24http://math.shekou.comftp://math.shekou.com

8.1

, , . , , , , ; , , , , , , , , . , , .

, , . . , (, , , ); ().

. , , , ; , . , A,B,C,, , A1,A2,.

1 , . , . :

, , , . , , , ., . , .

, Ar, A1,A2,,Ar, Ai(i=1,2,,r), , r, :(1) ;(2) ;(3) .

, , , imi, H0: m1=m2==mr.H1: m1,m2,,mr.H1.

Ai(i=1,2,,r), ni,

,

.

:

(1) rN(i,2) (i=1,2,,r);

(2) 1,2,,r,2.

_1211872623.unknown

_1211872669.unknown

, Ai

ST

()SA()SEST=SA+SE(1.4)

, SESAST=SA+SEH0, XijN(m,s2), , :(1) ST/s2~c2(n-1);(2) SE/s2~c2(n-r);(3) SA/s2~c2(r-1).(4) SESA.

, , , r, H0. , , F, H0, F~(r-1,n-r).

F~(r-1,n-r)a, Fa(r-1,n-r), (1) F>Fa(r-1,n-r), H0, A;(2) F

F

A

SA

r1

E

SE

nr

T

ST

n1

_1211894816.unknown

_1211894882.unknown

_1211894783.unknown

8.2

, . , . . , , . ..

, A,B, ArA1,A2,,Ar, BsB1,B2,,Bs. A,B(Ai,Bj), (i=1,2,,r,j=1,2,,s), rsXij,

BA

B1B2BsA1X11X12X1sA2X21X22X2sArXr1Xr2Xrs

1. , :(1) Xij~N(mij,s2), mij, s2, i=1,,r;j=1,,s.(2) ;(3) Xij, i=1,,r;j=1,,s

, , H0A: m1j=m2j==mrjj=1,,s,H0B: mi1=mi2==misi=1,,r.H1A: m1j,m2j,,mrj.H1B: mi1,mi2,,mis.

2.

:A:B::ST=SA+SB+SE,

H0A,H0B, (1) ST/s2, SA/s2, SB/s2, SE/s2rs-1, r-1, s-1, (r-1)(s-1)c2.(2) SA,SB,SE.(3)

3. a, H0AFAFa(r-1,(r-1)(s-1));H0BFBFa(s-1,(r-1)(s-1));

F

A

SA

r1

B

SB

s1

SE

(r1)(s1)

ST

rs1

_1211920101.unknown

_1211920262.unknown

_1211920397.unknown

_1211920170.unknown

_1211919982.unknown

, A,B. ArA1,A2,,Ar, BsB1,B2,,Bs. A,B(Ai,Bj), (i=1,2,,r, j=1,2,,s)t(t2)(), rstXijk (i=1,,r; j=1,,s; k=1,,t).

Xijk, Xijk~N(mij,s2),, mijmij=m+ai+bj+gij(i=1,,r; j=1,,s),aiAi, bijBj, gijAiBj.

:H0A: a1=a2==ar=0.H1A: a1,a2,,ar.H0B: b1=b2==bs=0.H1B: b1,b2,,bs.H0AB: g11=g12==grs=0,H1AB: g11,g12,,grs.

2. :

ST::ST=SE+SA+SB+SAB

, H0A,H0B, H0AB, (1) ST/s2, SA/s2, SB/s2, SAB/s2,SE/s2rst-1, r-1, s-1, (r-1)(s-1), rs(t-1)c2(2) SA,SB,SAB,SE.

3. H0A, a, H0AFAFa(r-1,rs(t-1))

H0B, a, H0BFBFa(s-1,rs(t-1))

H0AB, a, H0ABFABFa((r-1)(s-1),rs(t-1))

F

A

SA

r-1

B

SB

s-1

SA(B

(r-1)(s-1)

SE

rs(t-1)

ST

rst-1

_1211986573.unknown

_1211986835.unknown

_1211987081.unknown

_1211987198.unknown

_1211986922.unknown

_1211986605.unknown

_1211986502.unknown

8.3

., , , , , . . .

. Y=f(x), , , Y=f(x)+eY, x, e().

, , , , ., .

, xY. :xi, yi, xOy

xi100110120130140150160170180190yi45515461667074788589

xi100110120130140150160170180190yi45515461667074788589

Chart1

45

51

54

61

66

70

74

78

85

89

Sheet1

100110120130140150160170180190

45515461667074788589

Sheet1

0

0

0

0

0

0

0

0

0

0

Sheet2

Sheet3

, , , , :yi=b0+b1xi+ei,i=1,2,,10ei, .

, , Yx, Y=b0+b1x+e,(3.3)e~N(0,s2), b0,b1.(x1,Y1),(x2,Y2),,(xn,Yn)(x,Y), (x1,y1),(x2,y2),,(xn,yn).

Yi=0+1xi+i,

i=1,2,,n

(3.2)

1,2,,n. ,

Y~N(0+1x,2), E(Y)=0+1x

(3.3)

0,1

. x,

(3.4)

E(Y)=0+1x, (3.4)Yx, ,

.

_1212092545.unknown

_1212092676.unknown

_1212092502.unknown

,

(x1,y1),(x2,y2),,(xn,yn), xi,

yi

yi

.

_1212133066.unknown

_1212133108.unknown

_1212133195.unknown

_1212133014.unknown

xi, yi

, .

01

,

. , Q0, 1, ,

_1212133425.unknown

_1212133555.unknown

_1212133591.unknown

_1212133382.unknown

,

(3.5)

(3.5)(3.8)b0,b1. Yx.

,

1

0,1,

0,1,

.

_1212136873.unknown

_1212136900.unknown

_1212136819.unknown

, Y=b0+b1x+e, e~N(0,s2), b1=0, Yx, :H0:b1=0,H1:b10.H0, y1,y2,,yn, ,

S=S+S(3.10). S, S.

2 , H0,

,

~2(n2),

~2(1).

H0:

T, F, .

_1212138165.unknown

_1212138184.unknown

_1212138258.unknown

_1212138007.unknown

1. T-H0, Tt, |t|>ta/2(n-2), H0, , H0, .

2. F-H0, FF0, F0>Fa(1,n-2), H0, , H0, .

3. |r|>ra(n-2), H0, , H0, .ra(n-2).

, , , , , .

b0,b1,s2x.x'=1/x, :Y'=b0+b1x'+e, e~N(0,s2),

2. Y=aebxe, lne~N(0,s2),(3.23)a,b,s2x.Y=aebxelnY=lna+bx+lneY'=lnY, b0=lna, b1=b, x'=x, e'=lne, (3.23):Y'=b0+b1x'+e', e'~N(0,s2),

3. Y=axbe, lne~N(0,s2),(3.24)a,b,s2x.Y=axbelnY=lna+blnx+lneY'=lnY, b0=lna, b1=b, x'=lnx, e'=lne, (3.24):Y'=b0+b1x'+e', e'~N(0,s2),

4. Y=a+bh(x)+e, e~N(0,s2),(3.25)a,b,s2x. h(x)x, Y'=Y, b0=a, b1=b, x'=h(x), (3.25)Y'=b0+b1x'+e, e~N(0,s2).