DJAFB3 ABA9A7ATB1A5DHA7AT B0A0AKAMAPAZ 1. B0B2AVAXAAA8 (1)A0BRBYBL A0CZAADBADBC Y CCADBC X A2BPDACQB6CMB4 Y = β 0 + β 1 X + e, CCCY β 0 + β 1 X AFD8 Y AAX BKADD2BXBABOADD2BKAMC4A5 eD9AADBB1AUA4e ～ N(0,σ 2 ). AY CTA0f(X)=β 0 +β 1 X ASC0CFBABOD5COCTA0A1β 0 ,β 1 ASD5COB4A0A1AY X ASD5COD8ADBCA2D9 D5COC3D7A3A5AY Y ASD5COC3ADBCA2D9BEC6ADBCA3A5 CT(x 1 ,y 1 ),(x 2 ,y 2 ),...(x n ,y n )D9(X,Y )BKC0DBCNARCTA5CLC0CFBABOD5COBYBLAWAFD8AS y i = β 0 + β 1 x i + e i i =1,2,...n, CCCY E(e i )=0,i=1,2,...n. (2)AKBVD5COC2B2 C9DCBIBYB1BZCIB5ATCRAPA0 β 0 , β 1 BKCKDG ? β 0 , ? β 1 . BK Q(β 0 ,β 1 )= n summationdisplay i=1 (y i ? β 0 ? β 1 x i ) 2 , CL β 0 , β 1 BKDCBIBYB1CKDGD9CUD6 Q( ? β 0 , ? β 1 )=min β 0 ,β 1 Q(β 0 ,β 1 ) B0B7BK ? β 0 , ? β 1 . AKDGA9AWBJ ? β 0 = y ? ? β 1 ˉx, ? β 1 = n summationtext i=1 (x i ? ˉx)(y i ? ˉy) n summationtext i=1 (x i ? ˉx) 2 = S xy S xx , CCCY ˉx = 1 n n summationtext i=1 x i , ˉy = 1 n n summationtext i=1 y i , S xx = n summationtext i=1 (x i ? ˉx) 2 ,S xy = n summationtext i=1 (x i ? ˉx)(y i ? ˉy). 1 2 C9B8AWBJD5COC2B2AS ? Y = ? β 0 + ? β 1 X,A2D9AYAKBVD5COC2B2A3A5AKAWCK ?σ 2 = n summationtext i=1 (y i ? ? β 0 ? ? β 1 x i ) 2 n ?2 ASAPA0 σ 2 BKCKDGBCA4A2BYAYAS σ 2 BKDCBIBYB1CKDGA3A5AWC1CQBV ?σ 2 D9 σ 2 BKAZC8CKDGA4DE E?σ 2 = σ 2 . (3)D5COC2B2BKB7D2BOA3BV H 0 : β 1 =0 ←→ H 1 : β 1 negationslash=0. AKAWAOC8CUCZC2BZA6 (i) tA3BVBZ BH H 0 B0B7D3AODGBC T = ? β 1 √ S xx ?σ ～ t n?2 , BVCBCGBQBKB7D2BOA2CA α,A3BVBKAOARCDAS W = braceleftbigg |T|≥t n?2 parenleftbigg α 2 parenrightbiggbracerightbigg . (ii) F A3BVBZ BH H 0 B0B7D3AODGBC F = ? β 2 1 S xx ?σ 2 ～ F 1,n?2 , BVCBCGBQBKB7D2BOA2CA α,A3BVBKAOARCDAS W = {F ≥ F 1,n?2 (α)}. (iii) BBCMB4A0A3BVBZ DH R = S xy radicalbig S xx S yy , AYRASBWABBBCMB4A0A4BVCBCGBQBKB7D2BOA2CA αASBBCMB4A0BGAFCTAFAWBJ r n?2 (α),CLA3 BVBKAOARCDAS W = {|R| >r n?2 (α)}. BHAOARH 0 D3A4CNASBABOD5COC2B2D9B7D2BKA5 3 (4)CEAR BVCB X BKCGBQCT x 0 , y 0 BKCWBKBTAS 1? αBKCEARCJA2AS (?y 0 ? l, ?y 0 + l),CCCY l = t n?2 parenleftbigg α 2 parenrightbigg ?σ radicalBigg 1+ 1 n + (ˉx ?x 0 ) 2 S xx (9.1). DE P{?y 0 ? l<y 0 < ?y 0 + l} =1? α. B5A6CJD5DIAWAFCYA4BHBWABCPBC n CZBED3A4BVCBCJ ˉx C8AIBK x 0 , AWC1BJBIA4D2BKCEARCJ A2A4B8D3 (9.1) D7CYBKCHD7AIA6BLCB 1. CG t n?2 ( α 2 ) ≈ Z α/2 ,CBD9 y 0 BKCWBKBTAS 1? α BKCE ARCJA2AIA6BNBLCB (?y 0 ? ?σZ α/2 , ?y 0 +?σZ α/2 ). (9.2) (5)AYCX AYCXD9CEARBKC0AWAFA4DEBXCICNATCT y CJC0C0CJA2(y 1 ,y 2 )C2CKCTD3A4AWC6A8 xAYCX CJD4BQC1ARC2A1C9 (9.2)D7A4BK ? ? ? y 1 =?y ? ?σZ α/2 = ? β 0 + ? β 1 x? ?σZ α/2 y 2 =?y +?σZ α/2 = ? β 0 + ? β 1 x +?σZ α/2 C4AG?B5 xB1A4AWC1DEASAYCX x BKCWB6B9A1 2. A2B2AVAXAAA8A6AS (1)A0BRBYBL CZADBC Y CCADBC X 1 , X 2 , ···, X p?1 A2CABABOCMB4 Y = β 0 + β 1 X 1 +···+ β p?1 X p?1 + e, CCCY e ～ N(0,σ 2 ), β 0 ,β 1 ,···,β p?1 ,σ 2 D9BZCRAPA0A4 p ?1 ≥ 2,AYASBWCFBABOD5COBYBLA5 (2)APA0CKDG CZ (x i1 ,x i2 ,···,x ip?1 ,y i ),i=1,2,···,nD9 (X 1 ,X 2 ,···,X p?1 ,Y) BK n B9BSB7CNARCTA4 BK y =(y 1 ,y 2 ,···,y n ) T ,β=(β 0 ,β 1 ,···,β p?1 ) T ,e=(e 1 ,e 2 ,···,e n ) T , CX X = ? ? ? ? ? ? ? ? ? 1 x 11 x 12 ··· x 1p?1 1 x 21 x 22 ··· x 2p?1 . . . . . . . . . . . . 1 x n1 x 2n ··· x np?1 ? ? ? ? ? ? ? ? ? , 4 AWC1CQBV β BKDCBIBYB1CKDG ? β = parenleftBig X T X parenrightBig ?1 X T y. BABXAWBJAKBVD5COC2B2AS ? Y = ? β 0 + ? β 1 X 1 +···+ ? β p?1 X p?1 . AY ?e = y ? X ? β ASAQAUBGBCA1AKAWCK ?σ 2 =?e T ?e/(n ? p) AS σ 2 BKCKDGA2AYAS σ 2 BKDCBIBYB1 CKDGA3A4AWC1CQBVA6 E ? σ 2 = σ 2 . (3)B7D2BOA3BV (i) D5COB4A0BKB7D2BOA3BV H j0 : β j =0,j=1,2,···,p?1. BH H j0 B0B7D3A4AODGBC T j = ? β j ?σ √ c jj ～ t n?p . CCCY c jj D9 C =(X T X) ?1 BKBVAABACWBO j +1CFA8A1BVCBCGBQBKB7D2BOA2CA α,A3BVBKAO ARCDAS W = braceleftbigg |T|≥t n?p parenleftbigg α 2 parenrightbiggbracerightbigg . (ii) D5COC2B2BKB7D2BOA3BV H 0 : β 1 = β 2 = ···= β p?1 =0 ←→ H 1 : β 1 ,β 2 ,···,β p?1 AKCLAS0. BH H 0 B0B7D3A4AODGBC F = SS D6 /(p ?1) SS B2 /(n ? p) ～ F p?1,n?p , CCCY SS D6 = n summationtext i=1 (?y i ? ˉy) 2 , SS B2 = n summationtext i=1 (y i ? ?y i ) 2 . BVCBCGBQBKB7D2BOA2CA α, A3BVBKAOARCD AS W = {F>F p?1,n?p (α)}. 3. A4DGA6AS (1)BGC3A8C2AUC4B3 CZDDBVCYADD2BKC3A8ASA,C3A8ADB7BKAKALD6?AYASA2CAA4DHAS A 1 , A 2 , ···A r . CJA2 CA A i B6DDCTCAB9DDBVA4AXBTA8A2CA A i B6BKDDBVADCP x i1 , x i2 , ···, x in i AUDEB1D8BO iCECP 5 ?D9AGX i ～ N(μ + α i ,σ 2 )BKBWABCNARCTA4COB5 μAFD8D9BKASCTA4 α i ASA2CA A i BVCU? BKBJC6A4AWC1BVCQ r summationtext i=1 n i α i =0.ACABC3A8A BK r CEA2CABKBJC6DEA3BVA0CZA6 H 0 : α 1 = α 2 = ···= α r =0,H 1 : α 1 ,α 2 ,···,α r AKCLASBHA5 DH S A = r summationdisplay i=1 n i summationdisplay j=1 (x i. ? x) 2 = r summationdisplay i=1 n i (x i. ? x) 2 , x i. = 1 n i n i summationdisplay j=1 x ij ,S E = r summationdisplay i=1 n i summationdisplay j=1 (x ij ? x i. ) 2 , CQCPCGA0CZH 0 B0B7A4CLCA F = S A /(r ?1) S E /(n ? r) ～ F r?1,n?r . BVCGBQBKB7D2BOA2CA α CT F>F r?1,n?r (α), CLAOARCGA0CZA4CNASC3A8 A BK r CEA2CA CAB7D2AUC2A1AXBTBYAWC1AKCQDGA9 P CTBKC2BZB1AQBQD9ACDHD3D9AOARCGA0CZA1 P CTAS P = P{Fr?1,n? r>F},BH P CTBICBα D3AXBTAOARH 0 . AKAWA8DGA9ADCPBFB0AFBKBMD7 A2A5AF9.1A3A1 AF9.1 BGC3A8C2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A S A r ?1 MS A = S A r?1 B1 AU S E n? r MS E = S E n?r F = MS A MS E D9 CX S T n?1 (2)A1C3A8C2AUC4B3 CZCABBCEC3A8 ACXB,C3A8ACAr CEA2CA A 1 , A 2 , ···, A r ,C3A8B CAsCEA2CA B 1 , B 2 , ···, B s . (i) AKAVBNA9D1DEC8 CJC3A8 A, B BKBSC0CZA2CABCC7 (A i ,B j ) B6AHBNC0B9BSB7DDBVBJBICNARCT x ij , i = 1,2,···,r, j =1,2,...,s. A0BQ X ij ～ N(μ + α i + β j ,σ 2 ),i=1,2,···,r, j=1,2,···,s, CGCF X ij BBD1BSB7A5 α i ASC3A8ABKBOiCEA2CABKBJC6A4 β j ASC3A8B BKBOj CEA2CABKBJ C6A5B8D3C6BUC3A8A, B BKC7BED9C5B7D2BLA1CBA3BVB6BFA0CZA6 H 01 : α 1 = α 2 = ···= α r =0, H 02 : β 1 = β 2 = ···= β s =0. 6 DH S T = r summationdisplay i=1 s summationdisplay j=1 (x ij ? x) 2 , S E = r summationdisplay i=1 s summationdisplay j=1 (x ij ? x i. ? x .j + x) 2 , S A = s r summationdisplay i=1 (x i. ? x) 2 , S B = r s summationdisplay j=1 (x .j ? x) 2 , x i. = 1 s s summationdisplay j=1 x ij ,i=1,2,···,r, x .j = 1 r r summationdisplay i=1 x ij ,j=1,2,···,s, x = 1 rs r summationdisplay i=1 s summationdisplay j=1 x ij , S T ASD9B3AUCAC2CXA4S E ASB1AUCAC2CXA4S A ASC3A8ABKCAC2CXA4S B ASC3A8B BKCAC2 CXA5AWC1CQBVBH H 01 B0B7D3 F A = S A /(r ?1) S E /(r ?1)(s ?1) ～ F r?1, (r?1)(s?1) , B2A6BNA4BHH 02 B0B7D3 F B = S B /(s ?1) S E /(r ?1)(s ?1) ～ F s?1, (r?1)(s?1) , C4AGC1 F A , F B DEASH 01 , H 02 BKA3BVAODGBCA4A8A3BVADCPBFB0C2AUC4B3AFA5 AF9.2 A1C3A8C2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A S A r ?1 MS A = S A r?1 F A = MS A MS E C3A8B S B s ?1 MS B = S B s?1 F B = MS B MS E B1 AU S E (r ?1)(s ?1) MS E = S E (r?1)(s?1) D9 CX S T rs?1 A8AFCYBBC6BK P CTCCB7D2BOA2CA α ACABA4BH P<αD3AOARCGA0CZH 01 D9 H 02 ,CNASC9C3 A8BKCFA2CABJC6A2BBCJB7D2AUC2A5 7 (ii) AVBNA9D1DEC8 CZCABBCEC3A8 A, B. C3A8 A CA r CEA2CA A 1 , A 2 , ···, A r , C3A8 B CA s CEA2CA B 1 , B 2 , ···, B s ,BSCZA2CABKBCC7 (A i ,B j )B6ASDED0C7DDBV t B9A5DHBOk B9BKCNARCTASx ijk . A8 x ijk ,k=1,2,···,tAUDEB1D8BO ij CED9AGX ij BKBWABCNARCTA4A0CZ X ij ～ N(μ + α i + β j + δ ij ,σ 2 ),i=1,2,···,r; j =1,2,···,s. CGCF X ij BBD1BSB7A4CCCY δ ij AFD8 A i CX B i BKA9D1BJC6A4 α i ASC3A8ABKBOiCEA2CABKBJ C6A4β j ASC3A8B BKBOj CEA2CABKBJC6A5B8D3C6BUC3A8A, B DDA9D1BJC6BKC7BED9C5B7D2 BLA1CBA3BVB6BFA0CZA6 H 01 : α 1 = α 2 = ···= α r =0, H 02 : β 1 = β 2 = ···= β s =0, H 03 : δ ij =0,i=1,2,···,r; j =1,2,···,s. DH S T = r summationdisplay i=1 s summationdisplay j=1 t summationdisplay k=1 (x ijk ? x) 2 S E = r summationdisplay i=1 s summationdisplay j=1 t summationdisplay k=1 (x ijk ? x ij. ) 2 S A = st r summationdisplay i=1 (x i. ? x) 2 S B = rt s summationdisplay j=1 (x .j ? x) 2 S A×B = t r summationdisplay i=1 s summationdisplay j=1 (x ij. ? x i.. ? x .j. + x) 2 x ij. = 1 t t summationdisplay k=1 x ijk ,i=1,2,···,r, j=1,2,...,s, x i.. = 1 st s summationdisplay j=1 t summationdisplay k=1 x ijk ,i=1,2,···,r, x .j. = 1 rt r summationdisplay i=1 t summationdisplay k=1 x ijk ,j=1,2,···,s, x = 1 rst r summationdisplay i=1 s summationdisplay j=1 t summationdisplay k=1 x ijk 8 S T ASD9B3AUCAC2CXA4S E ASB1AUCAC2CXA4S A ASC3A8ABKCAC2CXA4S B ASC3A8B BKCAC2 CXA4S A×B ASA9D1BJC6CAC2CXA5AWC1CQBVA6 BH H 01 B0B7D3A4 F A = S A /(r ?1) S E /(rs(t ?1)) ～ F r?1,rs(t?1) . BH H 02 B0B7D3A4 F B = S B /(s ?1) S E /(rs(t ?1)) ～ F s?1,rs(t?1) . BH H 03 B0B7D3A4 F A×B = S A×B /(r ?1)(s ?1) S E /(rs(t ?1)) ～ F (r?1)(s?1),rs(t?1) . C4AGC1 F A , F B , F A×B DEASH 01 , H 02 , H 03 BKA3BVAODGBCA4A8A3BVADCPBFB0C2AUC4B3AFA6 AF9.3 A1C3A8C2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A S A r ?1 MS A = S A r?1 F A = MS A MS E C3A8B S B s ?1 MS B = S B s?1 F B = MS B MS E A9D1BJC6A × B S A×B (r ?1)(s ?1) MS A×B = S A×B (r?1)(s?1) F A×B = MS A×B MS E B1 AU S E rs(t ?1) MS E = S E rs(t?1) D9 CX S T rst?1 A3A0ACAYAZAL 1. CNAYC0CFBABOD5COC4B3BKDAABA4BDCXDAABC2BZA4D7CID5COC2B2CYATCRAPA0BKCKDGCTA4 D7DEBBCMBOA3BVA4D7B6C8BABOD5COC2B2AHBNCEARA5 2. BD?BWCFBABOD5COBKDAABC2BZA4BD?BWCFBABOBBCMBKB7D2BOA3BVA1 3. CNAYBGC3A8C2AUC4B3BKDAABA4BDCXDAABC2BZA5 4. BD?A1C3A8C2AUC4B3BKDAABA4BDCXDAABC2BZA5 B4A0: C0CFBABOD5COC4B3BKDAABA4BDCXDAABC2BZA5BGC3A8C2AUC4B3BKDAABA4BDCXDAABC2 BZA5 AJA0: C8D5COC4B3A4C2AUC4B3BKDAABA4BDB7B4D5DIAWAFA4B6C8DGA9DBD9C6C8A0BRCSA6DDBB C6BKAODGDGA9A5 9 ANA0A1AWAHAQA6AS AG1. B8CA10DBCNARA0APA4C9B6AFCGB5A6 x 0.5 ?0.80.9 ?2.86.52.31.65.1 ?1.9 ?1.5 y ?0.3 ?1.21.1 ?3.54.61.80.53.8 ?2.80.5 (1)CI Y BV X BKBABOD5COC2B2A7(2)A3BVD5COC2B2BKB7D2BOA5 AD(1)DGA9AWCJB6AFCWAHBN BPCW x i y i x 2 i y 2 i x i y i 1 0.50 ?0.30 0.25 0.09 ?0.15 2 ?0.80 ?1.20 0.64 1.44 0.96 3 0.90 1.10 0.81 1.21 0.99 4 ?2.80 ?3.50 7.84 12.25 9.80 5 6.50 4.60 42.25 21.16 29.90 6 2.30 1.80 5.29 3.24 4.14 7 1.60 0.50 2.56 0.25 0.80 8 5.10 3.80 26.01 14.44 19.38 9 ?1.90 ?2.80 3.61 7.84 5.32 10 ?1.50 0.50 2.25 0.25 ?0.75 summationtext 9.90 4.50 91.51 62.17 70.39 C9AFCYA0APDGA9AWBJ x = 1 n n summationdisplay i=1 x i = 9.9 10 =0.99, y = 1 n n summationdisplay i=1 y i = 4.5 10 =0.45, S xx = n summationdisplay i=1 (x i ? x) 2 = n summationdisplay i=1 x 2 i ? n(x) 2 =91.51 ?10×0.99 2 =81.71, S yy = n summationdisplay i=1 (y i ? y) 2 = n summationdisplay i=1 y 2 i ? n(y) 2 =62.17 ?10×0.45 2 =60.15, S xy = n summationdisplay i=1 (x i ? x)(y i ?y)= n summationdisplay i=1 x i y i ? nxy =70.4?10 ×0.99×0.45 = 65.94, 10 ? β 1 = S xy S xx = 65.94 81.71 =0.81, ? β 0 = y ? ? β 1 x =0.45 ?0.81 ×0.99 = ?0.35, ? σ 2 = n summationtext i=1 (y i ? ? β 0 ? ? β 1 x i ) 2 n ?2 =0.867. AKBVD5COC2B2AS ? Y = ?0.35 + 0.81X. (2)C2BZC0A6B6C8 F A3BVBZA4DGA9 F = ? β 2 1 S xx ?σ 2 = 0.81 2 ×81.71 0.87 =61.61, ASAFBJF 1,8 (0.05) = 5.32. C3ASF =61.61 > 5.32,ADC1AOARH 0 ,CNAS X CC Y BKBABOCMB4B7 D2A5 C2BZBYA6B6C8BBCMB4A0A3BVBZA4DGA9 R = S xy radicalbig S xx S yy = 65.94 √ 81.71 ×60.15 =0.94, ASBBCMB4A0AFBJ r 8 (0.01) = 0.765. C3ASR =0.94 > 0.765, ADC1CNAS X CC Y BKBABOCMB4B7 D2A5 AH2. CZ y 1 = β 1 + e 1 y 2 =2β 1 ?β 2 + e 2 y 3 = β 1 +2β 2 + e 3 CCCY e 1 , e 2 , e 3 BBD1BSB7A4CGCA E(e i )=0,Var(e i )=σ 2 , i =1,2,3, CI β 1 , β 2 BKDCBIBYB1CK DGA5 ? X = ? ? ? ? ? 10 2 ?1 12 ? ? ? ? ? ,X T X = ? ? 60 05 ? ? , ? β =(X T X) ?1 X T y 11 = ? ? 1 6 0 0 1 5 ? ? ? ? 121 0 ?12 ? ? ? ? ? ? ? y 1 y 2 y 3 ? ? ? ? ? = ? ? 1 6 (y 1 +2y 2 + y 3 ) 1 5 ( ? y 2 +2y 3 ) ? ? DE β 1 , β 2 BKDCBIBYB1CKDGAS ? β 1 = 1 6 (y 1 +2y 2 + y 3 ), ? β 2 = 1 5 (?y 2 +2y 3 ). AH3. CHAPAKBVCRA4CJCMBKD0CDBBBLBKAJA6B6A4CCBSBTBKDEACBTY CCAGD0X 1 A0C4BI X 2 CACMA5B8DEDCBD 13BWC1D7BKARBCA0APA4A5AF 9.4. DDA7B7Y CMCB X 1 ,X 2 BKBABOD5COC2 B2A1 AF9.4 BSBTA0AP AGD0 x 1 (kg) 76 91.585.582.57980.574.579 8576.582 9592.5 C4BI x 2 (AB) 50 20 20 30 30 50 60 50 40 55 40 40 20 DEACBTy(CUBUCID3) 120 141 124 126 117 125 123 125 132 123 132 155 147 ?: ? β =(X T X) ?1 X T y = ? ? ? ? ? 13 1079.5 505 1079.5 90159.75 41167.5 505 41167.5 21925 ? ? ? ? ? ?1? ? ? ? ? 1690 141138.5 64935 ? ? ? ? ? = ? ? ? ? ? ?62.9634 2.1366 0.4002 ? ? ? ? ? BJBIy CC X 1 ,X 2 BKAKBVD5COC2B2AS ? Y = ?62.9634 + 2.1366X 1 +0.4002X 2 . AKDGA9BJBISS D6 = 1430.5699, SS B2 =81.4301, C3B8CAA4 F = SS D6 /(p ?1) SS B2 /(n ? p) = 1430.5699/2 81.4301/10 =87.8404. ASAFBJF 2,10 (0.05) = 4.1028. C3ASF =87.8404 > 4.1028,ADC1CNASD5COC2B2C3CYB2BTBACVA5 12 AH4. B6C8A5CZAKALC7C2BKANBE A 1 ,A 2 ,A 3 ,A 4 D1AVB5B1BKCFA6A4ARBJCCD6C8DFBXCQB6 AF9.5 CFA6DFBXA0AP ANBE D6 C8 DF BX A 1 1600 1610 1650 1680 1700 1700 1780 A 2 1500 1640 1400 1700 1750 A 3 1640 1550 1600 1620 1640 1600 1740 1800 A 4 1510 1520 1530 1570 1640 1600 AWA6A5CZAKALC7C2B6CFA6BKD6C8DFBXCAAZB7D2BKAUC2A8 ? ANBEBKC7C2ASC3A8A4A5CZAKALBKC7C2ASA5CEA2CAA4A5CZAKALC7C2D1AVB5BKCFA6BK D6C8DFBXDCASA5CED9AGA4A5CED9AGBKASCTASμ i , i =1,···,4A4CTBXA3BVA5CZAKALC7C2D1AV B5BKCFA6BKCAASD6C8DFBXD9C5CAB7D2BKAUC2DEA3BVA6 H 0 : μ 1 = μ 2 = μ 3 = μ 4 ←→ H 1 : μ 1 ,···,μ 4 CYCVCXCABBCEAKBBBLA5 AKCQDGA9A8ADCPAICRC2AUC4B3AF AF9.6 CFA6DFBXA0APBKC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A 49212.35 3 16404.12 B1 AU 166622.26 22 7573.74 2.166 0.1208 D9 CX 215834.62 25 CK α =0.05 ASAFBJBGAFCT F 0.05 (3,22) = 3.05. C3AS2.161 < 3.05, ADC1ACDH H 0 , CNASA5CZ ANBED1AVB5BKCFA6BKCAASDFBXAZB7D2AUC2A1BJAPCHAP PCTBECB0.05BYAWC1A3BVALBWBKAD BOA1 AH5. BIA9DICJACCZBD 3CZAKALATBLBKCVCSCBATD0BKBBD8AHA0CQB6 AF9.7 A9DIDDBVA0AP ATBL BB D8 CO A0 1 2432477 2 254 2 5 6 851071212 6 6 3 71166 7 9 5 5 106310 13 C6BUBIA9DIAAD4CYCUCZATBLD0BKCAASBBD8AHA0CAAZB7D2AUC2A8 ? CZBIA9DIAAD4CYBKCVCSCBATASC3A8A4CUCZAKALBKATBLASCUCEA2CAA4ACCZD0BKBBD8 AHA0AUDEB1D8CUCECP?C4ALD9AG N(μ i ,σ 2 )BKBWABCNARCTA4 i =1,2,3. AWAFCOADASA3BVA6 H 0 : μ 1 = μ 2 = μ 3 ←→ H 1 : μ 1 ,μ 2 ,μ 3 AKCLBBBLA5 AKDGA9AWBJ AF9.8 A9DIDDBVC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A 94.26 2 47.13 B1 AU 166.65 30 5.56 8.484 0.0012 D9 CX 260.91 32 PCTCIBICB0.01C6AOARCGA0CZA4DECNASBIA9DICJACCZCUCZAKALATBLBKCVCSCBATD0BKBBD8 AHA0CAB7D2BKAUC2A5 AH6. CJC0CEC5BZDDBVCYA4AVBNA5CZAKALBKCZD7C9CZ A 1 , A 2 , A 3 , A 4 CXCUCZAKALBKD2 C3C2BZ B 1 , B 2 , B 3 BJBIAVBCA0APCQAF 9.9(BGAUA6 kg). AF9.9 C5BZDDBVA0AP B 1 B 2 B 3 A 1 325 292 316 A 2 317 310 318 A 3 310 320 318 A 4 330 370 365 DDC4B3CZD7CCD2C3BVAVBCCAAZB7D2C7BEA8 ? AKCQDGA9AHA8ADCPAICRC2AUC4B3AF AF9.10 C5BZDDBVBKC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A(C9CZ) 3824.25 3 1274.75 5.226 0.04126 C3A8B(D2C3BZ) 162.50 2 81.25 0.3331 0.72915 B1 AU 1463.50 6 243.90 D9 CX 5444.75 11 14 CHAPPCTA3BVAKALC9CZBVAVBCCAB7D2C7BEA4BXBRCAB3C4B4C9A3BVD2C3C2BZBVAVBCCAB7D2 BKC7BEA1 AH7. BUANDJCZCCBNB4AUCWBVA7DJD1AXBKC7BEA4BVA5CEBNCJBKCUCZALBIA7DJBKCSAMAH BNARBCBJBIA0APCQB6 (BGAUA6 cm) AF9.11 A7DJCSAMA0AP B 1 B 2 B 3 B 4 23 25 21 14 15 20 17 11 A 1 26 21 16 19 13 16 24 20 21 18 27 24 28 30 19 17 22 26 24 21 A 2 25 26 19 18 19 20 25 26 26 28 29 23 18 15 23 18 10 21 25 12 A 3 12 22 19 23 22 14 13 22 13 12 22 19 A 1 ,A 2 ,A 3 AFD8CUCEAKALDJCZA4B 1 ,B 2 ,B 3 ,B 4 AFD8A5CEAKALBNCJA1BVBSC0CZA2CADBCYA4AH BNBD5B9ARBCA4BVB8DDBVADCPAHBNC2AUC4B3A5 ? AKDGA9A4AHA8DGA9ADCPAICRC2AUC4B3AF AF9.12 A7DJCSAMA0APBKA1C3A8C2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A 352.53 2 176.27 9.1369 0.0004341 C3A8B 58.05 3 19.35 1.0030 0.3996331 A9D1BJC6A× B 119.60 6 19.93 1.0333 0.4156274 B1 AU 926.00 48 19.29 D9 CX 1456.18 59 15 AWA5CJB7D2BOA2CA α =0.05B6DJCZ(BN)BJC6D9CDBTB7D2BKA4BXAUCW(BF)BJC6DDA9D1BJC6 AHAKB7D2A5 AOA0AIAUAQ 1. AIAXAF (1)D5COC4B3D9BUANADBCA2 CMB4BKC0CZA0B4AODGC2BZA5 (2)C0CFBABOD5COBYBLCYβ 0 , β 1 BKDCBIBYB1CKDGD9CUD6 BDBIDCBIBK ? β 0 CX ? β 1 . AKDGA9AWBJ ? β 0 = , ? β 1 = . (3)C0CFBABOD5COBYBLCYA4D5COB4A0BKB7D2BOA3BVAKAWAOC8 CZC2BZA4CCCY A3BVBZCC A3BVBZBLA1A5 t A3BVBZBKA3BVAODGBCAS , A3BVBKAOARCDAS .FA3BVBZBKA3BVAODGBCAS , A3BVBKAOARCDAS . (4) C0CFBABOD5COCYA4BVCB X BKCGBQCT x 0 , Y 0 BKCWBKBTAS 1 ? α BKCEARCJA2AS . (5)BVBWCFBABOD5COBYBLBKAODGC4B3D1BXBX?AQBKCUCEAWAFD9 , CX . (6) C2AUC4B3D1BXD9BVBWCECP?D9AGBKASCTDEA3BVA4C2BZD1BXDACB BKA4BDA5 (7)CJC2AUC4B3CYDCAWC8BKA3BVBZAS . 2. BVC0CZB0B4C6D2CBCAASAVBTCCC6D2AHA0ARDDBJA0APCQB6 C6D2CBCAASAVBT x( 0 C) 11.814.715.616.817.118.819.520.4 C6D2AHA0y(AH) 30.117.316.713.611.910.78.36.7 (1)CI Y BV X BKC0CFBABOD5COC2B2A7 (2)BVD5COC2B2DEB7D2BOA3BV (α =0.05); (3)CIBH x 0 =12D3 Y 0 BKCWBKBTAS 0.95BKCEARCJA2A5 3. C0CZD2D5C9CJCFAZDBCYBKBHDGBC Y CCC9AZDBBKCMAZ X 1 DDCMASDECR X 2 CACMA4B6 AFBFB515CEAZDBBKBHDGDHBM 16 AF9.13 D2D5C9BHDGA0AP AZDB BHDGBC(BC) CMA0(CECM) CMASDFBTDECR(CF) 1 120 180 3254 2 162 274 2450 3 131 205 2838 4 223 375 3802 5 169 265 3782 6 67 86 2347 7 192 330 2450 8 81 98 3008 9 212 370 2605 10 103 157 2088 11 144 236 2660 12 232 372 4427 13 252 430 4020 14 55 53 2560 15 116 195 2137 (1)CI Y CC X 1 , X 2 BKBABOD5COC2B2A4AHBVD5COC2B2DEB5?DAA7 (2)BVD5COC2B2DEB7D2BOA3BV (α =0.01); (3)CI x 1 = 220, x 2 = 2500D3A4BHDGBCBKCEARCTA5 4. ASA3ASB6BBCJB0CZAKALCPCDBKC4BECYADCRBKB5ATBKCEA0D9C5BBALA4BABSCZCPCDCY AADBBQCKBLANA4AHCKB5C0BMCJB7AQALB6D2BVA4ARBJA0APCQB6 AF9.14 B5ATCNARA0AP ANCW B5ATCEA0 /BSBM 1 24 15 21 27 33 23 2 14 712171416 3 11 9 7 13 12 18 4 77471218 5 19 24 19 15 10 20 AWCPCDBVC4BECYBKB5ATCEA0D9C5CAB7D2C7BEA8 17 5. C8CUCZAKALANBEBKBICHARBQC5B8AWA0BKDDBVADCPCQB6 AF9.15 C5B8AWA0DDBVA0AP ANBE C5B8AWA0 AIB9 6.678 6.671 6.675 6.672 6.674 AG 6.683 6.681 6.676 6.678 6.679 6.672 AJ 6.661 6.661 6.667 6.667 6.664 AWAKALBKANBEBVC5B8AWA0BKARBQD9C5CAB7D2C7BEA8 6. CJC0BFDDBVCYA4AVBNCUCZAKALBKCRAMBC A 1 , A 2 , A 3 ,CXA5CZAKALBKAVBT B 1 , B 2 , B 3 , B 4 B6A4BJBICCANCFBTA0APCQB6A5 AF9.16 CCANCFBTA0AP B 1 B 2 B 3 B 4 A 1 10.67.04.24.2 A 2 11.611.16.86.3 A 3 14.513.311.58.7 DDC4B3CRAMBC A CCAVBT B BVCCANCFBTCAAZB7D2C7BEA8 ARA0AIAUAQDIDF 1. (1)BBCM (2) Q(β 0 ,β 1 )= n summationtext i=1 (y i ? β 0 ? β 1 x i ) 2 ; Y ? ? β 1 x; S xy S xx = n summationtext i=1 (x i ?x)(y i ?y) n summationtext i=1 (x i ?x) 2 . (3)CUA7 t; F; T = ? β 1 √ S xx ?σ ～ t n?2 ; W = braceleftbig |T|≥t n?2 parenleftbig α 2 parenrightbigbracerightbig ; F = ? β 2 1 S xx ?σ 2 ～ F 1,n?2 ; W = {F ≥ F 1,n?2 (α)}. (4) parenleftbigg ?y 0 ? t n?2 parenleftbig α 2 parenrightbig ?σ radicalBig 1+ 1 n + (x?x 0 ) 2 S xx , ?y 0 + t n?2 parenleftbig α 2 parenrightbig ?σ radicalBig 1+ 1 n + (x?x 0 ) 2 S xx parenrightbigg . (5) BVD5COB4A0 β 0 ,β 1 ,···,β p?1 DDC2AUσ 2 BKCKDGA7 BVCACMD5COB4A0A0D5COC2B2BK BABOA0CZBKA3BVA7 CEARCXAYCXA1 (6)BVD9ADAUBKCAC2CXC4?BKA4BDA1 18 (7) FA3BVBZ 2. (1)D5COC2B2AS ? Y =57.0393 ?2.5317X. (2)B7D2BOA3BV F =89.868 >F 1,6 (0.05) = 5.9874, B7D2A1 (3) x 0 =12D3 Y 0 BKCWBKBTAS 0.95BKCEARCJA2AS (26.6594 ?6.0415, 26.6594 + 6.0415) = (20.6179, 32.7009). 3. (1) D5COC2B2AS ? Y =3.4526 + 0.4960X 1 +0.0092X 2 . C9AKBVD5COC2B2AWCRA4CTCLBQ CMASDFBTDECRAKADA4CLCMAZBSCMDJ 1CECMA4BHDGBCCMDJ 0.496BCA7CTCLBQCMAZA0AKADA4CL DECRBSCMDJ 1CFA4BHDGBCCMDJ 0.0092 BCA5 (2)DGA9BJ F = 5680 >F 2,12 (0.01) = 3.89, C3B8CNAS Y CC X 1 , X 2 BKBABOCMB4CDBTB7 D2A5 (3) A8 x 1 = 220, x 2 = 2500 BFCRAKBVD5COC2B2BJBHDGBCBKCEARCT (BPCKDG) AS 135.573(BC). 4. A8CPCDAUDEC3A8DEBGC3A85A2CAC2AUC4B3A4DGA9ADCPBFCRC2AUC4B3AF AF9.17 B5ATA0APBKC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A 803 4 200.7 B1 AU 557.2 25 22.29 9.008 1.1971 ×10 ?4 D9 CX 1360 29 PCTCIBICB0.01,ADC1CNASCPCDBVC4BECYBKB5ATCEA0CAB7D2C7BEA5 5. A8ANBEAUDEC3A8A4DEBGC3A83A2CAC2AUC4B3A4ASD6DGA9ADCPCADACJBKAJBTA4BVBS CEDDBVADCP x ij DDBABOADD4y ij =(x ij ?6.660) ×1000D0A8DGA9ADCPBFCRC2AUC4B3AF AF9.18 C5B8AWA0DDBVA0APBKC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A 565.1 2 282.6 B1 AU 140.8 13 10.83 26.08 2.8158 ×10 ?5 D9 CX 1360 29 PCTCIBICB0.01,ADC1CNASANBEBVC5B8AWA0ARBQBKC7BED9CDBTB7D2BKA5 19 6. DEA1C3A8C2AUC4B3A8DGA9ADCPBFCRC2AUC4B3AF AKCQDGA9AHA8ADCPAICRC2AUC4B3AF AF9.19 CCANCFBTA0APBKC2AUC4B3AF C2AUB1CH CAC2CX D8C9BT ASC2 FAC PCT C3A8A(CRAMBC) 60.74 2 30.37 33.54 0.5535 ×10 ?3 C3A8B(AVBT) 64.58 3 21.53 23.77 0.9923 ×10 ?3 B1 AU 5.433 6 0.9056 D9 CX 130.7 11 BBCE P CTBRCIBICB0.01,C3B8CNASCRAMBC A CCAVBT B BVCCANCFBTCAB7D2C7BEA5