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1、精選優(yōu)質(zhì)文檔-傾情為你奉上 第二章 簡(jiǎn)單線(xiàn)性回歸模型2.1(1) 首先分析人均壽命與人均GDP的數(shù)量關(guān)系,用Eviews分析:Dependent Variable: YMethod: Least SquaresDate: 12/27/14 Time: 21:00Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C56.647941.28.889920.0000X.0001R-squared0. M
2、ean dependent var62.50000Adjusted R-squared0. S.D. dependent var10.08889S.E. of regression7. Akaike info criterion6.Sum squared resid1013.000 Schwarz criterion6.Log likelihood-73.34257 Hannan-Quinn criter.6.F
3、-statistic22.20138 Durbin-Watson stat0.Prob(F-statistic)0.有上可知,關(guān)系式為y=56.64794+0.x1關(guān)于人均壽命與成人識(shí)字率的關(guān)系,用Eviews分析如下:Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C38.7
4、94243.10.983400.0000X.0000R-squared0. Mean dependent var62.50000Adjusted R-squared0. S.D. dependent var10.08889S.E. of regression5. Akaike info criterion6.Sum squared resid605.2873 Schwarz criterion6.
5、Log likelihood-67.67792 Hannan-Quinn criter.6.F-statistic50.62761 Durbin-Watson stat1.Prob(F-statistic)0.由上可知,關(guān)系式為y=38.79424+0.x2關(guān)于人均壽命與一歲兒童疫苗接種率的關(guān)系,用Eviews分析如下:Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:14Sample: 1 22Included obse
6、rvations: 22VariableCoefficientStd. Errort-StatisticProb. C31.7995001X.0001R-squared0. Mean dependent var62.50000Adjusted R-squared0. S.D. dependent var10.08889S.E. of regression7. Akaike info criterion6.
7、Sum squared resid987.6770 Schwarz criterion6.Log likelihood-73.06409 Hannan-Quinn criter.6.F-statistic23.28338 Durbin-Watson stat0.Prob(F-statistic)0.由上可知,關(guān)系式為y=31.79956+0.x3(2)關(guān)于人均壽命與人均GDP模型,由上可知,可決系數(shù)為0.,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。 對(duì)于回歸系數(shù)
8、的t檢驗(yàn):t(1)=4.>t0.025(20)=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,人均GDP對(duì)人均壽命有顯著影響。關(guān)于人均壽命與成人識(shí)字率模型,由上可知,可決系數(shù)為0.,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。對(duì)于回歸系數(shù)的t檢驗(yàn):t(2)=7.>t0.025(20)=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,成人識(shí)字率對(duì)人均壽命有顯著影響。關(guān)于人均壽命與一歲兒童疫苗的模型,由上可知,可決系數(shù)為0.,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。 對(duì)于回歸系數(shù)的t檢驗(yàn):t(3)=4.>t0.025(20)=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,一歲兒童疫苗接種率對(duì)人均壽命有顯著影
9、響。2.2(1)對(duì)于浙江省預(yù)算收入與全省生產(chǎn)總值的模型,用Eviews分析結(jié)果如下:Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb. X56390.0000C-154.306339.08196-3.0.0004R-squared0.
10、0; Mean dependent var902.5148Adjusted R-squared0. S.D. dependent var1351.009S.E. of regression175.2325 Akaike info criterion13.22880Sum squared resid.7 Schwarz criterion13.31949Log likelihood-216.2751
11、160;Hannan-Quinn criter.13.25931F-statistic1871.115 Durbin-Watson stat0.Prob(F-statistic)0.由上可知,模型的參數(shù):斜率系數(shù)0.,截距為154.3063關(guān)于浙江省財(cái)政預(yù)算收入與全省生產(chǎn)總值的模型,檢驗(yàn)?zāi)P偷娘@著性:1)可決系數(shù)為0.,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。2)對(duì)于回歸系數(shù)的t檢驗(yàn):t(2)=43.25639>t0.025(31)=2.0395,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,全省生產(chǎn)總值對(duì)財(cái)政預(yù)算總收入有顯著影響。用規(guī)范形式寫(xiě)出檢驗(yàn)結(jié)果如下:Y
12、=0.X154.3063 (0.) (39.08196)t= (43.25639) (-3.)R2=0. F=1871.115 n=33經(jīng)濟(jì)意義是:全省生產(chǎn)總值每增加1億元,財(cái)政預(yù)算總收入增加0.億元。(2)當(dāng)x=32000時(shí),進(jìn)行點(diǎn)預(yù)測(cè),由上可知Y=0.X154.3063,代入可得:Y= Y=0.*32000154.3063=5481.6617進(jìn)行區(qū)間預(yù)測(cè):先由Eviews分析:XY Mean 6000.441 902.5148 Median 2689.280 209.3900 Maximum 27722.31&
13、#160;4895.410 Minimum 123.7200 25.87000 Std. Dev. 7608.021 1351.009 Skewness 1. 1. Kurtosis 4. 4. Jarque-Bera 12.69068 18.69063 Probability 0. 0. Sum .5 29782.99 Sum Sq. Dev. 1.85E+09
14、160; Observations 33 33由上表可知,x2=(XiX)2=2x(n1)= 7608.0212 x (331)=.473(XfX)2=(32000 6000.441)2=.2當(dāng)Xf=32000時(shí),將相關(guān)數(shù)據(jù)代入計(jì)算得到:5481.66172.0395x175.2325x1/33+.473/.2Yf5481.6617+2.0395x175.2325x1/33+.473/.2即Yf的置信區(qū)間為(5481.661764.9649, 5481.6617+64.9649)(3) 對(duì)于浙江省預(yù)算收入對(duì)數(shù)與全省生產(chǎn)總值對(duì)數(shù)的模型,由Evi
15、ews分析結(jié)果如下:Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 18:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb. LNX82680.0000C-1.0.-7.0.0000R-squared0. Mean dependent var5.Adjust
16、ed R-squared0. S.D. dependent var1.S.E. of regression0. Akaike info criterion0.Sum squared resid3. Schwarz criterion0.Log likelihood-8. Hannan-Quinn criter.0.F-statistic816.9699 Durbin-
17、Watson stat0.Prob(F-statistic)0.模型方程為:lnY=0.lnX-1.由上可知,模型的參數(shù):斜率系數(shù)為0.,截距為-1.關(guān)于浙江省財(cái)政預(yù)算收入與全省生產(chǎn)總值的模型,檢驗(yàn)其顯著性:1)可決系數(shù)為0.,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。2)對(duì)于回歸系數(shù)的t檢驗(yàn):t(2)=28.58268>t0.025(31)=2.0395,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,全省生產(chǎn)總值對(duì)財(cái)政預(yù)算總收入有顯著影響。經(jīng)濟(jì)意義:全省生產(chǎn)總值每增長(zhǎng)1%,財(cái)政預(yù)算總收入增長(zhǎng)0.%2.4(1)對(duì)建筑面積與建造單位成本模型,用Eviews分析結(jié)果如下:Dependent Variable: Y
18、Method: Least SquaresDate: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticProb. X-64.184004.-13.344340.0000C1845.47519.2644695.796880.0000R-squared0. Mean dependent var1619.333Adjusted R-squared0.
19、160;S.D. dependent var131.2252S.E. of regression31.73600 Akaike info criterion9.Sum squared resid10071.74 Schwarz criterion9.Log likelihood-57.42275 Hannan-Quinn criter.9.F-statistic178.0715 Durbin-Watson sta
20、t1.Prob(F-statistic)0.由上可得:建筑面積與建造成本的回歸方程為:Y=1845.475-64.18400X(2)經(jīng)濟(jì)意義:建筑面積每增加1萬(wàn)平方米,建筑單位成本每平方米減少64.18400元。(3)首先進(jìn)行點(diǎn)預(yù)測(cè),由Y=1845.475-64.18400X得,當(dāng)x=4.5,y=1556.647再進(jìn)行區(qū)間估計(jì):用Eviews分析:YX Mean 1619.333 3. Median 1630.000 3. Maximum 1860.000 6. Minimum 141
21、9.000 0. Std. Dev. 131.2252 1. Skewness 0.-0. Kurtosis 2. 1. Jarque-Bera 0. 0. Probability 0. 0. Sum 19432.00 42.28000 Sum Sq. Dev. .7 43.53567 Observations 12 12由上表可知,x2=(XiX)2=2x
22、(n1)= 1. x (121)=43.5357(XfX)2=(4.5 3.)2=0.當(dāng)Xf=4.5時(shí),將相關(guān)數(shù)據(jù)代入計(jì)算得到:1556.6472.228x31.73600x1/12+43.5357/0.Yf1556.647+2.228x31.73600x1/12+43.5357/0.即Yf的置信區(qū)間為(1556.647478.1231, 1556.647+478.1231)3.1(1)對(duì)百戶(hù)擁有家用汽車(chē)量計(jì)量經(jīng)濟(jì)模型,用Eviews分析結(jié)果如下:Dependent Variable: YMethod: Least SquaresDate: 11/25/14 Time:
23、12:38Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X.0002X3-0.0.-2.0.0069X4-2.0.-4.0.0002C246.854051.975004.0.0001R-squared0. Mean dependent var16.77355Adjusted R-squared0. S.D. dependent var8.S.E.
24、of regression5. Akaike info criterion6.Sum squared resid682.2795 Schwarz criterion6.Log likelihood-91.90460 Hannan-Quinn criter.6.F-statistic17.95108 Durbin-Watson stat1.Prob(F-statistic)0.得到模型得:Y=246.8540+5.
25、X2-0. X3-2. X4對(duì)模型進(jìn)行檢驗(yàn):1) 可決系數(shù)是0.,修正的可決系數(shù)為0.,說(shuō)明模型對(duì)樣本擬合較好2) F檢驗(yàn),F(xiàn)=17.95108>F(3,27)=3.65,回歸方程顯著。3)t檢驗(yàn),t統(tǒng)計(jì)量分別為4.,4.,-2.,-4.,均大于t(27)=2.0518,所以這些系數(shù)都是顯著的。依據(jù):1) 可決系數(shù)越大,說(shuō)明擬合程度越好2) F的值與臨界值比較,若大于臨界值,則否定原假設(shè),回歸方程是顯著的;若小于臨界值,則接受原假設(shè),回歸方程不顯著。3) t的值與臨界值比較,若大于臨界值,則否定原假設(shè),系數(shù)都是顯著的;若小于臨界值,則接受原假設(shè),系數(shù)不顯著。(2)經(jīng)濟(jì)意義:人均增加萬(wàn)元,
26、百戶(hù)擁有家用汽車(chē)增加5.輛,城鎮(zhèn)人口比重增加個(gè)百分點(diǎn),百戶(hù)擁有家用汽車(chē)減少0.輛,交通工具消費(fèi)價(jià)格指數(shù)每上升,百戶(hù)擁有家用汽車(chē)減少2.輛。(3)用EViews分析得:Dependent Variable: YMethod: Least SquaresDate: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. X.0000LNX3-22.810056.-3.0.0023LNX4-230.848149.4
27、6791-4.0.0001C1148.758228.29175.0.0000R-squared0. Mean dependent var16.77355Adjusted R-squared0. S.D. dependent var8.S.E. of regression4. Akaike info criterion6.Sum squared resid629.3818 Schwarz criterion6.Lo
28、g likelihood-90.65373 Hannan-Quinn criter.6.F-statistic20.21624 Durbin-Watson stat1.Prob(F-statistic)0.模型方程為:Y=5. X2-22.81005 LNX3-230.8481 LNX4+1148.758此分析得出的可決系數(shù)為0.>0.,擬合程度得到了提高,可這樣改進(jìn)。3.2()對(duì)出口貨物總額計(jì)量經(jīng)濟(jì)模型,用Eviews分析結(jié)果如下:Dependent Variable: YMethod: Lea
29、st SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb. X84540.0000X318.8534729C-18231.588638.216-2.0.0520R-squared0. Mean dependent var6619.191Adjusted R-squared0.
30、; S.D. dependent var5767.152S.E. of regression730.6306 Akaike info criterion16.17670Sum squared resid. Schwarz criterion16.32510Log likelihood-142.5903 Hannan-Quinn criter.16.19717F-statistic522.0976 Dur
31、bin-Watson stat1.Prob(F-statistic)0.由上可知,模型為:Y = 0.X2 + 18.85348X3 - 18231.58對(duì)模型進(jìn)行檢驗(yàn):1)可決系數(shù)是0.,修正的可決系數(shù)為0.,說(shuō)明模型對(duì)樣本擬合較好2)F檢驗(yàn),F(xiàn)=522.0976>F(2,15)=4.77,回歸方程顯著3)t檢驗(yàn),t統(tǒng)計(jì)量分別為X2的系數(shù)對(duì)應(yīng)t值為10.58454,大于t(15)=2.131,系數(shù)是顯著的,X3的系數(shù)對(duì)應(yīng)t值為1.,小于t(15)=2.131,說(shuō)明此系數(shù)是不顯著的。 (2)對(duì)于對(duì)數(shù)模型,用Eviews分析結(jié)果如下:Dependent Variable: LNYMetho
32、d: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb. LNX77890.0000LNX.0209C-20.520485.-3.0.0018R-squared0. Mean dependent var8.Adjusted R-squared0. S
33、.D. dependent var0.S.E. of regression0. Akaike info criterion-1.Sum squared resid0. Schwarz criterion-1.Log likelihood14.66782 Hannan-Quinn criter.-1.F-statistic539.7364 Durbin-Watson stat0.Prob(F-statistic)0
34、.由上可知,模型為:LNY=-20.52048+1. LNX2+1. LNX3對(duì)模型進(jìn)行檢驗(yàn):1)可決系數(shù)是0.,修正的可決系數(shù)為0.,說(shuō)明模型對(duì)樣本擬合較好。2)F檢驗(yàn),F(xiàn)=539.7364> F(2,15)=4.77,回歸方程顯著。3)t檢驗(yàn),t統(tǒng)計(jì)量分別為-3.,17.57789,2.,均大于t(15)=2.131,所以這些系數(shù)都是顯著的。(3)(1)式中的經(jīng)濟(jì)意義:工業(yè)增加1億元,出口貨物總額增加0.億元,人民幣匯率增加1,出口貨物總額增加18.85348億元。(2)式中的經(jīng)濟(jì)意義:工業(yè)增加額每增加1%,出口貨物總額增加1.%,人民幣匯率每增加1%,出口貨物總額增加1.%3.3(
35、1)對(duì)家庭書(shū)刊消費(fèi)對(duì)家庭月平均收入和戶(hù)主受教育年數(shù)計(jì)量模型,由Eviews分析結(jié)果如下:Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. X.0101T52.370315.10.067020.0000C-50.0163849.46026-1.0.3279R-squared0.
36、 Mean dependent var755.1222Adjusted R-squared0. S.D. dependent var258.7206S.E. of regression60.82273 Akaike info criterion11.20482Sum squared resid55491.07 Schwarz criterion11.35321Log likelihood-97.84334
37、0;Hannan-Quinn criter.11.22528F-statistic146.2974 Durbin-Watson stat2.Prob(F-statistic)0.模型為:Y = 0.X + 52.37031T-50.01638對(duì)模型進(jìn)行檢驗(yàn):1)可決系數(shù)是0.,修正的可決系數(shù)為0.,說(shuō)明模型對(duì)樣本擬合較好。2)F檢驗(yàn),F(xiàn)=539.7364> F(2,15)=4.77,回歸方程顯著。3)t檢驗(yàn),t統(tǒng)計(jì)量分別為2.,10.06702,均大于t(15)=2.131,所以這些系數(shù)都是顯著的。經(jīng)濟(jì)意義:家庭月平均收入增加1元,家庭書(shū)刊年
38、消費(fèi)支出增加0.元,戶(hù)主受教育年數(shù)增加1年,家庭書(shū)刊年消費(fèi)支出增加52.37031元。(2)用Eviews分析:Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 22:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. T63.016764.13.854160.0000C-11.5817158.02290-0.0.8443R-squared0. &
39、#160;Mean dependent var755.1222Adjusted R-squared0. S.D. dependent var258.7206S.E. of regression73.97565 Akaike info criterion11.54979Sum squared resid87558.36 Schwarz criterion11.64872Log likelihood-101.9481
40、;Hannan-Quinn criter.11.56343F-statistic191.9377 Durbin-Watson stat2.Prob(F-statistic)0.Dependent Variable: XMethod: Least SquaresDate: 12/01/14 Time: 22:34Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. T123.151631.841503.0.0014C4
41、44.5888406.17861.0.2899R-squared0. Mean dependent var1942.933Adjusted R-squared0. S.D. dependent var698.8325S.E. of regression517.8529 Akaike info criterion15.44170Sum squared resid. Schwarz criterion15.54063
42、Log likelihood-136.9753 Hannan-Quinn criter.15.45534F-statistic14.95867 Durbin-Watson stat1.Prob(F-statistic)0.以上分別是y與T,X與T的一元回歸模型分別是:Y = 63.01676T - 11.58171X = 123.1516T + 444.5888(3)對(duì)殘差進(jìn)行模型分析,用Eviews分析結(jié)果如下:Dependent Variable: E1Method: Least SquaresDa
43、te: 12/03/14 Time: 20:39Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. E.0078C3.96E-1413.880832.85E-151.0000R-squared0. Mean dependent var2.30E-14Adjusted R-squared0. S.D. dependent var71.76693S.E. o
44、f regression58.89136 Akaike info criterion11.09370Sum squared resid55491.07 Schwarz criterion11.19264Log likelihood-97.84334 Hannan-Quinn criter.11.10735F-statistic9. Durbin-Watson stat2.Prob(F-statistic)0.模型
45、為:E1 = 0.E2 + 3.96e-14參數(shù):斜率系數(shù)為0.,截距為3.96e-14(3)由上可知,2與2的系數(shù)是一樣的?;貧w系數(shù)與被解釋變量的殘差系數(shù)是一樣的,它們的變化規(guī)律是一致的。3.6(1)預(yù)期的符號(hào)是X1,X2,X3,X4,X5的符號(hào)為正,X6的符號(hào)為負(fù)(2)根據(jù)Eviews分析得到數(shù)據(jù)如下:Dependent Variable: YMethod: Least SquaresDate: 12/04/14 Time: 13:24Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-Stati
46、sticProb. X.2336X.6326X4-3.3.-1.0.3346X.3600X.6422C-13.7773215.73366-0.0.3984R-squared0. Mean dependent var12.76667Adjusted R-squared0. S.D. dependent var9.S.E. of regression0. Akaike info
47、 criterion2.Sum squared resid8. Schwarz criterion3.Log likelihood-18.55865 Hannan-Quinn criter.2.F-statistic465.3617 Durbin-Watson stat1.Prob(F-statistic)0.與預(yù)期不相符。評(píng)價(jià):1) 可決系數(shù)為0.,數(shù)據(jù)相當(dāng)大,可以認(rèn)為擬合程度很好。2) F檢驗(yàn),F(xiàn)=465.3617>F(5.12)=3,89,回歸方
48、程顯著3) T檢驗(yàn),X1,X2,X3,X4,X5,X6 系數(shù)對(duì)應(yīng)的t值分別為:1.,0.,-1.,0.,0.,均小于t(12)=2.179,所以所得系數(shù)都是不顯著的。(3)根據(jù)Eviews分析得到數(shù)據(jù)如下:Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 11:12Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb. X50.2.20E-0546.799460.0000X6-0
49、.0.-1.0.0983C.2266R-squared0. Mean dependent var12.76667Adjusted R-squared0. S.D. dependent var9.S.E. of regression0. Akaike info criterion2.Sum squared resid10.33396 Schwarz criterion2.Log likelihood-
50、20.54646 Hannan-Quinn criter.2.F-statistic1164.567 Durbin-Watson stat1.Prob(F-statistic)0.得到模型的方程為:Y=0. X5-0. X6+4.評(píng)價(jià):1) 可決系數(shù)為0.,數(shù)據(jù)相當(dāng)大,可以認(rèn)為擬合程度很好。2) F檢驗(yàn),F(xiàn)=1164.567>F(5.12)=3,89,回歸方程顯著3) T檢驗(yàn),X5 系數(shù)對(duì)應(yīng)的t值為46.79946,大于t(12)=2.179,所以系數(shù)是顯著的,即人均GDP對(duì)年底存款余額有顯著影響
51、。 X6 系數(shù)對(duì)應(yīng)的t值為-1.,小于t(12)=2.179,所以系數(shù)是不顯著的。4.3(1)根據(jù)Eviews分析得到數(shù)據(jù)如下:Dependent Variable: LNYMethod: Least SquaresDate: 12/05/14 Time: 11:39Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb. LNGDP05820.0000LNCPI-0.0.-1.0.0832C-3.0.-6.0.0000R-squared0
52、. Mean dependent var9.Adjusted R-squared0. S.D. dependent var1.S.E. of regression0. Akaike info criterion-0.Sum squared resid0. Schwarz criterion-0.Log likelihood12.39155 Hannan-Quinn c
53、riter.-0.F-statistic992.2582 Durbin-Watson stat0.Prob(F-statistic)0.得到的模型方程為:LNY=1. LNGDPt-0. LNCPIt-3.(2) 該模型的可決系數(shù)為0.,可決系數(shù)很高,F(xiàn)檢驗(yàn)值為992.2582,明顯顯著。但當(dāng)=0.05時(shí),t(24)=2.064,LNCPI的系數(shù)不顯著,可能存在多重共線(xiàn)性。得到相關(guān)系數(shù)矩陣如下:LNYLNGDPLNCPILNY 1. 0. 0.LNGDP 0. 1. 0.LNCPI 0. 0. 1.LNGDP, LNCPI之間的相關(guān)系數(shù)很高,證實(shí)確實(shí)存在多重共線(xiàn)性。(3)由Eviews得:a)Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14
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