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1、PPT模板下载：/moban/ 行业PPT模板：/hangye/ 节日PPT模板：/jieri/ PPT素材下载：/sucai/PPT背景图片：/beijing/ PPT图表下载：/tubiao/ 优秀PPT下载：/xiazai/ PPT教程： /powerpoint/ Word教程： /word/ Excel教程：/excel/ 资料下载：/ziliao/ PPT课件下载：/kejian/ 范文下载：/fanwen/ 试卷下载：/shiti/ 教案下载：/jiaoan/ 字体下载：/ziti/ 统计第六章回归分析与 yabx y yabx2,YN abx2,0,YabxN2, ,a b,ii
2、x yiyixiyyiiyabx21()niiiQyy21,niiiQ a byabx1100niiiniiiiyabxyabx x112111nniiiinnniiiiiiinaxbyxaxbx y11niixxn11niiyyn211nniiiiinanxbnynxaxbx y1,2,ix in22221110nnniiiiiinnxnxnxnxxnxx1122211nniiiiiinniiiix ynxyxxyybxnxxxaybx 2221111nnnxxiiiiiilxxxxn11111nnnnxyiiiiiiiiiilxxyyx yxyn2221111nnnyyiiiiiilyyy
3、ynxxlyylxylxyxxlblaybxyabxa by y yy y aybxyyb xx 1122,nnx yxyxy, x y360284.140,31.56799xy299211160009xxiiiilxx999111129959xyiiiiiiilx yxy29921111533.389yyiiiilyy29950.49926000 xyxxlbl11.599aybx11.5990.4992yxC,1,2,iix yinyabx, x Y, x Y,1,2,iix yin12,ny yy n21nyyiilyy(6-1-16)1,2,iiyabxin(6-1-17)=22221
4、1116 1 18nnnniiiiiiiiiiiyyyyyyyyyy 21niiiQyy（6-1-19）21niiUyy（6-1-20）21niiyyQU12,ny yy1,2,iy in（6-1-22）（6-1-23）回归效果的好坏取决于U及Q的大小，取决于U在总离差平方和中的比重，比重越大，回归效果越好。则相关系数yyl22xyxyyyyyxx yylblUrlll l(6-1-24)xyxx yylrl l(6-1-25)作为相关系数的估计值。, x Y由（6-1-13）式及（6-1-24）式得r与的关系xxyylrbl(6-1-26)yyxxlbrl(6-1-27)2yyUr l （6
5、-1-28）21yyQrl（6-1-29）由于U是总离差平方和中的一部分，而Q又不能为负，因此，可以推出，从而，即yyUlyyl21r 1r 当 时，Q=0，表明变量Y与x线性相关。此时，在散点图上，所有的观测点全部在同一条直线上。1r 当时，表明变量Y完全不与x发生关系。此时，变量Y与x之间不存在线性关系。一般有两种情况，一是变量Y与x之间的变化的确不存在任何统计0r yyQlr0r 0b 0r 0b r0:0Hr （6-1-30）r12UQn1,2Fn（6-1-31）（6-1-32） 1,2nFrrrrrrr0:0Hr 0r rr0:0Hr 0.05rr0.050.01rrr0.01rr6
6、000,2995,1533.38xxxyyylll0.987xyxx yylrl lr0.050.010.666,0.798rr0.01rr,xxxyyylllrb a,1,2,iix yinyabx0 x0y00yabx10y0y10 y0 y2,YN abx(6-1-34)200,yN abx（6-1-35）0 x00yyb xx（6-1-36）（6-1-37）00yabx0y2,1,2,iiyN abxinbb E bb（6-1-38）0y0y12,ny yy0y 00uyy （6-1-39） 000E uE yE y（6-1-40）（6-1-41）0,1uuN（6-1-42）uu2Q2
7、22nQ222unutQn（6-1-43）0022011nxxyytxxsnl（6-1-44）222xx yyxyxxl llQsnnl0y1（6-1-45）（6-1-46）10 x0 x0 xx0 x0 x（6-1-47）（6-1-48） 12,yyxyxyyxyxyabx1122,yus yus（6-1-49）1.96 ,1.96ys ys0 x0 x25xC11.5990.4992 2524.1yabx240,6000,1533.38,2995,2.34142xx yyxyxxyyxyxxl llxlllsnl9 20.0252.3646t227254011250.02512.3646
8、2.341415.933696000 xxxxtsnl12,y y0b 1x2x0b 12,x x0b 21,x x12,y y21yy122us1X2X01122Ybb Xb X（6-2-1）20,N1X2X2X2X1X1X01122 ybb Xb X（6-2-2）Y kg1X元 kg2X元012,b b b12,b b12,XX12,XX1,2,ijxjn1,2,jyjn101 112211201 122222101 122nnnybb xb xybb xb xybb xb x（6-2-3）012,bb b1,2,jjn20,N12;,1,2,jjjyxxjn111X11121nxxx21
9、222nxxx12nyyYy（6-2-4）0112TTbBbX XX Yb（6-2-5）1284080.45TX X840610505577.580.455577.5544.2075121.99950.08762.3542TX X 0.08760.00060.00672.35420.00670.28081200804508170.25TX Y0112116.1571.30811.245TTbBbX XX Yb 12116.157 1.30811.245yXXyylQU221nTyyiilyYY YnY11niiYyn（6-2-6）yyl2TTUB X YnY（6-3-7）TTTQY YB X
10、Y（6-2-8）012:0Hbb0H12,XX0H22,2 12 1UFFnQn（6-2-9）2,2 1Fn2,2 1 ,Fn0F022 1UFQn0F12,XX0.052,122 14.26F0.012,122 18.02F2111100,126300nnTiiiiYyY Yyn0F22120116.157, 1.308,11.2458045012 1006034.268170.25TTUB X YnY12012630116.157, 1.308,11.24580450265.748170.25TTTQY YB X Y02102.182 1UFQn102.188.0212,XX12,kXXX
11、iX0:01,2iiHbi201,2 11,22 1iiiibcFFniQn（6-2-10）iic1TX X1i1,2 1Fn1,2 1 ,Fn01,2iFi 0iF1,2 1 ,Fnix00.051,2 1iFFnixixix0.0500.011,2 11,2 1iFnFFn 0.0101,2 1iFnFix0.050.051,2 11,95.12FnF0.010.011,2 11,910.6FnF2 129.53Qn2101.3080.000696.5629.53F22011.245 0.280815.2529.53F010.61,2iFi12,XX22012,0,ybb xb xN 20
12、12,b b bx与 y0b1b x22b x1x2x3x3x3x3x1x1x1x2x2x2x12301 12233,x x xbb xb xb x1x2x3x,21AA,21rAAA), 2 , 1(riAii012:.rH.,:211不全相等rH), 2 , 1(riAiin,21iiniiXXX.1riinijX),(2iNi2ijXi), 0(2NijXiij未知和相互独立各个2i2, ), 0(, 2 , 1, 2 , 1,ijijiijiijNnjriX（6-3-1）),(2iN), 2 , 1(rir,212,11riiinn1riin,ii, 2 , 1riiiAii, 0)(
13、11riiiriiinn未知和相互独立各个2i21,), 0(0, 2 , 1, 2 , 1,ijijriiirijiijNnnjriX（6-3-2）.,:.:211210不全为零rrHHijXiinjijiXX1. iX,11injijiXnXrinjijiXn111riiXr1.1ijXri, 2 , 1kj, 2 , 1TSrinjijiXX112)(（6-3-3）TS0HijX),(2NijX0HTSEASS （6-3-4）AS,)(12.riiiXXnES2.11()inriijijXXASESiATSEASS TSrinjijiXX112)(rinjiiijiXXXX112.)()
14、(rinjiijiXX112.)()( )(2.11.XXXXirinjiiji,)(2.1XXnirii. iXX0)( )(.11.XXXXirinjiijiTSrinjiijiXX112.)(2.1)(XXniriiEASSESAS0HijX),(2N22(1)TSn2/ES)(2rn )(ESEsjtkijkXst1112)( /rnSE22/AS) 1(2r2) 1()( rSEA) 1( rSA2AESS 与0HEASrSrn) 1()()() 1(rnSrSFEAEASrSrn) 1()(0HEASrSrn) 1()(1,)rnraF), 1(rnrESASAS0HaFaF),
15、1(rnr), 1(rnr0H0H iTinjijX1, 2 , 1ririnjijiX11.1riiX111AAAAEEEETFSSASrSFrSSESnrSnrTSn方 差 来 源平 方 和自 由 度均 方 和值因 素误 差总 和TS=rinjijiX112nT2TS=rinjijiX112nT2ASriiinT12.nT2ESATSS in1A2A3A3A4321,AAAAiijmjix, 2 , 1; 4 , 3 , 2 , 1,(在本例中,2, 3, 3, 24321mmmm).12,rA AA12,sB BBiAjB,1,2, ,1,2,ijA Bir js123,A AA和12,
16、B B3 26 111221223132,A BA BA BA BA BA Brs12,rA AA12,sB BB,1,2, ;1,2,ijA Bir js2t t 1B2BsB1A2ArA11111211,txxx21121221,txxx11121,rrr txxx12112212,txxx22122222,txxx21222,rrr txxx12,rsrsrstxxx2 12 22,ssstxxx1 11 21,ssstxxx2,1,2, ,1,2, ,1,2,ijkijxNir js kt ijkx2,ij 2,1,2, ,1,2, ,0,1,2,ijkijijkijkijkxir j
17、sNkt各独立（6-3-5）111rsijijrs.11,1,2,siijjirs.11,1,2,rjijijsr.,1,2,iiir.,1,2,jjjs（6-3-7）10,rii10sjjiiAjjB（6-3-6）ij.,1,2, ,1,2,ijijijijir js.,1,2, ,1,2,ijijijir jsijijij（6-3-8）ijiAiAjBjB10,1,2,rijijs10,1,2,sijjir21111,1,2, ,1,2, ,0,1,2,0,0,0,0ijkijijijkijkijkrsrsijijxir jsNktijijij各独立（6-3-9）2,ijij 及（6-3-
18、11）01121112:0:,rrHH 不全为零（6-3-10）02121212:0:,ssHH 不全为零031112131112:0:,rsrsHH不全为零（6-3-12）1111rstijkijkxxrst.11,1,2, ,1,2,tijijkkxxir jst.111,1,2,stiijkjkxxirst. .111,1,2,rtjijkikxxjsrt2111rstTijkijkSxxTS 22. . .1111112222. . .1111111rstrstTijkijkijijijijijkijkrstrsrsijkijijijijijkijijSxxxxxxxxxxxxxxst
19、xxrtxxtxxxxTEABA BSSSSS（6-3-13）2.111rstEijkijijkSxx（6-3-14）2.1rAiiSstxx（6-3-15）2. .1sBjjSrtxx（6-3-16）2. .11rsA BijijijStxxxx（6-3-17）ES,ABSSA BSTSES,ABSSA BS1rst 1rs t 1r 1s11rs11rs21ESErs t（6-3-18）22111riiAstSErr（6-3-19）21211sjjBrtSEss（6-3-20）21121111rsijijA BtSErsrs（6-3-21）0112:0rH11,11AAESrFF rrs
20、tSrs t（6-3-22）11,11AAESrFFrrs tSrs t（6-3-23）11,11BBESsFFsrs tSrs t（6-3-24）01H02H1111 ,11A BA BESrsFFrsrs tSrs t（6-3-25）ASBSA BSESTS1r 1s11rs1rs t 1rst 1AASSr1BBSSs11A BA BSSrs1EESSrs tAAESFSBBESFSA BA BESFS.111rstijkijkTx.1,1,2, ,1,2,tijijkkTxir js.11,1,2,stiijkjkTxir. .11,1,2,rtjijkikTxjs22111.rstT
21、ijkijkTSxrst22.11rAiiTSTstrst22. .11sBjjTSTrtrst22.111.rsA BijABijTSTSStrstETABA BSSSSS1B2B3B1A2A3A4A010203,HHH. .,ijijT TT T.ijT1B2B3B.iT1A2A3A4A. . jT4,3,2rst22221319.858.252.641.42638.2983324TS 2222211319.8334.3296.5342.4346.6261.67500624AS 222211319.8468.4455.3396.1370.98083824BS 222211319.8110.
22、891.990.11768.69250224A BABSSS236.95000ETABA BSSSSSAB4.42AF 9.39BF 14.9A BF0.050.053,123.49,2,123.89ABFF FF0.050102,H H0.056,123.00A BFF03H0.0016,128.38F14.9A BF41AB与32AB与,ijA B1,ijijk,ijA B1B2BsB11x21x1rx1A2ArA12x22x2rx1sx2sxrsx2,1,2, ,1,2,ijijxNir js ijx2,ij 2,1,2, ,1,2, ,0,ijijijijijxir jsN各独立（6-
23、3-27）0ij1,2,ir1,2,jsijij211,1,2, ,1,2, ,0,0,0ijijijijijrsijxir jsNij各独立（6-3-28）2,ij 及01121112:0:,rrHH 不全为零（6-3-29）02121212:0:,ssHH 不全为零（6-3-30）AAESFSBBESFS1AASSr1BBSSs11EESSrsASBSESTS1s1r 11rs1rs01H02H1,11AAESFFrrsS（6-3-31）1,11BBESFFsrsS（6-3-32）2211.rsTijijTSxrs22.11rAiiTSTsrs22.11sBjjTSTrrsETABSSSS
24、.11rsijijTx.1,1,2,siijjTx ir.1,1,2,rjijiTxjsABACBC0.052211,nniiiiiQ a byabx ab和,Q a b y abx2,0,yabxN 1122,nnx yxyxy2,iiyN abx12,ny yy12,ny yy22222111111expexp2222nniiiiiiLyabxyabx21niiiyabx y abx abx yexbby1001. 00:10bHsx7500y95. 01m323. 02025115875. 391.184511117551111111221111iiiiixxyxyxb375. 4453
25、23. 091.1810 xbybxy323. 0375. 4111222111531.14645881.35711539811)(iiiiyyyyS总11111111122212212)11()()(iiiiiixxbxxbyyS回8744.1418)20251135875(323. 026565.45残总残SSS0:, 0:110bHbH0H0H)2, 1 ()2/(nFnSSF残回6 .10)9 , 1 ()2, 1 (01. 0FnF)2, 1 (6 .10697.279)2/(nFnSSF残回01. 001b87. 70755. 12523. 22498. 3)(112)2(202x
26、xSxxnnSnt残0y99. 01),(010010 xbbxbb),(00 xx2(120100nSubybx残36.31)2523. 258. 2375. 410(323. 012(120210nSubybx残43.34)2523. 258. 2375. 420(323. 01exbby100), 0(22Ne01. 00:10bH01,bb87. 0406084.3535999122911iiiiixxyxyxb51.6710 xbybxY87. 051.6791912222194.309114.90917.762189iiiiyyyyS）（总014.3073)(912iiyyS回18
27、.18回总残SSS0:10bH0H0H0H)2, 1 (2nFnSSF残回25.12)7 , 1 ()2101. 0FnF，（)2, 1 (nFF)2, 1 (25.122 .11442nFnSSF残回01. 00:10bH01b0H)2(21ntnSSbTxx残0H0H499. 3)7()2(005. 02tnt)2(2ntT4060)(912iixxxxS87. 01b18.18残S)2(499. 3398.342-21ntSSbTxx残01. 00:10bH01b复习题六复习题六一、填空题：1、一试验对9个不同的x值，测得y的9个对应值，通过对样本的分析已知：9130.3iix9191.1iiy91345.09iiix y921115.11iix921103.65iiy回归分析与方差分析回归分析方差分析一元线性回归分析二元线性回归分析单因子方差分析双因子方差分析yabx ab2,iiyN abx,1,2,10iix yi y abx,1,2,10iix yi ,1,2,10iix yi ,1,2,10iix yi , x y0)(, 0)(,210eDeEexbbYl)(mml)(kvViiiieielbbV),5 , 4 , 3 , 2 , 1(10), 0(2N2l05. 00)(, 0)(,210eDeEexbbY10,bb210,bb205. 0