng gi tr ca tr thng k kim nh v qui tc bc b

xc nh xem c bc b H0 hay khng



TS. Cao Ho Thi 70

KIM NH V TRUNG BNH CA KIM NH V TRUNG BNH CA TNG TH: KHNG BIT TNG TH: KHNG BIT

s c dng c lng Phn phi t c th c dng suy din v Tr thng k kim nh l

208

Tr thng k kim nh l

df = n-1 C mu nh (n < 30) v tng th tun theo mt phn phi

chun hoc gn chun cng dng cng thc ny

ns/ - Xt 0


Kim nh 1-phaH0 : 0 H0 : 0H : < H : >

209

Ha : < 0 Ha : > 0Bc b H0 nu t < -t, n-1 Bc b H0 nu t > t, n-1

Kim nh 2-phaH0 : = 0Ha : 0Bc b H0 nu t < -t/2, n-1 hay nu t > t/2, n-1


p-value v phn phi t X Dng bng t l

210


ns/Xt 0

g gp-value

df = n-1



TS. Cao Ho Thi 71

KIM NH V T L CA TNG THKIM NH V T L CA TNG TH

Gi p : t l ca tng thp0 : gi tr c th ca gi thuyt i vi t l ca tng th

211

Gi thuytHo : p p0 H : p p0 H0 : p = pHa : p < p0 H : p > p0 Ha : p p0

Tr thng k kim nh

p

0

ppZ

n)p(1p 00p

KIM NH KIM NH V T L CA V T L CA TNG THTNG TH

Qui tc bc b

212

HI QUI TUYN TNH N

CHNG 10



TS. Cao Ho Thi 72

HI QUI TUYN TNH NHI QUI TUYN TNH N

M hi qui tuyn tnh n

Phng php bnh phng ti thiu

H s c nh

214

H s xc nh

Cc gi nh ca m hnh

Kim nh mc ngha

S dng m hnh hi qui c lng c

lng v d on

M HNH HI QUI TUYN TNHM HNH HI QUI TUYN TNH

M hnh hi qui tuyn tnh n l:

Phng trnh m t y lin h vi x nh th no v mt

s hng sai s c gi l m hnh hi qui.

215

yy = = 00 + + 11xx ++

Vi:

0 v 1 c gi l cc tham s ca m hnh,

l bin ngu nhin c gi l s hng sai s.

PHNG TRNH

HI QUI TUYN TNH N

Phng trnh hi qui tuyn tnh nPhng trnh hi qui tuyn tnh n l: l:

EE((yy) = ) = 00 + + 11xx

216

EE((yy) ) l gi tr k vng ca l gi tr k vng ca yy i vi gi tr i vi gi tr xx cho trc.cho trc. 11 l dc ca ng hi quil dc ca ng hi qui 00 l tung gc ca ng hi quil tung gc ca ng hi qui

th ca phng trnh hi qui l ng thng. th ca phng trnh hi qui l ng thng.



TS. Cao Ho Thi 73

PHNG TRNH PHNG TRNH HI QUI TUYN TNH NHI QUI TUYN TNH N

Quan h tuyn tnh ng binQuan h tuyn tnh ng bin

EE((yy))EE((yy))

217xxxx

dc dc 11

dngdng

ng hi quing hi qui

Tung gcTung gc

00

PHNG TRNH PHNG TRNH

HI QUI TUYN TNH NHI QUI TUYN TNH N Quan h tuyn tnh nghch binQuan h tuyn tnh nghch bin

EE((yy))EE((yy))

hi i hi i

218

xxxx

dc dc 11

mm

ng hi quing hi quiTung gcTung gc

00

PHNG TRNH

HI QUI TUYN TNH N Khng quan hKhng quan h

EE((yy))EE((yy))

219

xxxx

dc dc 11

Bng 0Bng 0

ng hi quing hi quiTung gcTung gc

00



TS. Cao Ho Thi 74

PHNG TRNH HI QUI

TUYN TNH N C LNG

Phng trnh hi qui tuyn tnh n c lng Phng trnh hi qui tuyn tnh n c lng

^ b b

220

y^ = b0 + b1x

y^ y^ l gi tr c lng ca y i vi gi tr x cho trc.l gi tr c lng ca y i vi gi tr x cho trc. bb11 l dc ca ngl dc ca ng bb00 l tung gc ca ng.l tung gc ca ng. th c gi l ng hi qui c lng. th c gi l ng hi qui c lng.

QU TRNH C LNGQU TRNH C LNG

M hnh hi quiM hnh hi quiyy = = 00 + + 11xx ++

Phng trnh hi quiPhng trnh hi quiEE((yy) = ) = 00 + + 11xx

Tham s cha bitTham s cha bit

D liu muD liu mux yx y

xx11 yy11. .. .. .. .

221

00, , 11. .. .xxnn yynn

bb00 vv bb11

c lng cac lng ca

00 vv 11

Phng trnh Phng trnh

hi qui c lnghi qui c lng

Tr thng k muTr thng k mu

bb00, , bb11

0 1y b b x

PHNG PHP PHNG PHP BNH PHNG TI THIUBNH PHNG TI THIU

Tiu ch bnh phng ti thiu

min (y yi i )2

222

Vi:Vi:

yyii = gi tr = gi tr quan stquan st ca bin ph thuc ca bin ph thuc

i vi quan st th ii vi quan st th iyyii ^ = = gi tr gi tr c lngc lng ca bin ph thuc ca bin ph thuc

i vi quan st th I i vi quan st th I



TS. Cao Ho Thi 75

dc ca phng trnh hi qui c lng

PHNG PHP PHNG PHP BNH PHNG TI THIUBNH PHNG TI THIU

223

1 2

( )( )( )

i i

i

x x y yb

x x

Tung gc ca phng trnh hi qui c lngTung gc ca phng trnh hi qui c lng

PHNG PHP PHNG PHP

BNH PHNG TI THIUBNH PHNG TI THIU

0 1b y b x

224

Vi:Vi:xxii = gi tr ca bin c lp i vi quan st th i= gi tr ca bin c lp i vi quan st th i

nn = tng s quan st = tng s quan st

__yy = gi tr trung bnh ca bin ph thc = gi tr trung bnh ca bin ph thc

__xx = gi tr trung bnh ca bin c lp = gi tr trung bnh ca bin c lp

yyii = gi tr ca bin ph thuc i vi quan st th i= gi tr ca bin ph thuc i vi quan st th i

HI QUI TUYN TNH NHI QUI TUYN TNH N

V d: Doanh s xe hiV d: Doanh s xe hi

225

Qung co Qung co

TVTV

Doanh s Doanh s

xe hixe hi11

33

22

11

1414

2424

1818

1717



TS. Cao Ho Thi 76

PHNG TRNH PHNG TRNH HI QUI C LNGHI QUI C LNG

1 2

( ) ( ) 2 0 5( ) 4

i i

i

x x y yb

x x

dc ca phng trnh hi qui c lng

226

10 5y x

0 1 2 0 5 ( 2 ) 1 0b y b x Tung gc ca phng trnh hi qui c lng

Phng trnh hi qui c lng

TH PHN TN IM V TH PHN TN IM V NG XU HNGNG XU HNG

20

25

30

hi

227

y = 5x + 10

0

5

10

15

20

0 1 2 3 4Qung co TV

Doa

nh s

xe

H S XC NHH S XC NH

Mi lin h gia SST, SSR, SSE

228

Vi:Vi:SST = Tng bnh phng ton phnSST = Tng bnh phng ton phnSSR = SSR = Tng bnh phng hi quiTng bnh phng hi quiSSE = SSE = Tng bnh phng sai sTng bnh phng sai s

SST = SSR + SSESST = SSR + SSE

2( )iy y 2( )iy y 2( )i iy y



TS. Cao Ho Thi 77

H s xc nhH s xc nh l:l:

H S XC NH

229

Vi:Vi:

SSR = Tng bnh phng hi quiSSR = Tng bnh phng hi qui

SST = Tng bnh phng ton phnSST = Tng bnh phng ton phn

rr22 = SSR/SST= SSR/SST

H S XC NHH S XC NH

rr22 = SSR/SST = 100/114 = .8772= SSR/SST = 100/114 = .8772Mi h hi i h 88%Mi h hi i h 88%

230

Mi quan h hi qui rt mnh; 88% Mi quan h hi qui rt mnh; 88% s bin thin ca doanh s xe hi c th c s bin thin ca doanh s xe hi c th c gii thch bi mi quan h tuyn tnh gia gii thch bi mi quan h tuyn tnh gia s qung co trn TV v doanh s xe hi.s qung co trn TV v doanh s xe hi.

H S TNG QUAN MUH S TNG QUAN MU

ionDeterminat oft Coefficien ) of(sign 1brxy

231

21 ) of(sign rbrxy

ViVi

bb11 = dc ca phng trnh hi qui c lng= dc ca phng trnh hi qui c lngxbby 10



TS. Cao Ho Thi 78

21 ) of(sign rbrxy

10 5y x

H S TNG QUAN MUH S TNG QUAN MU

232

Du ca Du ca bb11 trong phng trnhtrong phng trnh

l +.l +.

10 5y x

= + .8772xyr

rrxyxy = +.9366= +.9366

CC GI NH V S HNG SAI S CC GI NH V S HNG SAI S

1.1. Sai s l bin ngu nhin vi trung bnh bng 0

2.2. Phng sai ca , k hiu 2, s ging nhau

233

i vi tt c cc gi tr ca bin c lp.

3.3. Cc gi tr ca l c lp.

4. Sai s l bin ngu nhin tun theo

phn phi chun

KIM NH NGHAKIM NH NGHA

kim nh ngha ca mi quan h hi qui, chng

Ta phi tin hnh kim nh gi thuyt xc nh xem

gi tr ca 1 c bng 0 hay khng.

234

gi tr ca 1 c bng 0 hay khng.Hai kim nh c dng ph bin l:

t Test v F Test

C kim nh t v F u yu cu mt c lng ca

2, phng sai ca trong m hnh hi qui



TS. Cao Ho Thi 79

c lng ca


Trung bnh ca sai s bnh phng (MSE) s cung cp Trung bnh ca sai s bnh phng (MSE) s cung cp

235

2102 )()(SSE iiii xbbyyyViVi

ss 22 = MSE = SSE/(= MSE = SSE/(n n 2)2)

c lng cac lng ca 22, v , v ss22 cng c s dng.cng c s dng.


c lng ca

c lng c lng chng ta ly cn bc hai cachng ta ly cn bc hai ca 22..

236

2SSEMSE

n

s

Kt qu Kt qu ss c gi l c gi l sai s chun ca c lngsai s chun ca c lng

Gi thuyt

KIM NH NGHA: KIM NH KIM NH NGHA: KIM NH tt

0 1: 0H : 0H

237

Tr thng k

1: 0aH

1

1

b

bts



TS. Cao Ho Thi 80

Qui tc bc bQui tc bc b


238

ViVi

tt c da trn phn phi tc da trn phn phi t

vi bc t do l n vi bc t do l n --2 2

Bc bBc b HH00 nu nu pp--valuevalue tt

1. Xc nh gi thuyt.1. Xc nh gi thuyt.


0 1: 0H

1: 0aH

239

2. Xc nh mc ngha2. Xc nh mc ngha..

3. La chn tr thng k kim nh.3. La chn tr thng k kim nh.

= .05= .05

4. Qui tc bc b.4. Qui tc bc b. Bc b Bc b HH00 nu nu pp--valuevalue 3.182 (> 3.182 (vi t do l 3vi t do l 3))

1

1

b

bts

KIM NH NGHA: KIM NH t

5. Tnh gi tr ca tr thng k kim nh.5. Tnh gi tr ca tr thng k kim nh.

1 5 4.631 08b

bts

240

6. Xc nh c bc b 6. Xc nh c bc b HH00 hay khnghay khng

tt = 4.541 cho mt din tch .01 phn ui= 4.541 cho mt din tch .01 phn ui

pha trn. V vy, pha trn. V vy, pp--value nh hn .02. (Cng vy,value nh hn .02. (Cng vy,

tt = 4.63 > 3.182.) chng ta c th bc b = 4.63 > 3.182.) chng ta c th bc b HH00..

11.08bs



TS. Cao Ho Thi 81

KHONG TIN CY CA KHONG TIN CY CA 11

Chng ta c th dng mt khong tin cy 95% ca Chng ta c th dng mt khong tin cy 95% ca 11

kim nh cc gi th t a mi dng trong kim nh cc gi th t a mi dng trong

241

HH00 b bc b nu gi tr c gi thuyt cab bc b nu gi tr c gi thuyt ca 11

khng nmkhng nm trong khong tin cy catrong khong tin cy ca 11..

kim nh cc gi thuyt va mi dng trong kim nh cc gi thuyt va mi dng trong

kim nh t.kim nh t.

Cng thc ca khong tin cy i vi 1 l:


1/2 bt s

242

11 /2 bb t s

ViVi l gi tr l gi tr tt cho mt din tch lcho mt din tch l

/2 /2 trong phn ui pha trn ca phn phi trong phn ui pha trn ca phn phi tt

Vi t do l n Vi t do l n -- 22

2/t

bb11 l l

c c

lng lng

imim

l bin l bin

ca sai ca sai

ss


Bc b Bc b HH00 nu 0 khng nm trong nu 0 khng nm trong

khong tin cy cakhong tin cy ca 11..

Qui tc bc b

243

0 0 khng nm trong khong tin cy khng nm trong khong tin cy . .

Bc b Bc b HH00

= 5 +/= 5 +/-- 3.182(1.08) = 5 +/3.182(1.08) = 5 +/-- 3.443.4412/1 bstb

or 1.56 to 8.44or 1.56 to 8.44

Khong tin cy 95% ca 1

Kt lun



TS. Cao Ho Thi 82

Gi thuyt

KIM NH NGHA: KIM NH F

0 1: 0H

1: 0aH

244

Tr thng kFF = MSR/MSE= MSR/MSE

1a

Qui tc bc b


B bB b HH

245

ViVi::

FF da trn phn phi F vi t do l 1da trn phn phi F vi t do l 1

t s v t s v t do l n t do l n -- 2 mu s2 mu s

Bc bBc b HH00 nunu

pp--valuevalue > FF

1. Xc nh gi thuyt.1. Xc nh gi thuyt.


0 1: 0H 1: 0aH

246

2. Xc nh mc ngha.2. Xc nh mc ngha.

3. La chn tr thng k kim nh.3. La chn tr thng k kim nh.

= .05= .05

4. Qui tc bc b.4. Qui tc bc b. Bc b Bc b HH00 nu nu pp--valuevalue > 10.13 (vi 10.13 (vi d.fd.f t s t s

l l 1 v d.f mu s l 3)1 v d.f mu s l 3)

FF = MSR/MSE= MSR/MSE



TS. Cao Ho Thi 83


5. Tnh gi tr ca tr thng k kim nh.5. Tnh gi tr ca tr thng k kim nh.

6 X h b b6 X h b b HH h khh kh

FF = MSR/MSE = 100/4.667 = 21.43= MSR/MSE = 100/4.667 = 21.43

247

6. Xc nh c bc b 6. Xc nh c bc b HH00 hay khnghay khng

FF = 17.44 cho mt din tch l .025 phn ui = 17.44 cho mt din tch l .025 phn ui

pha trn. V vy, pha trn. V vy, pp--value tng ng vi value tng ng vi FF = 21.43 = 21.43

s nh hn 2(.025) = .05. V vy, chng ta bc b s nh hn 2(.025) = .05. V vy, chng ta bc b

HH00..Chng c thng k kt lun c mi quan h Chng c thng k kt lun c mi quan h

c ngha gia s lng qung co TV v doanh s c ngha gia s lng qung co TV v doanh s xe hixe hi

MT VI LU V MT VI LU V GII THCH CC KIM NH NGHAGII THCH CC KIM NH NGHA

Bc b Bc b HH00: : 11 = 0 v kt lun rng mi quan h = 0 v kt lun rng mi quan h

giagia xx vv yy c ngha chng ta khng th ktc ngha chng ta khng th kt

248

Bi v chng ta c th bc b Bi v chng ta c th bc b HH00: : 11 = 0 v= 0 v

chng t c ngha v thng k chng t c ngha v thng k , chng ta khng th kt, chng ta khng th kt

lun c lun c mi quan h tuyn tnhmi quan h tuyn tnh gia gia xx v v yy

gia gia xx v v yy c ngha, chng ta khng th kt c ngha, chng ta khng th kt

lun c lun c mi quan h nhn qumi quan h nhn qu gia gia xx v v yy

S DNG PHNG TRNH HI QUI C LNGS DNG PHNG TRNH HI QUI C LNG

C LNG V D ON C LNG V D ON

/ y t sp yp 2

Khong tin cy ca E(yp)

249

Vi:Vi:h s tin cy l 1h s tin cy l 1 -- vvtt/2 /2 da trn phn phi tda trn phn phi tvi t do l n vi t do l n -- 22

/2 indpy t s

D on khong tin cy ca yp



TS. Cao Ho Thi 84

Nu 3 qung co TV c tin hnh trc khi bn, chng ta k vng trung bnh doanh s xe hi l:

C LNG IMC LNG IM

250

yy = 10 + 5(3) = 25 xe h= 10 + 5(3) = 25 xe hii

Kt qu khong tin cy t Excel D E F G1 CONFIDENCE INTERVAL2 x p 33 xbar 2.04 x -xbar 1 0

KHONG TIN CY CA KHONG TIN CY CA EE((yypp))

251

4 x p -xbar 1.05 (x p -xbar)2 1.06 (x p -xbar)2 4.07 Variance of yhat 2.10008 Std. Dev of yhat 1.44919 t Value 3.1824

10 Margin of Error 4.611811 Point Estimate 25.012 Lower Limit 20.3913 Upper Limit 29.61

c lng khong tin cy 95% ca trung bnh doanh s c lng khong tin cy 95% ca trung bnh doanh s xe hi khi 3 qung co TV c thc hin l:xe hi khi 3 qung co TV c thc hin l:

KHONG TIN CY CA E(yp)

252

25 25 ++ 4.61 = 20.39 to 29.61 xe hi4.61 = 20.39 to 29.61 xe hi



TS. Cao Ho Thi 85

Kt qu khong d on t Excel

H I1 PREDICTION INTERVAL

KHONG D ON CA yp

253

2 Variance of y ind 6.766673 Std. Dev. of y ind 2.601284 Margin of Error 8.278455 Lower Limit 16.726 Upper Limit 33.287

c lng khong d on 95% ca doanh s xe hi c lng khong d on 95% ca doanh s xe hi

trong 1 tun c th khi 3 qung co TV c thc hin l:trong 1 tun c th khi 3 qung co TV c thc hin l:

KHONG D ON CA yp

254

g q gg q g

25 25 ++ 8.28 = 16.72 to 33.28 xe h8.28 = 16.72 to 33.28 xe hii

PHN TCH PHN D

Nu cc gi nh v s hng sai s khng m bo

th cc kim nh gi thuyt v ngha ca mi quan h

hi qui v cc kt qu c lng khong khng cn

255

i iy y

Rt nhiu phn tch phn d da trn Rt nhiu phn tch phn d da trn

vic kho st th phn dvic kho st th phn d

Phn d ca quan st th Phn d ca quan st th ii

Cc phn d s cho thng tin tt nht vCc phn d s cho thng tin tt nht v ..hiu lc



TS. Cao Ho Thi 86

TH PHN D THEO X

Nu gi nh phng sai ca ging nhau i vi tt

c cc gi tr ca x c tha, v m hnh hi qui gi

nh l mt biu din y ca mi quan h gi cc

256

nh l mt biu din y ca mi quan h gi cc

bin, th th phn d s cho mt n tng tng th v gii bng cc im nm ngang

y y

Dng ttDng tt

TH PHN D THEO X

257

xx

00

Ph

n d

Ph

n d

TH PHN D THEO X TH PHN D THEO X

y y

Phng sai thay iPhng sai thay i

258

xx

00

Ph

n d

Ph

n d



TS. Cao Ho Thi 87

TH PHN D THEO X

y y

Dng m hnh khng thch hpDng m hnh khng thch hp

259

xx

00

Ph

n d

Ph

n d

Phn d

Observation Predicted Cars Sold Residuals1 15 -1

TH PHN D THEO X

260

1 15 12 25 -13 20 -24 15 25 25 2

TH PHN D THEO X TH PHN D THEO X

th phn d

2

3

261

-3

-2

-1

0

1

0 1 2 3 4Qung co TV

Phn

d


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Bài giảng Thống kê Tác giả: TS. Cao Hào Thi, Trường Đại học Bách khoa, ĐHQG Tp.HCM, 2010

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