預(yù)測(cè)學(xué)課后作業(yè)答案

1、12/12作業(yè)：P706已知某百貨企業(yè)三個(gè)躺售人員對(duì)明年銷售的展望建議與主觀概率以下表，又知計(jì)劃人員展望銷售的希望值為1000萬(wàn)元，統(tǒng)計(jì)人員的展望銷售的希望值為900萬(wàn)元，計(jì)劃、統(tǒng)計(jì)人員的展望能力分別是銷售人員的1.2倍和1.4倍。試用主觀概率加權(quán)均勻法求：(1)每位銷售人員的展望銷售希望值。(2)三位銷售人員的均勻展望希望值。(3)該企業(yè)明年的展望銷售額。解：（1）甲：銷售希望值=銷售額主觀概率=1120*0.25+965*0.5+640*0.25=922.5（萬(wàn)元）同理，可求得乙和丙的銷售希望值為900萬(wàn)元和978萬(wàn)元（2）922.5*0.3+900*0.35+978*0.35=934.0

2、5（萬(wàn)元）（3）（934.05+1000*1.2+900*1.4）/（1+1.2+1.4）=942.79（萬(wàn)元）7已知某工業(yè)企業(yè)選定10位專家用德爾菲法進(jìn)行展望，最后一輪征詢建議，對(duì)明年收益率的預(yù)計(jì)的累計(jì)概率分布以下表：試用累計(jì)概率中位數(shù)法：(1)計(jì)算每種概率的不一樣建議的均勻數(shù)，用累計(jì)概率確立中位效，作為點(diǎn)預(yù)計(jì)值。(2)當(dāng)要求展望偏差不超出1時(shí)的區(qū)間預(yù)計(jì)值，及其區(qū)間概率。1%12.50%25%37.50%50%62.50%75%87.50%99%188.18.28.38.48.58.68.78.827.888.28.48.68.88.999.1366.26.56.777.27.57.7846

3、6.577.588.58.68.79555.566.577.588.58.9688.28.38.48.58.68.899.276.56.777.788.28.48.68.887.27.688.28.48.68.899.3999.29.39.49.59.69.79.810107.588.28.48.68.899.19.5均勻數(shù)7.17.47.677.958.28.438.638.819.06解：（1）中位數(shù)為8.2，明年收益率的預(yù)計(jì)值為8.2%（2）展望偏差為1%，則展望區(qū)間為8.2%1%，為7.2%，9.2%，區(qū)間概率為1-1%=99%作業(yè)（P116）1江蘇省2004年111月社會(huì)花費(fèi)品零售總

4、數(shù)以下表所示，試分別以3個(gè)月和5個(gè)月挪動(dòng)均勻法，展望12月份的銷售額，并比較它們的好壞。月份銷售額3個(gè)月均勻值5個(gè)月均勻值3個(gè)月均勻展望值5個(gè)月均勻展望值3個(gè)月均勻預(yù)5個(gè)月均勻預(yù)測(cè)值測(cè)值1380.042729.15720.663333331052.8720.66333331049.351043.67841366.11049.35720.66333331369.7333331369.96851690.31369.7333331043.6781049.351689.2966671691.01862011.491689.2966671369.9681369.7333331043.6782012.06

5、33332011.07672334.42012.0633331691.0181689.2966671369.9682332.9933332339.01282653.092332.9933332011.0762012.0633331691.0182664.4233332676.91293005.782664.4233332339.0122332.9933332011.0763012.893025.794103379.83012.892676.9122664.4233332339.0123380.493333113755.93380.4933333025.7943012.892676.912338

6、0.4933333025.794219952002年全國(guó)財(cái)政收入以下表所示，試用加權(quán)挪動(dòng)均勻法展望2003年財(cái)政收入(三年加權(quán)系數(shù)為0.5、1、1.5)。年份財(cái)政收入3年加權(quán)均勻3年加權(quán)均勻3年加權(quán)均勻19956242.2199674087835.2519978651.17835.259056.366667199898769056.3666677835.2510455.9199911444.110455.99056.36666712158.3200013395.212158.310455.914565.4166720011638614565.4166712158.317146.33333200

7、218903.617146.3333314565.4166717146.333333、我國(guó)19952002年全社會(huì)固定財(cái)富投資額以下表所示，試用一次指數(shù)光滑法展望2003年全社會(huì)固定財(cái)富投資額(取=0.3，初始值為21466.4)。年份固定財(cái)富投資一次指數(shù)光滑值199520019.321466.4199622913.521032.27199724941.121596.639199828406.222599.977199929854.724341.844200032917.725995.701200137213.528072.301200243499.930814.6634620.2324我國(guó)1

8、9952002年全國(guó)城鄉(xiāng)居民年關(guān)按期存款余額以下表所示：(1)試用趨向挪動(dòng)均勻法(取N=3)成立全國(guó)城鄉(xiāng)居民年關(guān)按期存款余額展望模型。(2)分別取=0.3，=0.6，以及S0(1)S0(2)(Y1Y2Y3)328292.8成立全國(guó)城鄉(xiāng)居民年關(guān)按期存款余額的直線指數(shù)光滑展望模型。(3)計(jì)算模型擬合偏差。(4)比較3個(gè)模型的好壞。(5)用最優(yōu)的模型展望2003年全國(guó)城鄉(xiāng)居民年關(guān)按期存款余額。解：一次挪動(dòng)均勻二次挪動(dòng)平一次指數(shù)平二次指數(shù)光滑一次指數(shù)光滑二次指數(shù)光滑年份定額存款（N=3）均（N=3）滑（=0.3）（=0.3）（=0.6）（=0.6）199523778.228292.828292.828

9、292.828292.8199630873.426938.4228292.825584.0428292.8199736226.730292.7666728118.91427886.48628757.65626667.544199841791.636297.2333330551.249827956.214433239.082427921.6112199944955.140991.1333335860.3777833923.3548628734.7250238370.5929631112.09392200046141.744296.1333340528.1666737232.878430291.3

10、139742321.2971835467.19334200151434.947510.5666744265.9444439905.5248832373.783344613.5388739579.65565200258788.952121.8333347976.1777843364.3374234633.3057848706.3555542599.9855870000600005000040000系列130000200001000001994199519961997199819992000200120022003（1）a20022M2002(1)M2002(2)2*52121.8347976.1

11、8=56267.48b20022(M2002(1)M2002(2)52121.8347976.18=4145.6531?a2002b2002T56267.48+4145.65*T所以：y2002T（2）指數(shù)光滑展望=0.3時(shí)，a20022S2002(1)S2002(2)2*43364.34-34633.31=52095.37b20021(S2002(1)S2002(2)3741.87所以，?Ta2002b2002T52095.37+3741.87*Ty2002=0.6時(shí)，a20022S2002(1)S2002(2)2*48706.36-42599.99=54812.73b2002(S2002(

12、1)S2002(2)9159.561所以，?Ta2002b2002T54812.73+9159.56*Ty2002（3）用1995-2000年的數(shù)據(jù)成立模型，求得2001和2002年的展望值與實(shí)質(zhì)值進(jìn)行比較，計(jì)算模型擬合偏差。趨向挪動(dòng)均勻法：a20002M2000(1)M2000(2)2*44296.1340528.17=48064.09b20002(M2000(1)M2000(2)44296.1340528.17=3767.9631所以：?Ta2000b2000T48064.09+3767.96*Ty2000指數(shù)光滑展望=0.3時(shí)，a20002S2000(1)S2000(2)2*37232.

13、88-30291.31=44174.45b20001(S2000(1)S2000(2)2974.96所以，?Ta2000b2000T44174.45+2974.96*Ty2000指數(shù)光滑展望=0.6時(shí)，a20002S2000(1)S2000(2)2*42321.3-35467.19=49175.41b20001(S2000(1)S2000(2)10281.165所以，?Ta2000b2000T49175.41+10281.165*Ty2000年份定額存款定額存款（趨定額存款（定額存款（相對(duì)偏差%勢(shì)外推）相對(duì)偏差%=0.3）相對(duì)偏差%=0.6）199523778.223778.223778.22

14、3778.2199630873.430873.430873.430873.4199736226.736226.736226.736226.7199841791.641791.641791.641791.6199944955.144955.144955.144955.1200046141.746141.746141.746141.7200151434.951832.1-0.007747149.410.08331959456.58-0.15596200258788.9556000.0542450124.37074-0.1862480000700006000050000系列

15、140000系列2系列330000系列4200001000001994199519961997199819992000200120022003（4）從上表和上圖可見，三種模型中趨向外推法的近期偏差最小，但跟著時(shí)間越遠(yuǎn)，偏差逐漸增大，如上圖序列2。指數(shù)光滑法偏差較大，且跟著權(quán)數(shù)的增大，在下一期展望數(shù)據(jù)中上期原始數(shù)據(jù)所占比重越大，修正幅度越大，遠(yuǎn)期精度越高，如上圖序列3（=0.3）和序列4（=0.6）。年份定額存款（趨向外推）定額存款（=0.3）定額存款（=0.6）199523778.223778.223778.2199630873.430873.430873.4199736226.736226.

16、736226.7199841791.641791.641791.6199944955.144955.144955.1200046141.746141.746141.7200151434.951434.951434.9200258788.958788.958788.9200360413.1355837.2463972.29200464558.7859579.1173131.85200568704.4363320.9882291.41200672850.0867062.8591450.97200776995.7370804.72100610.5312000010000080000系列160000系

17、列240000系列320000019941996199820002002200420062008（5）展望2003年的全國(guó)城鄉(xiāng)居民年關(guān)按期存款余額可用趨向外推法，如（4）中表可知，為60413.13億元。6我國(guó)1995-2002年全社會(huì)固定財(cái)富投資額以下表所示，試用差分指數(shù)光滑法展望2003年全社會(huì)固定財(cái)富投資額(=0.3)。年份固定財(cái)富投資差分差分指數(shù)光滑值展望值199520019.3199622913.52894.22894.2199724941.12027.62894.225807.7199828406.23465.12634.2227575.32199929854.71448.5288

18、3.48431289.684200032917.730632452.988832307.689200137213.54295.82635.9921635553.692200243499.96286.43133.93451240347.4354079.67415847579.574作業(yè)：P1455已知以下數(shù)據(jù)組：(1)成立一元線性回歸模型。(2)計(jì)算有關(guān)系數(shù)R。取明顯性水平=0.05，對(duì)回歸模型進(jìn)行明顯性檢驗(yàn)。(3)計(jì)算預(yù)計(jì)標(biāo)準(zhǔn)偏差Sy。解：（1）先繪制散點(diǎn)圖30252015系列1105002468101214參數(shù)預(yù)計(jì)：序號(hào)XYXYX2Y21261243623824964351155251214

19、614843619657161124925669191718136171022220100484812253001446255412197844821431n1n12154?yibxi1.93112.0901ani8ni118nnn?nxiyixiyi8*97854*121i1i1i11.9311bnnx2(nx)28*448542i1ii1i所以，一元線性回歸模型為：?2.09011.9311xy（2）Rnxiyixiyi8*97854*1210.9976xi2xi)2yi)2542n(nyi2(8*4488*21431212查表得R0.05(82)=0.7067，可見RR0.05(6)，表

20、示變量之間的線性關(guān)系明顯，檢驗(yàn)經(jīng)過(guò)。2?yiyibxiyi21432.0901*1211.9311*978（3）標(biāo)準(zhǔn)偏差Syan2820.49706某省19781986年居民花費(fèi)品購(gòu)置力和居民錢幣收入統(tǒng)計(jì)數(shù)據(jù)以下：依據(jù)上述統(tǒng)計(jì)數(shù)據(jù)：(1)成立一元線性回歸模型。(2)對(duì)回歸模型進(jìn)行明顯性檢驗(yàn)(取=0.05)。(3)若居民錢幣收入每年均勻增加19，試展望該省1987年居民花費(fèi)品購(gòu)置力。(4)對(duì)1987年居民花費(fèi)品購(gòu)置力做區(qū)間展望(取=0.05)。解：（1）序號(hào)年份居民花費(fèi)購(gòu)置力Y居民錢幣收入XXYX2Y2119788.511.698.6134.5672.252197911.114.1156.511

21、98.81123.213198013.617.1232.56292.41184.964198115.819.6309.68384.16249.645198217.622.1388.96488.41309.766198320.525.6524.8655.36420.257198427.833.6934.081128.96772.848198533.540.51356.751640.251122.259198639.247.81873.762284.841536.64187.62325875.77207.764791.8?1nyi?1n187.60.8472232abxi90.9945ni1ni1

22、9nnn?nxiyixiyi9*5875.7232*187.6i1ni1i10.8472bn9*7207.762322nxi2(xi)2i1i1所以，一元線性回歸模型為：?0.99450.8472xy（2）Rnxiyixiyi9*5875.7232*187.6x2(x)2ny2(y)29*7207.7623220.9997n9*4791.8187.62iiii查表得R0.05(92)0.6664，可見RR0.05(7)，表示變量之間的線性關(guān)系明顯，檢驗(yàn)經(jīng)過(guò)。（3）1987年居民錢幣收入為：47.8*（1+19%）=56.882所以1987年居民花費(fèi)品購(gòu)置力為：?0.99450.8472*56.

23、88247.1959?y19872?yiyibxiyi4791.80.9945*187.60.8472*5875.7（4）標(biāo)準(zhǔn)偏差Syan2920.2605查表得t2(92)t2(7)=2.3646展望區(qū)間為：?m2(7)Sy11(x1987x)2y1987tn(xix)20.260511(56.88225.7778)247.1959m0.687097274.2094所以，1987年居民花費(fèi)品購(gòu)置力區(qū)間為46.5089，47.8829作業(yè)：P174運(yùn)用多元線性回歸展望技術(shù)，對(duì)有關(guān)數(shù)據(jù)進(jìn)行計(jì)算，結(jié)果以下：y653.9641.309x20.728x383.026x4(2.17)(5.76)(2.2

24、7)(1.984)R20.97849R20.97418n19F227.398S22.445DW1.0429(1)取明顯性水平=0.05，對(duì)回歸模型進(jìn)行R檢驗(yàn)、F檢驗(yàn)、t檢驗(yàn)和DW檢驗(yàn)。(2)對(duì)檢驗(yàn)結(jié)果加以分析。解：R檢驗(yàn)：復(fù)有關(guān)系數(shù)2=0.4821，可RR0.978490.9892，查表得R(nk1)0.050.05(15)R(1931)R見RR0.05(15)，表示樣本回歸方程與樣本觀察值的擬合程度很好，有關(guān)關(guān)系明顯。檢驗(yàn)：查表得F(k,nk1)F0.05(3,15)=3.29，可見F277.398F0.05(3,15)3.29，表示這3個(gè)自變量與Y之間的線性關(guān)系明顯，回歸成效好。檢驗(yàn)：查表

25、得t2(nk1)t0.025(15)2.131，可見t12.17t0.025(15)2.131，t25.76t0.025(15)2.131，t32.27t0.025(15)2.131，t41.984t0.025(15)2.131，表示應(yīng)當(dāng)剔除x4，x4與y有關(guān)關(guān)系不明顯。DW檢驗(yàn)：查DW檢驗(yàn)表得，dL0.59,dU1.46，有dLDWdU，所以DW檢驗(yàn)無(wú)結(jié)論，應(yīng)采納其余方法進(jìn)行自有關(guān)檢驗(yàn)。6某市19771988年主要百貨商鋪營(yíng)業(yè)額、在業(yè)人員總收入、當(dāng)年完工住所面積的統(tǒng)計(jì)數(shù)據(jù)以下：依據(jù)統(tǒng)計(jì)數(shù)據(jù)，試：(1)成立多元線性回歸模型。(2)對(duì)回歸模型進(jìn)行R檢驗(yàn)、F檢驗(yàn)、t檢驗(yàn)和DW檢驗(yàn)(取=0.05)。

26、(3)假設(shè)該市在業(yè)人員總收入、當(dāng)年完工住所面積在1988年的基礎(chǔ)上分別增加15、17，請(qǐng)對(duì)該市1989年主要百貨商鋪營(yíng)業(yè)額作區(qū)間預(yù)計(jì)(取=0.05)。解：（1）序號(hào)年份營(yíng)業(yè)額y在業(yè)人員當(dāng)年完工住22x2x3X2yX3y23y2總收入x2宅面積x3Xx119778.276.495836.9681626.4873.8687.667.24219788.377.97.86068.4160.84646.5764.74607.6268.89319798.680.25.56432.0430.25689.7247.3441.173.964198098557225257654542581519819.485.2

27、10.87259.04116.64800.88101.52920.1688.36619829.488.25.57779.2430.25829.0851.7485.188.367198312.2116.26.213502.4438.441417.6475.64720.44148.848198415.712910.816641116.642025.3169.561393.2246.499198515.5147.518.421756.25338.562286.25285.22714240.2510198618.3185.215.734299.04246.493389.16287.312907.643

28、34.8911198725.3210.332.544226.091056.255320.59822.256834.75640.0912198827.3248.545.561752.252070.256784.051242.1511306.75745.29乞降167.21529.6172.7232777.764210.6125580.723266.1729443.362823.66成立二元線性回歸方程：y?01x22x3計(jì)算回歸系數(shù)：?1XYB(XX)176.419177.97.8180.25.5185511111111111185.210.8188.25.576.477.980.28585.2

29、88.2116.2129147.5185.2210.31248.5116.26.297.85.5510.85.56.210.818.415.732.5145.512910.811147.518.41185.215.71210.332.51248.545.58.28.38.69111111111119.4176.477.980.28585.288.2116.2129147.5185.2210.39.4248.597.85.5510.85.56.210.818.415.732.512.245.515.715.518.325.327.3121529.6172.71167.21529.6232777.

30、7629443.3625580.72172.729443.364210.613266.170.941970.011280.04023167.20.011280.000170.0007425580.720.040230.000740.003773266.170.3877290.0973090.07935所以，二元回歸模型為：y?0.3877290.097309x20.07935x3（2）R檢驗(yàn)、F檢驗(yàn)、t檢驗(yàn)和DW檢驗(yàn)(取=0.05)作業(yè)：P2052某地域某作物產(chǎn)量(億千克)，從19892003年按序?yàn)椋?.78，4.19，4.83，7.46，6.7l，7.99，8.60，9.24，9.67，9

31、.87，10.49，10.92，10.93，12.39，12.59。試作圖判斷樣本數(shù)據(jù)的散點(diǎn)分布，采納23種合適的曲線展望模型，展望2005年和2010年的作物產(chǎn)量。解：1、第一，繪制散點(diǎn)圖1412108系列16420198819901992199419961998200020022004從圖中可見，可采納直線模型、指數(shù)曲線模型、生長(zhǎng)曲線模型等。2、計(jì)算樣本序列的增加特色yt1yt1計(jì)算均勻增加，以下：以三年滑動(dòng)均勻值作yt，ut2序號(hào)t某作物產(chǎn)量yytutut/ytlgututlgutlg2ytyt13.7824.194.26666734.835.4933331.0333330.188107

32、0.01424-0.7256-1.4654347.466.3333330.9466670.149474-0.0238-0.82544-1.6270756.717.3866670.7166670.097022-0.14468-1.01313-1.8815867.997.7666670.6116670.078755-0.21349-1.10372-1.9939578.68.610.7016670.081494-0.15387-1.08887-2.0238889.249.170.4916670.053617-0.30833-1.2707-2.2330799.679.5933330.420.04378

33、-0.37675-1.35872-2.34069109.8710.010.4166670.041625-0.38021-1.38065-2.381081110.4910.426670.3850.036925-0.41454-1.43268-2.450831210.9210.780.4933330.045764-0.30686-1.33948-2.37211310.9311.413330.5950.052132-0.22548-1.2829-2.340311412.3911.971512.59從上表可見可見，可采納直線模型、龔珀茲曲線、皮爾曲線等。3、差分法tyt一階差分一階差的一對(duì)數(shù)一階差yt

34、-yt-1二階差分三階差分一階差比率比率階比率13.7824.190.411.10846634.830.640.231.1527450.6406250.72444547.462.631.991.761.5445130.2433460.32699156.71-0.75-3.38-5.370.899464-3.50667-4.1027167.991.282.035.411.19076-0.58594-0.6068878.60.61-0.67-2.71.0763452.0983612.37309289.240.640.030.71.0744190.9531251.02496299.670.43-0.

35、21-0.241.0465371.4883721.578046109.870.2-0.23-0.021.0206832.152.2219341110.490.620.420.651.0628170.3225810.3360261210.920.43-0.19-0.611.0409911.441861.5164851310.930.01-0.42-0.231.0009164343.88961412.391.461.451.871.1335770.0068490.0073011512.590.2-1.26-2.711.0161427.37.829713從上表可見，應(yīng)采納指數(shù)曲線模型。所以，依據(jù)題意，可采納直線模型、指數(shù)曲線模型和龔珀茲曲線模型進(jìn)行展望。直線模型：可用趨向挪動(dòng)均勻法進(jìn)行展望，可選N=3序號(hào)年份某作物產(chǎn)量一次挪動(dòng)均