计量经济学（庞皓）第三版课后习题答案.pdf

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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G D P的数量关系，用Ev i e w s分析：De p e n d e n t Var i abl e:YMe t h o d:Le as t Sq u ar e sDat e:12/27/14 Ti m e:21:00Sam p l e:1 22In c l u d e d o bs e r v at i o n s:22 Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i cPr o b.C 56.64794 1.960820 28.88992 0.0000

2、XI 0.128360 0.027242 4.711834 0.0001 R-s q u ar e d 0.526082 Me and e p e n d e n t v ar 62.50000Ad j u s t e d R-s q u ar e d 0.502386S.E.o f r e g r e s s i o n 7.116881Su m s q u ar e d r e s i d 1013.000Lo g l i k e l i h o o d -73.34257S.D.d e p e n d e n t v ar 10.08889Ak ai k e i n f o c r i

3、t e r i o n 6.849324Sc h w ar z c r i t e r i o n 6.948510Han n an-Qu i n n c r i t e r.6.872689F-s t at i s t i c 22.20138 Du r bi n-Wat s o n s t at 0.629074Pr o b(F-s t at i s t i c)0.000134 有上可知，关系式为 y=56.64794+0.128360 x 1关于人均寿命与成人识字率的关系，用Ev i e w s分析如下：De p e n d e n t Var i abl e:YMe t h o d:

4、Le as t Sq u ar e sDat e:11/26/14 Ti m e:21:10iSam p l e:1 22In c l u d e d o bs e r v at i o n s:22Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.C 38.79424 3.532079 10.98340 0.0000X2 0.331971 0.046656 7.115308 0.0000R-s q u ar e d 0.716825 Me and e p e n d e n t v ar 62.50

5、000Ad j u s t e d R-s q u ar e d 0.702666S.E.o f r e g r e s s i o n 5.501306Su m s q u ar e d r e s i d 605.2873Lo g l i k e l i h o o d -67.67792S.D.d e p e n d e n t v ar 10.08889Ak ai k e i n f o c r i t e r i o n 6.334356Sc h w ar z c r i t e r i o n 6.433542Han n an-Qu i n n c r i t e r.6.3577

6、21F-s t at i s t i c 50.62761 Du r bi n-Wat s o n s t at 1.846406Pr o b(F-s t at i s t i c)0.000001 由上可知，关系式为 y=38.79424+0.331971x 2关于人均寿命与一岁儿童疫苗接种率的关系，用Ev i e w s分析如下：De p e n d e n t Var i abl e:YMe t h o d:Le as t Sq u ar e sDat e:11/26/14 Ti m e:21:14Sam p l e:1 22In c l u d e d o bs e r v at i

7、o n s:22Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.C 31.79956 6.536434 4.864971 0.0001X3 0.387276 0.080260 4.825285 0.0001R-s q u ar e d 0.537929 Me and e p e n d e n t v ar 62.50000Ad j u s t e d R-s q u ar e d 0.514825S.D.d e p e n d e n t v ar 10.08889S.E.o f r e g r

8、e s s i o n 7.027364Ak ai k e i n f o c r i t e r i o n 6.8240092Sum squared resid 987.6770 Schwarz criterion 6.923194Log likelihood-73.06409 Hannan-Quinn criter.6.847374F-statistic 23.28338 D urbin-Watson stat 0.952555Prob(F-statistic)0.000103 由上可知，关系式为 y=31.79956+0.387276x3(2)关于人均寿命与人均GD P模型，由上可知，

9、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。对于回归系数的t 检验：t(8 1)=4.711834t0.025(20)=2.086,对斜率系数的显着性检验表明，人均GD P对人均寿命有显着影响。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 检验：t(B2)=7.115308t0.025(20)=2.086,对斜率系数的显着性检验表明，成人识字率对人均寿命有显着影响。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

10、：t(8 3)=4.825285t0.025(20)=2.086,对斜率系数的显着性检验表明，一岁儿童疫苗接种率对人均寿命有显着影响。2.2(1)对于浙江省预算收入与全省生产总值的模型，用 E views分析结果如下：D ependent Variable:YMethod:Least SquaresD ate:12/03/14 Time:17:003Sam p l e (ad j u s t e d):1 33In c l u d e d o bs e r v at i o n s:33 af t e r ad j u s t m e n t sVar i abl e Co e f f i c

11、 i e n t St d.Er r o r t-St at i s t i cX 0.176124 0.004072 43.25639C-154.3063 39.08196-3.948274R-s q u ar e d 0.983702 Me anAd j u s t e d R-s q u ar e d 0.983177S.E.o f r e g r e s s i o n 175.2325Su m s q u ar e d r e s i d 951899.7Lo g l i k e l i h o o d -216.2751d e p e n d e n t v arS.D.d e p

12、 e n d e n t v arAk ai k e i n f o c r i t e r i o nSc h w ar z c r i t e r i o nHan n an-Qu i n n c r i t e r.F-s t at i s t i c 1871.115Du r bi n-Wat s o n s t atPr o b(F-s t at i s t i c)0.000000Pr o b.0.0000 0.0004 902.5148 1351.009 13.22880 13.31949 13.259310.1 0 0 0 2 1由上可知，模型的参数：斜率系数0.176124,

13、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，检验模型的显着性：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 (8 2)=43.25639M0.025(31)=2.0395,对斜率系数的显着性检验表明，全省生产总值对财政预算总收入有显着影响。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)4R2=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

14、亿元。(2)当 x=32000 时,进行点预测，由上可知Y=0.176124X154.3063,代入可得：Y=Y=0.176124*32000154.3063=5481.6617进行区间预测：x 2=(X i X)2=8 2X(n l)=7608.0212 x (331)=1852223.473(Xf X)2=(32000 6000.441)2=675977068.2当Xf=32000时，将相关数据代入计算得到：68.2W即 Y f 的置信区间为(5481.661764.9649,5481.6617+64.9649)(3)对于浙江省预算收入对数与全省生产总值对数的模型，由 Ev i e w s

15、 分析结果如下：De p e n d e n t Var i abl e:LNYMe t h o d:Le as t Sq u ar e sDat e:12/03/14 Ti m e:18:00Sam p l e (ad j u s t e d):1 33In c l u d e d o bs e r v at i o n s:33 af t e r ad j u s t m e n t sVar i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.LNX 0.980275 0.034296 28.58268

16、0.0000C-1.918289 0.268213-7.152121 0.0000R-s q u ar e d 0.963442 Me an d e p e n d e n t v ar 5.573120Ad j u s t e d R-s q u ar e d 0.962263 S.D.d e p e n d e n t v ar 1.6841895S.E.of regression 0.327172 Akaike info criterion 0.662028Sum squared resid 3.318281 Schwarz criterion 0.752726Log likelihoo

17、d-8.923468 Hannan-Quinn criter.0.692545F-statistic 816.9699 D urbin-Watson stat 0.096208Prob(F-statistic)0.000000模型方程为：lnY=0.9802751nX-l.918289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，检验其显着性：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 检验：t(6 2)=28.58268X0.025(31)=2.0395,对斜率系数的显着性

18、检验表明，全省生产总值对财政预算总收入有显着影响。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 E views分析结果如下：D ependent Variable:YMethod:Least SquaresD ate:12/01/14 Time:12:40Sample:1 12Included observations:12 Variable Coefficient Std.E rror t-Statistic Prob,X-64.18400 4.809828-13.34434 0.0000C 1845.475 19.264

19、46 95.79688 0.0000 R-squared 0.946829 Meandependent var 1619.3336Ad j u s t e d R-s q u ar e d 0.941512S.D.d e p e n d e n t v ar 131.2252S.E.o f r e g r e s s i o n 31.73600 Ak ai k e i n f o c r i t e r i o n 9.903792Su m s q u ar e d r e s i d 10071.74 Sc h w ar z c r i t e r i o n 9.984610Lo g l

20、 i k e l i h o o d -57.42275 Han n an-Qu i n n c r i t e r.9.873871F-s t at i s t i c 178.0715 Du r bi n-Wat s o n s t at 1.172407Pr o b(F-s t at i s t i c)0.000000 由上可得：建筑面积与建造成本的回归方程为：Y=1845.47564.18400X(2)经济意义：建筑面积每增加1万平方米，建筑单位成本每平方米减少64.18400O(3)首先进行点预测，由 Y=1845.47564.18400X 得，当 x=4.5,y=1556.647

21、再进行区间估计：由上表可知，Ex 2=(X i X)2=S2x (n l)=1.9894192 x (121)=43.5357(Xf X)2=(4.5 3.523333)2=0.95387843当乂=4.5时-，将相关数据代入计算得到：1556.6472.228x 31.73600 x J 1/12+43.5357/0.95387843W即 Y f 的置信区间为(1556.647478.1231,1556.647+478.1231)3.1(1)对百户拥有家用汽车量计量经济模型，用Ev i e w s分析结果如下：De p e n d e n t Var i abl e:Y7Me t h o d

22、:Le as t Sq u ar e sDat e:11/25/14 Ti m e:12:38Sam p l e:1 31In c l u d e d o bs e r v at i o n s:31Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.X2 5.996865 1.406058 4.265020 0.0002X3-0.524027 0.179280-2.922950 0.0069X4-2.265680 0.518837-4.366842 0.0002C 246.8540 51.97500

23、4.749476 0.0001R-s q u ar e d 0.666062Me an d e p e n d e n t v ar 16.77355Ad j u s t e d R-s q u ar e d 0.628957S.E.o f r e g r e s s i o n 5.026889Su m s q u ar e d r e s i d 682.2795Lo g l i k e l i h o o d -91.90460S.D.d e p e n d e n t v ar 8.252535Ak ai k e i n f o c r i t e r i o n 6.187394Sc

24、 h w ar z c r i t e r i o n 6.372424Han n an-Qu i n n c r i t e r.6.247709F-s t at i s t i c 17.95108 Du r bi n-Wat s o n s t at 1.147253Pr o b(F-s t at i s t i c)0.000001得到模型得：Y=246.8540+5.996865X2-0.524027 X3-2.265680 X4对模型进行检验：1)可决系数是0.666062,修正的可决系数为0.628957,说明模型对样本拟合较好2)F 检验，F=17.95108F(3,27)=3

25、.6 5,回归方程显着。3)t 检验，t 统计量分别为 4.749476,4.265020,-2.922950,-4.366842,均大于8t (27)=2.0518,所以这些系数都是显着的。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，回归方程是显着的；若小于临界值，则接受原假设，回归方程不显着。3)t的值与临界值比较，若大于临界值，则否定原假设，系数都是显着的；若小于临界值，则接受原假设，系数不显着。(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0.52

26、 40 2 7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2.2 65680 辆。(3)用 EVi e w s 分析得：De p e n d e n t Var i abl e:YMe t h o d:Le as t Sq u ar e sDat e:1 2/0 8/1 4 Ti m e:1 7:2 8Sam p l e:1 31In c l u d e d o bs e r v at i o n s:31 Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.X2 5.1 35670 1.0

27、 1 0 2 70 5.0 83465 0.0 0 0 0LNX3-2 2.81 0 0 5 6.771 82 0 -3.368378 0.0 0 2 3LNX4-2 30.8481 49.46791 -4.66662 4 0.0 0 0 1C 1 1 48.758 2 2 8.2 91 7 5.0 31 974 0.0 0 0 0 R-s q u ar e d 0.691 952 Me an9d e p e n d e n t v ar 1 6.77355Ad j u s t e d R-s q u ar e d 0.65772 5S.D.d e p e n d e n t v ar 8.2

28、 52 535S.E.o f r e g r e s s i o n 4.82 80 88Ak ai k e i n f o c r i t e r i o n 6.1 0 6692Su m s q u ar e d r e s i d 62 9.381 8Sc h w ar z c r i t e r i o n 6.2 91 72 3Lo g l i k e l i h o o d -90.65373Han n an-Qu i n n c r i t e r.6.1 670 0 8F-s t at i s t i c 2 0.2 1 62 4Du r bi n-Wat s o n s t

29、at 1.1 50 0 90Pr o b(F-s t at i s t i c)0.0 0 0 0 0 0 模型方程为:Y=5.1 35670 X2-2 2.81 0 0 5 LNX3-2 30.8481 LNX4+1 1 48.758此分析得出的可决系数为0.691 9520.6660 62,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Ev i e w s分析结果如下：:De p e n d e n t Var i abl e:YMe t h o d:Le as t Sq u ar e sDat e:1 2/0 1/1 4 Ti m e:2 0:2 5Sam

30、p l e:1 994 2 0 1 1In c l u d e d o bs e r v at i o n s:1 8Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.X2 0.1 35474 0.0 1 2 799 1 0.58454 0.0 0 0 0X3 1 8.85348 9.7761 81 1.92 851 2 0.0 72 9C-1 82 31.58 8638.2 1 6-2.1 1 0 5730.0 52 0R-s q u ar e d 0.985838Me and e p e n d

31、e n t v ar 661 9.1 91Ad j u s t e d R-s q u ar e d 0.983950S.D.d e p e n d e n t v ar 5767.1 52S.E.o f r e g r e s s i o n 730.630 6Ak ai k e i n f o c r i t e r i o n 1 6.1 7670ioSu m s q u ar e d r e s i d 80 0 731 6.Sc h w ar z c r i t e r i o n 1 6.32 51 0Lo g l i k e l i h o o d -1 42.590 3 Han

32、 n an-Qu i n n c r i t e r.1 6.1 971 7F-s t at i s t i c 52 2.0 976 Du r bi n-Wat s o n s t at 1.1 73432Pr o b(F-s t at i s t i c)0.0 0 0 0 0 0由上可知，模型为:Y=0.1 35474X2 +1 8.85348X3-1 82 31.58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=52 2.0 976F(2,1 5)=4.7 7,回归方程显着3)t检 验，t统 计 量 分 别 为

33、X 2的 系 数 对 应t值 为1 0.58454,大 于t (1 5)=2.1 3 1,系数是显着的，X 3的系数对应t值 为1.92 851 2,小 于t (1 5)=2.1 3 1,说明此系数是不显着的。(2)对于对数模型，用Ev i e w s分析结果如下：De p e n d e n t Var i abl e:LNYMe t h o d:Le as t Sq u ar e sDat e:1 2/0 1/1 4 Ti m e:2 0:2 5Sam p l e:1 994 2 0 1 1In c l u d e d o bs e r v at i o n s:1 8Var i abl

34、e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.LNX2 1.5642 2 1 0.0 88988 1 7.57789 0.0 0 0 0LNX3 1.760 695 0.682 1 1 5 2.581 2 2 9 0.0 2 0 9C-2 0.52 0 48 5.432 487-3.777363 0.0 0 1 8R-s q u ar e d 0.9862 95Me and e p e n d e n t v ar 8.40 0 1 1 2Ad j u s t e d R-s q u ar e d 0.984467S

35、.D.d e p e n d e n t v ar 0.941 530liS.E.of regression 0.117343 Akaike info criterion-1.296424Sum squared resid 0.206540 Schwarz criterion-1.148029Log likelihood 14.66782 Hannan-Quinn criter.-1.275962F-statistic 539.7364 D urbin-Watson stat 0.686656Prob(F-statistic)0.000000 由上可知，模型为：LNY=-20.52048+1.

36、564221 LNX2+1.760695 LNX3对模型进行检验：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 验,F=539.7364 F(2,15)=4.77,回归方程显着。3)t 检验，t 统计量分别为-3.777363,17.57789,2.581229,均大于 t(15)=2.131,所以这些系数都是显着的。(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

37、币汇率每增加现,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 E views分析结果如下：D ependent Variable:YMethod:Least SquaresD ate:12/01/14 Time:20:3012Sample:1 18Included observations:18 Variable Coefficient Std.E rror t-Statistic Prob.X 0.086450 0.029363 2.944186 0.0101T 52.37031 5.202167 10.06702 0.0000C-

38、50.01638 49.46026-1.011244 0.3279 R-squared 0.951235 Meandependent var 755.1222Adjusted R-squared 0.944732 S.D.dependent var 258.7206S.E.of regression 60.82273 Akaike info criterion 11.20482Sum squared resid 55491.07 Schwarz criterionLog likelihood-97.84334 Hannan-Quinn criter.F-statistic 146.2974 D

39、 urbin-Watson statProb(F-statistic)0.000000模型为：Y=0.086450X+52.37031T-50.0163811.35321 11.22528 2.605783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,说明模型对样本拟合较好。2)F 检 验,F=539.7364 F(2,15)=4.77,回归方程显着。3)t 检验，t 统计量分别为2.944186,10.06702,均大于t(15)=2.131,所以这些系数都是显着的。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

40、数增加1 年，家庭书刊年消费支出增加52.37031元。(2)用 E views 分析:13De p e n d e n t Var i abl e:YMe t h o d:Le as t Sq u ar e sDat e:1 2/0 1/1 4 Ti m e:2 2:30Sam p l e:1 1 8In c l u d e d o bs e r v at i o n s:1 8Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.T 63.0 1 676 4.548581 1 3.8541 6 0.0

41、 0 0 0C-1 1.581 71 58.0 2 2 90 -0.1 9960 6 0.8443 R-s q u ar e d 0.92 30 54 Me and e p e n d e n t v ar 755.1 2 2 2Ad j u s t e d R-s q u ar e d 0.91 82 45S.E.o f r e g r e s s i o n 73.97565Su m s q u ar e d r e s i d 87558.36Lo g l i k e l i h o o d -1 0 1.9481S.D.d e p e n d e n t v ar 2 58.72 0

42、6Ak ai k e i n f o c r i t e r i o n 1 1.54979Sc h w ar z c r i t e r i o n 1 1.64872Han n an-Qu i n n c r i t e r.1 1.56343F-s t at i s t i c 1 91.9377 Du r bi n-Wat s o n s t at 2.1 340 43Pr o b(F-s t at i s t i c)0.0 0 0 0 0 0De p e n d e n t Var i abl e:XMe t h o d:Le as t Sq u ar e sDat e:1 2/0

43、 1/1 4 Ti m e:2 2:34Sam p l e:1 1 8In c l u d e d o bs e r v at i o n s:1 8Var i abl e Co e f f i c i e n t St d.Er r o r t-St at i s t i c Pr o b.T 1 2 3.1 51 6 31.841 50 3.867644 0.0 0 1 414C 444.5888 406.1786 1.094565 0.2899R-squared 0.483182Meandependent var 1942.933Adjusted R-squared 0.450881 S

44、.D.dependent var 698.8325S.E.of regression 517.8529 Akaike info criterion 15.44170Sum squared resid 4290746.Schwarz criterion 15.54063Log likelihood-136.9753 Hannan-Quinn criter.15.45534F-statistic 14.95867 D urbin-Watson stat 1.052251Prob(F-statistic)0.001364 以上分别是y与T,X与T的一元回归模型分别是：Y=63.01676T-11.5

45、8171X=123.1516T+444.5888(3)对残差进行模型分析，用E views分析结果如下：D ependent Variable:E lMethod:Least SquaresD ate:12/03/14 Time:20:39Sample:1 18Included observations:18 Variable Coefficient Std.E rror t-Statistic Prob.E 2 0.086450 0.028431 3.040742 0.0078C 3.96E-14 13.88083 2.85E-15dependent var 2.30E-14Adjusted

46、 R-squared 0.326629S.E.of regression 58.891361.0000 R-squared 0.366239 MeanS.D.dependent var 71.76693Akaike info criterion 11.0937015Sum squared resid 55491.07 Schwarz criterion 11.19264Log likelihood-97.84334 Hannan-Quinn criter.11.10735F-statistic 9.246111 D urbin-Watson stat 2.605783Prob(F-statis

47、tic)0.007788 模型为：E 1=0.086450E 2+3.96e-14参数：斜率系数a 为 0.086450,截距为3.96e-14(3)由上可知，8 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X 1,X 2,X 3.X 4.X 5 的符号为正，X 6 的符号为负(2)根据E views分析得到数据如下：D ependent Variable:YMethod:Least SquaresD ate:12/04/14 Time:13:24Sample:1994 2011Included observation

48、s:18 Variable Coefficient Std.E rror t-StatisticProb.X2 0.001382 0.001102 1.254330 0.2336X3 0.001942 0.003960 0.490501 0.6326X4-3.579090 3.559949-1.005377 0.3346X5 0.004791 0.005034 0.951671 0.3600X6 0.045542 0.095552 0.476621 0.6422C-13.77732 15.73366-0.875659 0.3984 R-squared 0.994869 Mean16depend

49、ent var 12.76667Adjusted R-squared 0.992731 S.D.dependent var 9.746631S.E.of regression 0.830963 Akaike info criterion 2.728738Sum squared resid 8.285993 Schwarz criterion 3.025529Log likelihood-18.55865 Hannan-Quinn criter.2.769662F-statistic 465.3617 D urbin-Watson stat 1.553294Prob(F-statistic)0.

50、000000 与预期不相符。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 检验，F=465.3617 F(5.12)=3,8 9,回归方程显着3)T 检验，X 1,X 2,X 3.X 4.X 5,X 6 系数对应的t 值分别为：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着的。(3)根据E views分析得到数据如下：D ependent Variable:YMethod:Least SquaresD ate:12/03/14 Time:11:12Sample:1