第二章简单线性回归模型.docx

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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 Variable: YMethod: Least SquaresDate: 12/27/14 Time: 21:00Sample: 1 22Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C 56.647941.960820 28.88992 0.0000XI 0.128360 0.027242 4.711834 0.0001 R-squared 0.526082 Mean de

2、pendent var62,50000Adjusted R-squared 0.502386 S.D. dependent var 10.08889S.E. of regression 7.116881 Akaike info criterion 6.849324Sum squared resid 1013.000 Schwarz criterion 6.948510Log likelihood -73.34257 Hannan-Quinn criter. 6.872689F-statistic 22.20138 Durbin-Watson stat 0.629074Prob(F-statis

3、tic) 0.000134有上可知，关系式为 y=56.64794+0.128360x1关于人均寿命与成人识字率的关系，用Eviews分析如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C38,79424 3.532079 10.98340 0.0000X2 0.331971 0.046656 7.115308 0.0000 R

4、-squared 0.716825 Mean dependent var62,50000Adjusted R-squared 0.702666 S.D. dependent var 10.08889S.E. of regression 5.501306 Akaike info criterion 6.334356Sum squared resid 605.2873 Schwarz criterion 6.433542Log likelihood -67.67792 Hannan-Quinn criter. 6.357721F-statistic 50.62761 Durbin-Watson s

5、tat 1.846406Prob(F-statistic) 0.000001 由上可知，关系式为 y=38.79424+0.331971x2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：Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:14Sample: 1 22Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C31.79956 6.536434 4.864971 0.0001X3 0.387

6、276 0.080260 4.825285 0.0001 R-squared 0.537929 Mean dependent var62,50000Adjusted R-squared 0.514825 S.D. dependent var 10.08889S.E. of regression 7.027364 Akaike info criterion 6.824009Sum squared resid 987,6770 Schwarz criterion 6.923194Log likelihood -73.06409 Hannan-Quinn criter. 6.847374F-stat

7、istic 23.28338 Durbin-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。对于回归系数的t检验：t (pl)=4.711834X0.025(20)=2.086,对斜率系数的显著性检验表明，人均GDP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检验：t (02)=

8、7.115308X0.025(20)=2.086,对斜率系数的显著性检验表明，成人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0537929,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 (03)=4.825285X0.025(20)=2.086,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 Variable: YMethod: Least SquaresDate: 12/03/14 Time: 17:00Sample

9、 (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-StatisticX 0.176124 0.004072 43.25639C -154.3063 39.08196 -3.948274R-squared 0.983702 Mean dependent varAdjusted R-squared 0.983177 S.D. dependent varS.E. of regression 175.2325 Akaike info criterionSum squ

10、ared resid 951899.7 Schwarz criterionLog likelihood -216.2751 Hannan-Quinn criter.F-statistic 1871.115 Durbin-Watson statProb(F-statistic) 0.000000Prob. 0.0000 0.0004 902.5148 1351.009 13.22880 13.31949 13.25931 0.100021 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，检验模型的显著性：1)可决系数为0.983

11、702,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 (p2) =43.25639t0,025(31)=2.0395,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=0.176124X154,3063(0.004072) (39.08196)t二(43.25639)(-3.948274)R2=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Y=0.176124X154.3063,代入可得：丫=

12、 Y=0.176124*32000154.3063=5481.6617进行区间预测：2x2= 2 (X i X ) 2=62x (n1)= 7608.0212 x (331)=1852223.473(Xf X) 2=(32000 6000,441)2=675977068.2当Xf二32000时，将相关数据代入计算得到：5481.66172.0395xl75.2325x V 1/33+1852223.473/675977068.2Yf5481.6617+2.0395xl75.2325xV 1/33+1852223.473/675977068.2即 Yf 的置信区间为(5481.661764.96

13、49, 5481.6617+64.9649)对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 18:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.LNX 0.980275 0.034296 28.58268 0.0000C -1.918289 0.2682

14、13 -7.152121 0.0000R-squared 0.963442 Mean dependent var 5.573120Adjusted R-squared 0.962263 S.D. dependent var 1.684189S.E. of regression 0.327172 Akaike info criterion 0.662028Sum squared resid 3.318281 Schwarz criterion 0.752726Log likelihood -8.923468 Hannan-Quinn criter. 0.692545F-statistic 816

15、.9699 Durbin-Watson stat 0.096208Prob(F-statistic) 0.000000模型方程为：InY=0.980275lnX-1.918289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检验：t (02) =28.58268t0,025(31)=2.0395,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 Variable: YMethod: Least SquaresDate: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X -64.18400