计量经济学张晓峒第三版课后作业
xx 7、已知我国粮食产量 Q(万吨、农业机械总动力1(万千瓦) 、化肥施用量2 x (万吨) 、土地灌溉面积3(千公顷) 。 (1) 试估计一元线性回归模型 ˆ 0 ˆ 1 X 1t e t Q t 50,000 45,000 40,000 35,000 X 130,000 25,000 20,000 15,000 10,000 30,00035,00040,000 Q 45,00050,00055,000 Dependent Variable Q Least Squares Date 10/09/12Time 2120 Sample 1978 1998 Included observations 21 X1 C R-squared Coefficient 0.608026 25107.08 Std. Error 0.039102 1085.940 t-Statistic 15.54972 23.12012 Prob. 0.0000 0.0000 41000.89 6069.284 17.78226 17.88174 17.80385 1.364650 0.927146 Mean dependent var 0.923311 S.D. dependent var 1680.753 Akaike info criterion 53673653 Schwarz criterion -184.7138 Hannan-Quinn criter. 241.7938 Durbin-Watson stat 0.000000 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic ProbF-statistic 0 25107.08 1 0.61t 0 23.12t 1 15.55 则样本回归方程为 Q t 25107.080.61X 1t ((23.12) (15.55)r20.93 括号内的数字为回归系数对应的 t 统计量的值,以下同。 ˆ ˆ XeQ t 012t1 4,400 4,000 3,600 3,200 2,800 X 2 2,400 2,000 1,600 1,200 800 30,00035,00040,000 Q 45,00050,00055,000 Dependent Variable Q Least Squares Date 10/09/12Time 2121 Sample 1978 1998 Included observations 21 X2 C R-squared Coefficient 5.909473 26937.69 Std. Error 0.356747 916.6972 t-Statistic 16.56488 29.38559 Prob. 0.0000 0.0000 41000.89 6069.284 17.66447 17.76395 17.68606 1.247710 0.935241 Mean dependent var 0.931833 S.D. dependent var 1584.623 Akaike info criterion 47709547 Schwarz criterion -183.4770 Hannan-Quinn criter. 274.3953 Durbin-Watson stat 0.000000 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic ProbF-statistic 0 26937.69 1 5.91 t 0 29.39t 1 16.56 则样本回归方程为 Q t 26937.69 5.91X 2t 29.3916.56r20.94 Q t ˆ 0 ˆ 1 X 3t e t 54,000 52,000 50,000 X 348,000 46,000 44,000 42,000 30,00035,00040,000 Q 45,00050,00055,000 Dependent Variable Q Least Squares Date 10/09/12Time 2123 Sample 1978 1998 Included observations 21 X3 C R-squared Coefficient 1.946877 -49775.62 Std. Error 0.270895 12650.60 t-Statistic 7.186827 -3.934645 Prob. 0.0000 0.0009 41000.89 6069.284 19.08825 19.18773 19.10984 0.300947 0.731070 Mean dependent var 0.716916 S.D. dependent var 3229.199 Akaike info criterion 1.98E08 Schwarz criterion -198.4266 Hannan-Quinn criter. 51.65048 Durbin-Watson stat 0.000001 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic ProbF-statistic 0 49774.62 1 1.95t 0 3.93t 1 7.19 -3.937.19r20.73 Q t 49775.62 1.95X 3t 2 对以上三个模型的估计结果进行结构分析和统计检验。 Q t 49775.62 1.95X 3t ①对回归方程的结构分析 α10.61 是样本回归方程的斜率,它表示我国粮食产量的边际消费倾向,说 明农业机械总动力每消耗 1 万千瓦,将生产 0.61 万吨粮食。α0 25107.08,是 样本回归方程的截距,它表示不受农业机械总动力的影响的粮食产量。他们的大 小,均符合经济理论及目前的实际情况。 ②统计检验 r20.93,说明总离差平方和的 93被样本回归直线解释,仅有 7未被解 释,因此,样本回归直线对样本的拟合优度是很高的。 给出显著水平α0.05, 查自由度 v21-219 的 t 分布,得临界值t0.025192.09, t023.12 t 0.02519 2.09,t 115.55 t0.02519 2.09,故回归系数均显著不为零,回 归模型中应包含常数项, X1对 Qt有显著影响。 Q t 26937.69 5.91X 2