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1、第二章简单线性回归模型2.1(1)首先分析人均寿命与人均GDP 的数量关系，用 Eviews分析:Dependent Var iabIe:YMethod:Least SquaresDate：12/23/15 Time:14:37Sample:1 22IncIuded observations:22Var i abIeCoefficientStd.Errort-Statistic P rob.C56.647941.96082028.889920.0000X 10.1283600.0272424.7118340.0001Mean dependentR-squared0.526082var62,50
2、000S.D.dependentAd justed R-squared0.502386var10.08889Akaike infoS.E.of regress ion7.116881cr i ter i on6.849324SchwarzSum squared resid1013.OOOcr iter ion6.948510Hannan-Q u i nnLog I ike Iihood-73.34257criter.6.872689Durbin-WatsonF-stat i st i c22.20138stat0.629074P rob(F-stat i st ic)0.000134有上可知，
3、关系式为y=56.64794+0.128360 xt关于人均寿命与成人识字率的关系，用 Eviews分析如下:Dependent Var i abIe:YMethod:Least SquaresDate:12/23/15 Time:15:01Samp Ie：1 22IncIuded observations：22CoefficienVariable t Std.Error t-Statistic P rob.C38.794243.53207910.983400.0000X 20.3319710.0466567.1153080.0000Mean dependentR-squared 0.7168
4、25var 62.50000关于人均寿命与一岁儿童疫苗接种率的关系，用 Eviews分析如下:S.D.dependentAdjusted R-squared0.702666var10.08889Aka i ke i nfoS.E.of regression5.501306cr iter ion6.334356SchwarzSum squared resid605.2873cr iter i on6.433542Hannan-Q u i nnLog Ii keIi hood-67.67792criter.6.357721Durb i n-WatsonF-stat i st i c50.62761
5、 stat1.846406P rob(F-stati stic)0.000001由上可知，关系式为y=38.79424+0.331971x2Dependent Var iabIe:YMethod：Least SquaresDate：12/23/14 Time:15:20Samp Ie:1 22IncIuded observations:22(2)关于人均寿命与人均GDP 模型，由上可知，可决系数为0.526082,说明所建模型整体上对样本数据拟合较好。Coeffi ci enVar iabIet Std.Error t-Statistic P rob.C31.79956 6.536434 4.
6、8649710.0001X 30.387276 0.080260 4.8252850.0001Mean dependentR-squared0.537929var62.50000S.D.dependentAdjusted R-squared0.514825var10.08889Aka i ke i nfoS.E.of regression7.027364cr iter ion6.824009SchwarzSum squared resid987.6770cr iter ion6.923194Hannan-Q u i nnLog Ii keIi hood-73.06409cr iter.6.84
7、7374Durb i n-WatsonF-statistic23.28338stat0.952555P rob(F-statistic)0.000103由上可知，关系式为y=31.79956+0.387276x3对于回归系数的t检验：t(13,)=4.711834to,o25(20)=2.0 8 6,对斜率系数的显著性检验表明，人 均G D P对人均寿命有显著影响。关于人均寿命与成人识字率模型，由上可知，可决系 数 为0.716825,说明所建模型整体上对样本数据拟合较好。对于回归系数的t检脸：t(B D =7.115308to,o25(20)=2.0 8 6,对斜率系数的显著性检验表明，成人
8、识字率对人均寿命有显著影响。关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为0.537929,说明所建模型整体上对样本数据拟合较好。对于回归系数的t检验：t(0 3)=4.825285to.o2S(2O)=2.0 8 6,对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。2.2(1)对于浙江省预算收入与全省生产总值的模型，用Eviews分析结果如下:Dependent Var iab Ie:YMethod:Least SquaresDate:12/23/15 Time:17:46Samp Ie(adjusted):1 33IncIuded observations:33
9、 after adjustmentsVar i abIeCoefficientStd.Error t-Statistic P rob.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004SchwarzMean dependentR-squared0.983702var902.5148S.D.dependentAd justed R-squared0.983177var1351.009Aka i ke i nfoS.E.of regress i on175.2325cr iter ion13.22880Sum squar
10、ed resid951899.7cr iter ion13.31949Hannan-Q u i nnLog Ii keI i hood-216.2751criter.13.25931Durb i n-WatsonF-stat i st i c1871.115stat0.100021P rob(F-stat i st ic)0.000000由上可知，模型的参数：斜率系数0.176124,截距为一154.3063关于浙江省财政预算收入与全省生产总值的模型，检脸模型的显著性：1)可决系数为0.983702,说明所建模型整体上对样本数据拟合较好。2)对于回归系数的t检验：t(0 2)=43.25639
11、to.o25(31)=2.0 3 9 5,对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。用规范形式写出检验结果如下：Y=0.176124X 154.3063(0.004072)(39.08196)t=(43.25639)(-3.948274)R 2=0.983702 F=1871.115 n=33经济意义是：全省生产总值每增加1亿元，财政预算总收入增加0.176124亿元。(2)当 x=32000 时,进行点预测，由上可知丫=0.176124X 154.306 3,代入可得：Y=Y=0.176124*32000 154.3063=5481.6617进行区间预测：先 由Ev
12、 iews分析:XYMean6000.441902.5148Med i an2689.280209.3900Maximum27722.314895.410Mini mum123.720025.87000Std.Dev.7608.0211351.009Skewness1.4325191.663108Kurtos i s4.0105154.590432Jarque-Bera12.6906818.69063P robab iIi ty0.0017550.000087Sum198014.529782.99Sum Sq.Dev.1.85E+0958407195Observations3333由上表可知，
13、Z x2=Z (X i X)2=5 (n 1)=7608.0212 x(33 1)=1852223.473(Xf X)2=(32000 6000.441)=675977068.2当X f=32000时，将相关数据代入计算得到：5481.6617 2.0395x175.2325x71/33+1852223.473/675977068.2 WY fW5481.6617+2.0395x175.2325x71/33+1852223.473/675977068.2即 Y f 的 置信区间为(5481.6617 64.9649,5481.6617+64.9649)(3)对于浙江省预算收入对数与全省生产总值
14、对数的模型，由Eviews分析结果如下:Dependent Variable:LNYMethod:Least SquaresDate:12/23/15 Time:18:04Samp Ie(adjusted):1 33IncIuded observations:33 after adjustmentsVar i abIeCoeffi c i entStd.Error t-Statistic P rob.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000模型方程为：I nY=0.980275 lnX-1.918289
15、Mean dependentR-squared0.963442varS.D.dependent5.573120Ad justed R-squared0.962263varAka i ke i nfo1.684189S.E.of regress i on0.327172cr iter ionSchwarz0.662028Sum squared res i d3.318281cr iter i onHannan-Q uinn0.752726Log Ii keIi hood-8.923468cr i ter.Durbin-Watson0.692545F-stat i st i c816.9699 s
16、tat0.096208P rob(F-statiStic)0.000000由上可知，模型的参数：斜率系数为0.980275,截距为-1.918289关于浙江省财政预算收入与全省生产总值的模型，检验其显著性：1)可决系数为0.963442,说明所建模型整体上对样本数据拟合较好。2)对于回归系数的t检脸：t(0 2)=28.58268to.o25(31)=2.0 3 9 5,对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。经济意义：全省生产总值每增长1%,财政预算总收入增长0.980275%2.4(1)对建筑面积与建造单位成本模型，用Eviews分析结果如下:Dependent
17、 Var iabIe:YMethod：Least SquaresDate：12/23/15 Time:20:11Samp Ie:1 12IncIuded observations:12VariableCoeff i c i entStd.Error t-Statistic P rob.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000Mean dependentR-squared0.946829var1619.333S.D.dependentAdjusted R-squared0.941512var131.2252A
18、ka i ke i nfoS.E.of regression31.73600cr iter ion9.903792SchwarzSum squared resid10071.74cr iter ion9.984610Hannan-Q u i nnLog Ii keIi hood-57.42275cr iter.9.873871Durb i n-WatsonF-statistic178.0715stat1.172407P rob(F-stat i st ic)0.000000由上可得：建筑面积与建造成本的回归方程为：Y=1845.475 64.18400X(2)经济意义：建筑面积每增加1万平方米
19、，建筑单位成本每平方米减少64.18400元。(3)首先进行点预测，由 丫 二1845.47564.18400X 得，当 x=4.5,y=1556.647再进行区间估计:用Ev i ews分析:YXMean1619.3333.523333Med i an1630.0003.715000Max imum1860.0006.230000Mini mum1419.0000.600000Std.Dev.131.22521.989419Skewness0.003403-0.060130Kurtos i s2.3465111.664917Jarque-Bera0.2135470.898454P robab
20、i Iity0.8987290.638121Sum19432.0042.28000Sum Sq.Dev.189420.743.53567Observations1212由上表可知，Z x2=Z (X X)2=S2x(n1)=1.9894192 x(121)=43.5357(XLX)2=(4.5 3.523333)2=0.95387843当X f=4.5时，将相关数据代入计算得到：1556.6472.228x31.73600 x71/12+43.5357/0.95387843F(3,27)=3.6 5,回归方程显著。3)t 检验，t 统计量分别为 4.749476,4.265020,-2.922
21、950,-4.366842,均大于t(27)=2.0518,所以这些系数都是显著的。依据：1)可决系数越大，说明拟合程度越好2)F的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。3)t的值与临界值比较，若大于临界值，则否定原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。(2)经济意义：人均G D P增 加1万元，百户拥有家用汽车增加5.996865辆，城镇人口比重 增 加1个百分点，百户拥有家用汽车减少0.524027辆，交通工具消费价格指数每上升1 ,百户拥有家用汽车减少2.265680辆。(3)用EViews分析得
22、：Dependent Var iabIe:YMethod:Least SquaresDate:12/23/15 Time:21:09Samp Ie:1 31IncIuded observations:31CoefficienVar i abIet Std.Error t-Statistic P rob.X 2 5.135670 1.010270 5.0834650.0000LNX 3-22.81005 6.771820-3.3683780.0023LNX 4-230.8481 49.46791-4.6666240.0001C 1148.758 228.2917 5.0319740.0000Me
23、an dependentR-squared 0.691952var16,77355S.D.dependentAdjusted R-squared 0.657725var8.252535Akaike infoS.E.of regress ion 4.828088cr iter ion6.106692SchwarzSum squared res id 629.3818cr iter ion6.291723Log IikeIihood-90.65373 Hannan-Q uinn6.167008cr iter.Durb i n-WatsonF-stati stic 20.21624stat 1.15
24、0090P rob(F-stat i st i c)0.000000模型方程为：Y=5.135670 X2-22.81005 LNX3-230.8481 LNX 4+1148.758此分析得出的可决系数为0.6919520.666062,拟合程度得到了提高，可这样改进。3.2(1 )对出口货物总额计量经济模型，用Eviews分析结果如下：Dependent Var iable:YMethod：Least SquaresDate:12/24/15 Time：08:23Sample:1994 2011IncIuded observat ions:18CoefficienMean dependent
25、Var i abIetStd.Error t-Statistic P rob.X 20.1354740.01279910.584540.0000X 318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838var6619.191S.D.dependentAdjusted R-squared0.983950var5767.152S.E.of regressionAka i ke i nfo730.6306cr iter ion16.17670Sum squared residSchwarz80
26、07316.cr iter ion16.32510Log Ii keIi hoodHannan-Q u i nn-142.5903cr iter.16.19717F-stat i st i cDurb i n-Watson522.0976stat1.173432P rob(F-stati stic)0.000000由上可知，模型为：Y =0.135474X 2+18.85348X 3-18231.58对模型进行检验：1)可决系数是0.985838,修正的可决系数为0.983950,说明模型对样本拟合较好2)F 检验，F=522.0976F(2,15)=4.7 7,回归方程显著3)t检验，t统计
27、量分别为X 2的系数对应t值 为10.58454,大于t(15)=2.1 3 1,系数是显著的，X 3的系数对应t值 为1.928512,小于t(15)=2.131,说明此系数是不显著的。(2)对于对数模型，用Eviews分析结果如下：Dependent Var i abIe：LNYMethod:Least SquaresDate:12/24/15 Time：08:47Sample:1994 2011IncIuded observations:18Log I i keIi hoodVar iabIeCoefficient Std.Error t-Statistic P rob.LNX 2LNX
28、 3C1.564221 0.088988 17.577890.00000.02090.00181.760695 0.682115 2.581229-20.52048 5.432487-3.777363R-squaredMean dependent0.986295var8.400112Adjusted R-squaredS.D.dependent0.984467var0.941530S.E.of regress i onAka i ke i nfo0.117343cr i ter i on-1.296424Sum squared res i dSchwarz0.206540cr iter i o
29、n-1.148029Hannan-Q u i nn14.66782cr i ter.-1.275962Durb i n-WatsonF-stat i st i cP rob(F-stat i st ic)539.7364stat0.0000000.686656由上可知，模型为：LNY=一20.52048+1.564221 LNX2+1.760695 LNX3对模型进行检脸：1)可决系数是0.986295,修正的可决系数为0.984467,说明模型对样本拟合较好。2)F 检脸，F=539.7364 F(2,15)=4.7 7,回归方程显著。3)t 检验，t 统计量分别为-3.777363,17.
30、57789,2.581229,均大于 t(15)=2.1 3 1,所以这些系数都是显著的。(3)(1)式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增 加1,出口货物总额增加18.85348亿元。(2)式中的经济意义：工业增加额每增加1%,出口货物总额增加1.564221%,人民币汇率每增加1%,出口货物总额增加1.760695%3.3(1)对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下：Dependent Var iabIe:YMethod:Least SquaresDate:12/24/15 Time：09:03Samp
31、 Ie:1 18IncIuded observations:18模型为：Y =0.086450X +52.37031T-50.01638Coeff icienVar iabIet Std.Error t-Statistic P rob.X0.086450 0.029363 2.944186 0.0101T52.37031 5.202167 10.06702 0.0000C-50.01638 49.46026-1.011244 0.3279Mean dependentR-squared0.951235var 755.1222S.D.dependentAd justed R-squared0.94
32、4732var 258.7206Aka i ke i nfoS.E.of regression60.82273cr iter ion 11.20482SchwarzSum squared resid55491.07criter ion 11.35321Hannan-Q u i nnLog I ike Iihood-97.84334criter.11.22528Durb i n-WatsonF-stati stic146.2974stat 2.605783P rob(F-stat i st i c)0.000000对模型进行检验：1)可决系数是0.951235,修正的可决系数为0.944732,
33、说明模型对样本拟合较好。2)F 检验，F=539.7364 F(2,15)=4.7 7,回归方程显著。3)t检险，t统计量分别为2.944186,10.06702,均大于t(15)=2.1 3 1,所以这些系数都是显著的。经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。(2)用 Eviews 分析：Dependent Var iable:YMethod:Least SquaresDate:12/24/15 Time:09:18Samp Ie：1 18Included observations:18Co
34、efficienVar iab Ie t Std.Error t-Statistic P rob.T 63.01676 4.548581 13.85416 0.0000C-11.58171 58.02290-0.199606 0.8443Mean dependentR-squared0.923054var755.1222S.D.dependentAd justed R-squared0.918245var258.7206Aka i ke i nfoS.E.of regression73.97565cr iter ion11.54979SchwarzSum squared resid87558.
35、36cr iter ion11.64872Hannan-Q uinnLog I i keIi hood-101.9481criter.11.56343Durbin-WatsonF-stat i st ic191.9377stat2.134043P rob(F-stat i st ic)0.000000Dependent Var iable:XMethod：Least SquaresDate：12/24/15 Time:09:34Sample:1 18IncIuded observat ions:18Var iableCoefficientStd.Error t-Statistic P rob.
36、T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899Mean dependentR-squared0.483182varS.D.dependent1942.933Adjusted R-squared0.450881varAka i ke i nfo698.8325S.E.of regression517.8529cr iter ionSchwarz15.44170Sum squared resid4290746.cr iter ionHannan-Q u i nn15.54063Log I ike Iihood-136.9
37、753cr iter.Durb i n-Watson15.45534F-stati sticP rob(F-statistic)14.95867stat0.0013641.052251以上分别是y 与 T,X与 T 的一元回归模型分别是：Y =63.01676T-11.58171X =123.1516T+444.5888(3)对残差进行模型分析，用Eviews分析结果如下:Dependent Var iabIe：E1Method：Least SquaresDate:12/24/15 Time:09:39Samp Ie:1 18IncIuded observations:18Var iableC
38、oeff i c i entStd.Error t-Statistic P rob.E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000Mean dependentR-squared0.366239var2.30E-14S.D.dependentAd justed R-squared0.326629var71.76693Aka i ke i nfoS.E.of regression58.89136cr iter ion11.09370SchwarzSum squared resid55491.07cr iter ion1
39、1.19264Hannan-Q u i nnLog Ii keIi hood-97.84334criter.11.10735Durb i n-WatsonF-statistic9.246111 stat2.605783P rob(F-stat i st ic)0.007788模型为：Ei=0.086450E2+3.96e-14参数：斜率系数a为0.086450,截距为3.96e74(3)由上可知，B 2与a 2的系数是一样的。回归系数与被解释变量的残差系数是一样的,它们的变化规律是一致的。3.6(1)预期的符号是Xi,X2,X3,X4,期的符号为正,X6的符号为负(2)根 据Eviews分析得
40、到数据如下：Dependent Var iabIe:YMethod:Least SquaresDate:12/24/15 Time:10:13Sample:1994 2011IncIuded observations:18Coeff i c i enVar i abIet Std.Error t-Statistic P rob.X 20.0013820.0011021.2543300.2336X 30.0019420.0039600.4905010.6326X 4-3.5790903.559949-1.0053770.3346X 50.0047910.0050340.9516710.3600X
41、 60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984Mean dependentR-squared0.994869varS.D.dependent12.76667Ad justed R-squared0.992731var9.746631S.E.of regress i on0.830963Aka i ke i nfo2.728738cr iter ionSchwarz与预期不相符。Sum squared res id8.285993cr i ter ion3.025529Hannan-Q u i nnLog Ii
42、keIi hood-18.55865cr iter.2.769662Durb i n-WatsonF-stati stic465.3617stat1.553294P rob(F-stati st i c)0.000000评价：1)可决系数为0.994869,数据相当大，可以认为拟合程度很好。2)F 检脸，FM65.3617F(5.12)=3,89,回归方程显著3)T 检脸，X i,X 2,X 3,X4,X s,X-系数对应的 t 值分另I为：1.254330,0.490501,-1.005377,0.951671,0.476621,均小于t(12)=2.179,所以所得系数都是不显著的。(3)
43、根 据 Eviews分析得到数据如下:Dependent Var i abIe:YMethod:Least SquaresDate:12/24/15 Time:10:20Sample:1994 2011IncIuded observations:18CoefficienVariablet Std.Error t-Statistic P rob.得到模型的方程为：X 5X 6C0.001032 2.20E-05 46.79946-0.054965 0.031184-1.7625814.205481 3.335602 1.2607860.00000.09830.2266R-squaredMean
44、dependent0.993601var12.76667Adjusted R-squaredS.D.dependent0.992748var9.746631S.E.of regress i onAka i ke i nfo0.830018cr iter ion2.616274Sum squared res i dSchwarz10.33396cr i ter i on2.764669Log I i keIi hoodHannan-Q uinn-20.54646cr iter.2.636736F-stat i st icDurbin-Watson1164.567stat1.341880P rob
45、(F-statistic)0.000000Y=0.001032 X5-0.054965 X6+4.205481评价：1)可决系数为0.993601,数据相当大，可以认为拟合程度很好。2)F 检验，F=1164.567F(5.12)=3,89,回归方程显著3)T检验，X 5系数对应的t值 为46.7 9 946,大于t(12)=2.179,所以系数是显著的，即人均G D P对年底存款余额有显著影响。X 6系数对应的t值为7.7 6 2 5 8 1,小 于t(12)=2.1 7 9,所以系数是不显著的。4.3(1)根 据Eviews分析得到数据如下:Dependent VariabIe:LNYMe
46、thod:Least SquaresDate:12/24/15 Time:10:39Sample:1985 2011IncIuded observations:27Coeffi c i enMean dependentVar i abIetStd.Error t-Statistic P rob.LNGDP1.3385330.08861015.105820.0000LNCP I-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051 var9.484710S.D.dependentAdju
47、sted R-squared0.987055varAka i ke i nfo1.425517S.E.of regression0.162189criter ionSchwarz-0.695670Sum squared resid0.631326cr iter ionHannan-Q u i nn-0.551689Log Ii keI i hood12.39155criter.Durb i n-Watson-0.652857F-stat i st i c992.2582stat0.522613P rob(F-stati stic)0.000000得到的模型方程为：LNY=1.338533 LN
48、GDP-O.421791 LNCP I-3.111486(2)该模型的可决系数为0.988051,可决系数很高，F 检验值为992.2582,明显显著。但 当 a=0.05时，t(24)=2.064,LNCP I的系数不显著，可能存在多重共线性。得到相关系数矩阵如下：LNYLNGDPLNCP ILNY1.0000000.9931890.935116LNGDP0.9931891.0000000.953740LNCP I0.9351160.9537401.000000LNGDP,LNCP I之间的相关系数很高，证实确实存在多重共线性。(3)由 Eviews 得：a)Dependent Var ia
49、bIe:LNYMethod:Least SquaresDate:12/24/15 Time:10:41Sample:1985 2011IncIuded observations:27Coeff ic i enVariable t Std.Error t-Statistic P rob.LNGDP1.185739 0.027822 42.61933 0.0000c-3.750670 0.312255-12.01156 0.0000Mean dependentR-squared0.986423var9.484710Adjusted R-squaredS.D.dependent0.985880var
50、1.425517S.E.of regressionAka i ke i nfo0.169389cr i ter ion-0.642056Sum squared residSchwarz0.717312cr ite r ion-0.546068Log Ii keIi hoodHannan-Qu i nn10.66776cr i ter.-0.613514F-stati sticDurb i n-Watson1816.407stat0.471111Prob(F-stat i st i c)0.000000b)Dependent Var iable：LNYMethod:Least SquaresDa