線性與對(duì)數(shù)模型比較分析

實(shí)驗(yàn)報(bào)告線性模型與對(duì)數(shù)模型舉例分析、實(shí)驗(yàn)?zāi)康谋緦?shí)驗(yàn)的目的在于研究GNP與貨幣是否有關(guān)系，若有關(guān)系有怎樣的數(shù)量關(guān)系，用哪種模型來(lái)描述二者之間關(guān)系較為合適。下面根據(jù)GNP/貨幣供給數(shù)據(jù)，得到的回歸結(jié)果(Y=GNP，X=貨幣供給）：年GNP（10億美元）M2年GNP（10億美元）M219731359.3861.019813052.61795.519741472.8908.519823166.01954.019751598.41023.219833405.72185.219761782.81163.719843772.22363.619771990.51286.719854014.92562.619782249.71389.019864240.32807.719792508.21500.219874526.72901.019802732.01633.1平均值2791.471755.70模型截距斜率2雙對(duì)數(shù)0.55310.9882r0.9926t=(3.1652)41.889對(duì)數(shù)-線性6.86160.000570.9493增長(zhǎng)模型）t=(100.05)15.597線性-對(duì)數(shù)-16329.02584.80.9832t=(-23.494)27.549線性101.201.53230.9915LIV模型）t=(1.369)38.867a.解釋每個(gè)模型斜率的意義。1.雙對(duì)數(shù)模型中斜率0.9882表示，貨幣供給每提高1個(gè)百分點(diǎn)，，GNP平均增加約0.98個(gè)百分點(diǎn)2.對(duì)數(shù)―線性模型中的斜率0.00057表示，貨幣供給每增加1（10億）美元，GNP將以0.057%的速度增長(zhǎng)。3.線性―對(duì)數(shù)模型中的斜率2584.8表示，貨幣供給每提高1個(gè)百分點(diǎn)，GNP將增加25.848（10億）美元。4?線性模型中的斜率1.5323表示，貨幣供給每增加1（10億）美元，GNP將增加1.53（10億）美元。b.估計(jì)每個(gè)模型GNP對(duì)貨幣供給的彈性，并解釋。分別用E1，E2，E3，E4表示四個(gè)模型中GNP對(duì)貨幣供給的彈性。Y/Y100X/X1001?對(duì)于雙對(duì)數(shù)模型，lnY=a+3lnXY/Y100X/X100所以Ej=0.98822?對(duì)于對(duì)數(shù)一線性模型lnY=a+3XY/Y100△Y/YE==X=3XX/X100△X由此可知：對(duì)于對(duì)數(shù)一線性模型中GNP對(duì)貨幣供給的彈性是隨著X(貨幣供給)的變化而變化的，為此可以通過(guò)X的樣本均值來(lái)計(jì)算平均彈性。所以E=3X=0.00057X1755.70=1.0023?對(duì)于線性一對(duì)數(shù)模型Y=a+3lnXY/Y100△Y11E===3X/X100△X/XYY由此可知：對(duì)于線性一對(duì)數(shù)模型中GNP對(duì)貨幣供給的彈性是隨著Y(GNP)的變化而變化的，為此可以通過(guò)Y的樣本均值來(lái)計(jì)算平均彈性。1所以E3=3一=2584.8/2791.47=0.926Y4.對(duì)于線性模型Y=a+3XY/Y100△YXXE=-=3X/X100△XYY由此可知：對(duì)于線性模型中GNP對(duì)貨幣供給的彈性是隨著X(貨幣供給)，丫(GNP)的共同變化而變化的，為此可以通過(guò)X與Y的樣本均值來(lái)計(jì)算平均彈性.X所以E=3—=1.5323X1755.66刀2791.47=0.9644YC?所有2的r值可直接比較嗎？如果不能，哪些可以直接進(jìn)行比較答:所有的r2值不能直接進(jìn)行比較，因?yàn)樗膫€(gè)模型的被解釋變量并不相同?雙對(duì)數(shù)模型與對(duì)數(shù)一線性模型可以進(jìn)行比較。線性一對(duì)數(shù)模型與線性模型進(jìn)行比較。d?你選擇哪個(gè)模型？在選擇模型時(shí)，考慮了哪些指標(biāo)？lnY對(duì)lnX的回歸

LnY=0.5531+0.9882InXDependentVariable:LOG(GNP)Method:LeastSquaresDate:05/26/10Time:20:35Sample:19731987Includedobservations:15VariableCoefficientStd.Errort-StatisticProb.C0.5531180.1747523.1651560.0075LOG(M2)0.9882240.02359241.888690.0000R-squared0.992646Meandependentvar7.863176AdjustedR-squared0.992080S.D.dependentvar0.399117S.E.ofregression0.035519Akaikeinfocriterion-3.713914Sumsquaredresid0.016401Schwarzcriterion-3.619508Loglikelihood29.85436Hannan-Quinncriter.-3.714920F-statistic1754.662Durbin-Watsonstat0.787478Prob(F-statistic)0.000000在顯著性水平a=0.05,查表得自由度n=n-2=13的臨界值t.(13)=2.160,t(3)=41.889>t.00250025(13)=2.160,說(shuō)明在95%的置信水平下’解釋變量InX通過(guò)了顯著性檢驗(yàn)，即InX對(duì)InY有顯著影響。lnY對(duì)X的回歸lnY=6.8616+0.00057XDependentVariable:LOG(GNP)Method:LeastSquaresDate:05/26/10Time:20:39Sample:19731987Includedobservations:15VariableCoefficientStd.Errort-StatisticProb.C6.8615680.068584100.04570.0000M20.0005713.66E-0515.597490.0000R-squared0.949275Meandependentvar7.863176AdjustedR-squared0.945373S.D.dependentvar0.399117S.E.ofregression0.093284Akaikeinfocriterion-1.782779Sumsquaredresid0.113124Schwarzcriterion-1.688372

LoglikelihoodF-statistic15.37084Hannan-Quinncriter.-1.783784243.2817Durbin-Watsonstat0.252175Prob(F-statistic)0.000000在顯著性水平a=0.05,t(3)=15.597>t.25(13)=2.160,說(shuō)明在95%的置信水平下，解釋變量X通過(guò)了顯著性檢驗(yàn)，即X對(duì)lnY有顯著影響Y對(duì)InX的回歸Y=-16329.0+2584.8lnXDependentVariable:GNPMethod:LeastSquaresDate:05/26/10Time:20:43Sample:19731987Includedobservations:15VariableCoefficientStd.Errort-StatisticProb.C-16328.64694.9991-23.494480.0000LOG(M2)2584.78993.8253127.548960.0000R-squared0.983159Meandependentvar2791.473AdjustedR-squared0.981864S.D.dependentvar1048.951S.E.ofregression141.2622Akaikeinfocriterion12.86268Sumsquaredresid259415.0Schwarzcriterion12.95708Loglikelihood-94.47008Hannan-Quinncriter.12.86167F-statistic758.9450Durbin-Watsonstat0.592403Prob(F-statistic)0.000000在顯著性水平a=0.05,t(3)=27.549>^^25(13)=2.160,說(shuō)明在95%的置信水平下，解釋變量X通過(guò)了顯著性檢驗(yàn)，即InX對(duì)Y有顯著影響Y對(duì)X的回歸Y=101.20+1.5323XDependentVariabIe:GNPMethod:LeastSquaresDate:05/24/10Time:23:32SampIe:19731987Ineludedobservations:15VariableCoefficientStd.Errort-StatisticProb.Variable101.201973.926471.3689530.1942

101.201973.926471.3689530.1942M21.5323360.03942538.866740.0000R-squared0.991468Meandependentvar2791.473AdjustedR-squared0.990811S.D.dependentvar1048.951S.E.ofregression100.5496Akaikeinfocriterion12.18274Sumsquaredresid131432.8Schwarzcriterion12.27715Loglikelihood-89.37059Hannan-Quinncriter.12.18174F-statistic1510.623Durbin-Watsonstat0.873998Prob(F-statistic)0.000000在顯著性水平a=0.05,t(3)=38.867>\。25(13)=2.160,說(shuō)明在95%的置信水平下，解釋變量X通過(guò)了顯著性檢驗(yàn)，即X對(duì)Y有顯著影響.上述4個(gè)模型均通過(guò)了統(tǒng)計(jì)檢驗(yàn)，且F值均較大，r2也都較大，回歸模型對(duì)各自因變量變異的解釋程度較高。所以，4個(gè)模型都可以。e.貨幣學(xué)家為，貨幣供給的變化率與GNP之間存在一一對(duì)應(yīng)關(guān)系上述結(jié)果證實(shí)了這個(gè)觀點(diǎn)嗎?如何驗(yàn)證？上述結(jié)果證實(shí)了這個(gè)