在当下这个社会中,报告的使用成为日常生活的常态,报告具有成文事后性的特点。报告的格式和要求是什么样的呢?下面我给大家整理了一些优秀的报告范文,希望能够帮助到大家,我们一起来看一看吧。
最新《计量经济学综合实验》实验报告总结篇一
(3)78.02 r,说明离差平方和的 78%被样本回归直线解释,还有22%未被解释。因此,样本回归至西安对样本点的拟合优度是较高的。
给出显著水平05.0 ,查自由度 v=14-2=12 的 t 分布表,得临界值 18.2)12(025.0 t,)12(12.10025.0 0t t ,)12(54.6025.0 1t t ,故回归系数均显著不为零,回归模型中英包含常数项,x 对 y 有显著影响。
(4)2000年的国内生产总值为620亿元,货物运输量预测值为29307.84万吨。
实验二 第二章第 7 题 x1 dependent variable: q method: least squares date: 12/17/13 time: 10:57 sample: 1978 1998
included observations: 21 variable coefficient t-statistic prob.c 40772.47 1389.795 29.33704 0.0000 x1 0.001220 0.001909 0.639194 0.5303 r-squared 0.021051 mean dependent var 40996.12 adjusted r-squared-0.030473 ent var 6071.868 regression 6163.687 akaike info criterion 20.38113 sum squared resid 7.22e+08 schwarz criterion 20.48061 log likelihood-212.0019 f-statistic 0.408568 durbin-watson stat 0.206201 prob(f-statistic)0.530328 tq =40772.47+0.001tx 1 +te x2 dependent variable: q method: least squares
date: 12/17/13 time: 10:58 sample: 1978 1998 included observations: 21 variable coefficient t-statistic prob.c 26925.65 915.8657 29.39912 0.0000 x2 5.912534 0.356423 16.58851 0.0000 r-squared 0.935413 mean dependent var 40996.12 adjusted r-squared 0.932014 ent var 6071.868 regression 1583.185 akaike info criterion 17.66266 sum squared resid 47623035 schwarz criterion 17.76214 log likelihood-183.4579 f-statistic 275.1787 durbin-watson stat 1.264400 prob(f-statistic)0.000000 tq =26925.65+5.91tx2 + te x3
dependent variable: q method: least squares date: 12/17/13 time: 10:58 sample: 1978 1998 included observations: 21 variable coefficient t-statistic prob.c-49865.39 12638.40-3.945545 0.0009 x3 1.948700 0.270634 7.200498 0.0000 r-squared 0.731817 mean dependent var 40996.12 adjusted r-squared 0.717702 ent var 6071.868 regression 3226.087 akaike info criterion 19.08632 sum squared resid 1.98e+08 schwarz criterion 19.18580 log likelihood-198.4064 f-statistic 51.84718 durbin-watson stat 0.304603 prob(f-statistic)0.000001
tq =-49865.39+1.95tx3+te(1)t t te x q 1 1 0ˆ ˆ tq =40772.47+0.001tx 1 +te t t te x q 2 1 0ˆ ˆ tq =26925.65+5.91tx2 + te t t te x q 3 1 0ˆ ˆ tq =-49865.39+1.95tx3+te(2)=0.001 为样本回归方程的斜率,表示边际农业机械总动力,说明农业机械总动力每增加 1 万千瓦,粮食产量增加 1 万吨。=40072.47 是截距,表示不受农业机械总动力影响的粮食产量。=0.02,说明总离差平方和的 2%被样本回归直线解释,有 98%未被解释,因此样本回归直线对样本点的拟合优度是很低的。给出的显著水平 =0.05,查自由度 v=21-2=19 的 t 分布表,得临界值09.2)19(025.0 t, 34.290t)19(025.0t,64.00 t<)19(025.0t,=5.91 为样本回归方程的斜率,表示边际化肥施用量,说明化肥使用量每增加 1 万吨,粮食产量增加 1 万吨。
=26925.65 是截距,表示不受化肥使用量影响的粮食产量。
=0.94,说明总离差平方和的 94%被样本回归直线解释,有 6%未被解释,因此样本回归直线对样本点的拟合优度是很高的。给出的显著水平 =0.05,查自由度 v=21-2=19 的 t 分布表,得临界值09.2)19(025.0 t,0t29.40>)19(025.0t,=16.6>,故回归系数均不为零,回归模型中应包含
常数项,x 对 y 有显著影响。
=1.95 为样本回归方程的斜率,表示边际土地灌溉面积,说明土地灌溉面积每增加 1 千公顷,粮食产量增加 1 万吨。
=-49865.39是截距,表示不受土地灌溉面积影响的粮食产量。
=0.73,说明总离差平方和的 73%被样本回归直线解释,有 27%未被解释,因此样本回归直线对样本点的拟合优度是较高的。给出显著性水平=0.05,查自由度 =21-2=19 的 t 分布表,得临界值 =2.09,=-3.95<,=7.2>,故回归系数包含零,回归模型中不应包含常数项,x 对 y 有无显著影响。
(3)根据分析,x2 得拟合优度最高,模型最好,所以选择 x2 得预测值。
tq =26925.65+5.91tx2 + te 54.52349ˆ 2000 q
实验三 p85 第 3 题 dependent variable: y method: least squares date: 12/19/13 time: 09:10 sample: 1 18 included observations: 18 variable coefficient t-statistic prob.c-0.975568 30.32236-0.032173 0.9748 x1 104.3146 6.409136 16.27592 0.0000 x2 0.402190 0.116348 3.456776 0.0035 r-squared 0.979727 mean dependent var 755.1500 adjusted r-squared 0.977023 ent var 258.6859 regression 39.21162 akaike info criterion 10.32684 sum squared resid 23063.27 schwarz criterion 10.47523
log likelihood-89.94152 f-statistic 362.4430 durbin-watson stat 2.561395 prob(f-statistic)0.000000(1)2 140.0 32.104 98.0ˆx x y (2)提出检验的原假设为 2 , 1 , 00 i hi。
给出显著水平05.0 ,查自由度 v=18-2=16 的 t 分布表,得临界值 13.2)15(025.0 t。
28.161t)15(025.0t,所以否定0h ,1 显著不等于零,即可以认为受教育年限对购买书籍及课外读物支出有显著影响。
46.32t)15(025.0t,所以否定0h,2 显著不等于零,即可以家庭月可支配收入对购买书籍及课外读物支出有显著影响。
(3)9797.0 12 tssrsstssessr 9770.0)1 /()1 /(12 n tssk n rssr 2r =0.9797,表示 y 中的变异性能被估计的回归方程解释的部分越多,估计的回归方程对样本观测值就拟合的越好。同样,2r =0.9770,很接近1,表示模型拟合度很好。
(4)把1x =10,2x =480 代入2 140.0 32.104 98.0ˆx x y 22.1234 480 * 40.0 10 * 32.104 98.0ˆ 2000 y 实验四 p86 第 6 题 dependent variable: y
method: least squares date: 12/19/13 time: 10:14 sample: 1955 1984 included observations: 30 variable coefficient t-statistic prob.c 0.208932 4.372218 0.047786 0.9623 x1 1.081407 0.234139 4.618649 0.0001 x2 3.646565 1.699849 2.145229 0.0414 x3 0.004212 0.011664 0.361071 0.7210 r-squared 0.552290 mean dependent var 22.13467 adjusted r-squared 0.500632 ent var 14.47115 regression 10.22618 akaike info criterion 7.611345 sum squared resid 2718.944 schwarz criterion 7.798171 log likelihood-110.1702 f-statistic 10.69112 durbin-watson stat 1.250501 prob(f-statistic)0.000093
3 2 10042.0 6466.3 0814.1 2089.0ˆx x x y 0814.11 ,表示该地区某农产品收购量随着销售量的增加而增加,=3.647 表示农产品收购量随出口量的增加而增加。
=3.647 表示农产品收购量随库存量的增加而增加。该回归方程系数的符号和大小均符合经济理论和实际情况。
统计检验 a.回归方程的显著性检验 f 检验:r =0.55 表示 和 和 联合起来对 y 的解释能力达到55,因此,样本回归方程的拟合优度是高的。显著性水平=0.05,查自由度 v=30-3-1=27,的 f 分布表的临界值05.0f(3,27)=2.96,f=10.69>f(3,27)=2.96,说明回归方程在总体上是显著的。
b.回归系数的显著性检验 t 检验:显著性水平=0.05,查自由度 v=30-3-1=26 的 t 分布表的临界值 t(26)=2.06,t =4.62>t(26),所以 显著不为零,即销售量对农产品收购量有显著影响;t =2.15 >t(26),所以显著不为零,即出口量对农产品收购量有显著影响;t =0.36
5523.02 tssessr,表示 y 中的变异性能被估计的回归方程解释的部分越多,估计的回归方程对样本观测值就拟合的越好。同样,2r =0.5006,表示模型拟合度一般。
实验五
p107 第四章第 1 题 dependent variable: logy method: least squares date: 12/19/13 time: 12:07 sample: 1990 1998 included observations: 9 variable coefficient t-statistic prob.c 1.130931 0.019529 57.91136 0.0000 t 0.281837 0.003470 81.21339 0.0000 r-squared 0.998940 mean dependent var 2.540117 adjusted r-squared 0.998788 ent var 0.772253 regression 0.026881 akaike info criterion-4.201659 sum squared resid 0.005058 schwarz criterion-4.157831 log likelihood 20.90746 f-statistic 6595.614 durbin-watson stat 1.128588 prob(f-statistic)0.000000
lny=1.13+0.28t+te(57.91)(81.21)结构分析 : =0.28 表示 1990 年到 1998 年期间,皮鞋销售额的年增长率为 28%。给出显著性水平=0.05,查自由度 =30-4=26 的 t 分布表,得临界值 =2.37,=57.91>,=81.21>故显著不为零,则回归模型中应包含常数项,可以认为时间对销售额有显著影响,, ,表示y 能对估计的回归方程进行很高解释,所以估计的回归方程对样本观测值就拟合的程度很高 t=10,lny=3.949 y=49.4024 则预测得该商场 1999 年的皮鞋销售额为 49.4024 万元 实验六 p107 第四章第 2 题 dependent variable: logy method: least squares date: 12/20/13 time: 15:08 sample: 1 21 included observations: 21 variable coefficie t-statistic c-35.40425 1.637922-21.61535 0.0000 t 0.020766 0.000866 23.97401 0.0000 r-squared 0.968000 mean dependent var 3.843167 adjusted r-squared 0.966316 ent var 1.309610 regression 0.240355 akaike info criterion 0.076997 sum squared resid 1.097644 schwarz criterion 0.176475 log likelihood 1.191533 f-statistic 574.7531 durbin-watson stat 0.110127 prob(f-statistic)0.000000 lny=-35.4042+0.02081x +1u
lnyf=6.127 y=458.0599 实验七 p108 第四章第 3 题 dependent variable: lnm method: least squares date: 12/20/13 time: 16:35 sample: 1948 1964 included observations: 17 variable coefficient t-statistic 1.265879 0.431393 2.934402 0.0116
lnr 0.864595 0.517228 1.671593 0.1185 lny 0.206210 0.308720 0.667952 0.5158 c-2.095090 1.790906-1.169850 0.2631 r-squared 0.859355 mean dependent var 5.481567 adjusted r-squared 0.826899 ent var 0.269308 regression 0.112047 akaike info criterion-1.337475 sum squared resid 0.163208 schwarz criterion-1.141425 log likelihood 15.36854 f-statistic 26.47717 durbin-watson stat 0.743910 prob(f-statistic)0.000008 lnt t tnty r p m 2062.0 ln 8646.0 ln 2659.1 0951.2)( (-1.1699)(2.9344)(1.6716)(0.6680)085942 r 8269.02 r(2)t 检验:
假设0h : 0 i,显著性水平=0.05,查自由度 v=17-3-1=13 的t 分布表的临界值 t(13)=2.16,t =2.9344>t(13),所以1ˆ 显著不为零,即内含价格缩减指数对名义货币存量有显著影响;2t =1.6716
f 检验:
假设0h : 03 2 1 1h :至少有一个i 不等于零(i=1,2,3)r =0.86 表示3 2 1 和 和 联合起来对)(ntm 的解释能力达到 86,因此,样本回归方程的拟合优度是很高的。显著性水平=0.05,查自由度 v=17-3-1=13,的 f 分布表的临界值05.0f(3,13)=3.41,f=26.4772>f(3,13)=3.41,所以否定0h,说明回归方程在总体上是显著的。即内含价格缩减指数,名义国名收入和长期利率与名义货币存量之间的关系是线性的。
经济意义分析:
0 1.2659 表示内含价格缩减指数每增加 1%,名义货币存量就增加 1.2659%,1 0.2062 表示名义国民收入每增加 1 亿,名义货币存量就增加 0.2062 亿,2 0.8646 表示长期利率每增加 1%,名义货币存量就增加 0.8646%。
(3)dependent variable: lnm method: least squares
date: 12/20/13 time: 16:41 sample: 1948 1964 included observations: 17 variable coefficient t-statistic 0.944253 0.489602 1.928614 0.0743 lny 0.226585 0.300069 0.755110 0.4627 c-1.006527 0.289766-3.473584 0.0037 r-squared 0.751490 mean dependent var 0.802225 adjusted r-squared 0.715989 ent var 0.205539 regression 0.109537 akaike info criterion-1.426321 sum squared resid 0.167977 schwarz criterion-1.279283 log likelihood 15.12373 f-statistic 21.16793 durbin-watson stat 0.656255 prob(f-statistic)0.000059 lnt t ty r m 2266.0 ln 9443.0 0065.1
(-3.4736)(1.9286)(0.7551)t 检验:
假设0h : 0 i,显著性水平=0.05,查自由度 v=17-2-1=14 的t 分布表的临界值 t(14)=2.15,rt =1.9286
f 检验:
假设0h : 02 1 1h :至少有一个i 不等于零(i=1,2,3)r =0.75 表示2 1 和 联合起来对tm 的解释能力达到 75,因此,样本回归方程的拟合优度是很高的。显著性水平=0.05,查自由度v=17-2-1=14,的 f 分 布 表 的 临 界 值05.0f(3,14)=3.34,f=21.1679>f(3,14)=3.34,所以否定0h,说明回归方程在总体上是显著的。即名义国名收入和长期利率与名义货币存量之间的关系是线性的。
经济意义分析:
1 0.9443 表示长期利率每增加 1%,名义货币存量就增加0.9443%,2 0.2266 表示名义国民收入每增加 1 亿,名义货币存量就增加 0.2266%。
(4)dependent variable: lnm method: least squares date: 12/20/13 time: 16:51
sample: 1948 1964 included observations: 17 variable coefficient t-statistic -0.209411 0.232757-0.899696 0.3825 c-1.287677 0.314926-4.088823 0.0010 r-squared 0.051201 mean dependent var-1.569623 adjusted r-squared-0.012053 ent var 0.127733 regression 0.128501 akaike info criterion-1.155637 sum squared resid 0.247686 schwarz criterion-1.057611 log likelihood 11.82291 f-statistic 0.809453 durbin-watson stat 1.474376 prob(f-statistic)0.382499 lnt tr m ln 2094.0 2877.1 (-4.0888)(-0.8997)
t 检验:
假设0h : 0 i,显著性水平=0.05,查自由度 v=17-1-1=15 的t 分布表的临界值 t(15)=2.13,rt =-0.8997
f 检验:
假设0h : 0 1h :
0 r =0.05,因此,样本回归方程的拟合优度是很低的。显著性水平=0.05,查自由度 v=17-1-1=15,的 f 分布表的临界值05.0f(3,15)=3.29,f=0.8095
经济意义分析:
-0.2094 表示长期利率每增加 1%,名义货币存量就减少0.2094%。
实验八 p133 第五章第 2 题 dependent variable: y method: least squares date: 12/24/13 time: 09:44 sample: 1 29 included observations: 29
variable coefficient t-statistic prob.c 58.31791 49.04935 1.188964 0.2448 x 0.795570 0.018373 43.30193 0.0000 r-squared 0.985805 mean dependent var 2111.931 adjusted r-squared 0.985279 ent var 555.5470 regression 67.40436 akaike info criterion 11.32577 sum squared resid 122670.4 schwarz criterion 11.42006 log likelihood-162.2236 f-statistic 1875.057 durbin-watson stat 1.893970 prob(f-statistic)0.000000 i iu x y 1 1 0 i iu x y 17956.0 3179.58(1.18)(43.3)=0.9852 f=1875.057(1)斯皮尔曼等级相关系数检验 x x 的等级 残差 残差的等 等级差 等级差的级平方 3547 26 59.79523 20-6 36 2769 21 60.7487 21 0 0 2334 14 17.17834 7-7 49 1957 4 55.24844 18 14 196 1893 1 20.66804 8 7 49 2314 13 77.73306 22 9 81 1953 3 16.06616 4 1 1 1960 5 42.36485 14 9 81 4297 28 53.11771 17-11 121 2774 22 45.77085 15-7 49 3626 27 87.05481 23-4 16 2248 11 0.759316 1-10 100 2839 23 24.0588 10-13 169 1919 2 8.016779 2 0 0 2515 18 112.1765 27 9 81 1963 6 11.02186 3-3 9 2450 17 40.53554 13-4 16 2688 20 109.8101 26 6 36 4632 29 33.60175 12-17 289 2895 24 58.49312 19-5 25 3072 25 98.30901 25 0 0
2421 15 49.60707 16 1 1 2313 12 22.47137 9-3 9 2653 19 17.03482 6-13 169 2102 8 16.60609 5-3 9 2003 7 28.15534 11 4 16 2127 9 119.5047 28 19 361 2171 10 91.49958 24 14 196 2423 16 150.9841 29 13 169 等级差平方和 2334 r=1-43.0 57.0 12436014004129 292334 * 63 假设0h :
0 1h :
0 r~n(0,11 n)=n(0,281)z=281r=0.43*5.2915=2.275345 给定显著性水平05.0 ,查正太分布表,得 96.12z,因为z=2.275345>1.96,所以拒绝原假设0h ,接受1h,即等级相关系数是显著的,说明城镇居民人均生活费模型的随机误差存在异方差。
(2)图示法
y 对 x 的散点图 残差与 x 的散点图(3)dependent variable: y method: least squares
date: 12/26/13 time: 10:32 sample: 1 29 included observations: 29 variable coefficient t-statistic prob.c 58.31791 49.04935 1.188964 0.2448 x 0.795570 0.018373 43.30193 0.0000 r-squared 0.985805 mean dependent var 2111.931 adjusted r-squared 0.985279 ent var 555.5470 regression 67.40436 akaike info criterion 11.32577 sum squared resid 122670.4 schwarz criterion 11.42006 log likelihood-162.2236 f-statistic 1875.057 durbin-watson stat 1.893970 prob(f-statistic)0.000000 white 检验 white heteroskedasticity test: f-statistic 1.368420 probability 0.27223
7 obs*r-squared 2.761902 probability 0.251339 test equation: dependent variable: resid^2 method: least squares date: 12/26/13 time: 10:34 sample: 1 29 included observations: 29 variable coefficient t-statistic prob.c-22151.26 16006.57-1.383885 0.1782 x 18.11067 10.95898 1.652586 0.1104 x^2-0.002858 0.001756-1.627322 0.1157 r-squared 0.095238 mean dependent var 4230.013 adjusted r-squared 0.025641 ent var 5479.442 regression 5408.737 akaike info 20.1271
criterion 2 sum squared resid 7.61e+08 schwarz criterion 20.26856 log likelihood-288.8432 f-statistic 1.368420 durbin-watson stat 1.209956 prob(f-statistic)0.272237 220029.0 1107.18 26.22151 ˆt t tx x u (-1.3839)(1.6526)(-1.6273)0952.02 r t=29 76196.2 0952.0 * 292 tr <0.6)2(205.0 所以该回归模型不存在异方差。
(4)戈德菲尔德-夸特检验 第一个样本输出 dependent variable: y method: least squares date: 12/26/13 time: 10:49 sample: 1 11 included observations: 11 variable coefficient t-statistic prob.c-287.1872 271.8586-1.056384 0.3183 x 0.974751 0.133926 7.278296 0.0000 r-squared 0.854777 mean dependent var 1688.545 adjusted r-squared 0.838641 ent var 122.2083 regression 49.09050 akaike info criterion 10.78817 sum squared resid 21688.89 schwarz criterion 10.86052 log likelihood-57.33496 f-statistic 52.97359 durbin-watson stat 2.306656 prob(f-statistic)0.000047 x y 9748.0 19.287ˆ 残差平方和=21688.89 第二个样本输出 dependent variable: y method: least squares date: 12/26/13 time: 10:50
sample: 19 29 included observations: 11 variable coefficient t-statistic prob.c-27.68345 106.7596-0.259306 0.8012 x 0.820337 0.032169 25.50095 0.0000 r-squared 0.986349 mean dependent var 2641.545 adjusted r-squared 0.984832 ent var 565.8140 regression 69.68393 akaike info criterion 11.48878 sum squared resid 43702.65 schwarz criterion 11.56113 log likelihood-61.18830 f-statistic 650.2986 durbin-watson stat 2.610584 prob(f-statistic)0.000000 x y 8203.0 6835.27ˆ 残差平方和=43702.65 提出原假设,0h :2292221...
备择假设,1h :2292221... 、互不相同。
构造 f 统计量 015.289.2168865.43702 f 给出显著性水平 =0.05,查 f 分布表 2-11 v v2 1 =9,18.3)9 , 9(05.0 f,因为 f=2.015<3.18,所以接受原假设,即城镇居民人均生活费计量模型的随机误差不存在异方差。
实验九 p158 第六章第 3 题 dependent variable: y method: least squares date: 12/26/13 time: 11:43 sample: 1975 1994 included observations: 20 variable coefficient t-statistic prob.c-1.454750 0.214146-6.793261 0.0000 x 0.176283 0.001445 122.0170 0.0000 r-squared 0.998792 mean dependent var 24.56900 adjusted r-squared 0.998725 ent var 2.410396
regression 0.086056 akaike info criterion-1.972991 sum squared resid 0.133302 schwarz criterion-1.873418 log likelihood 21.72991 f-statistic 14888.14 durbin-watson stat 0.734726 prob(f-statistic)0.000000(1)线性回归模型 tx y 176.0 455.1ˆ (-6.7933)(122.0170)998.02 r s.e=0.086 dw=0.7347 t=20 所以回归方程拟合效果较好,但是 dw 值比较低。
(2)残差图
lm 检验 breusch-godfrey serial correlation lm test: f-statistic 11.32914 probability 0.003669 obs*r-squared 7.998223 probability 0.004682 test equation: dependent variable: resid method: least squares date: 12/06/13 time: 16:38 presample missing value lagged residuals set to le coefficient t-statistic prob.c 0.060923 0.171655 0.354917 0.7270 x-0.000420 0.001158-0.362439 0.7215 resid(-1)0.638831 0.189796 3.365879 0.0037 r-squared 0.399911 mean dependent var-8.51e-16 adjusted r-squared 0.329312 ent var 0.083761 regression 0.068597 akaike info criterion-2.383669 sum squared resid 0.079993 schwarz criterion-2.234309 log likelihood 26.83669 f-statistic 5.664570 durbin-watson stat 1.738830 prob(f-statistic)0.013027 obs*r-squared 7.998223 lm(bg)自相关检验辅助回归式估计结果是
=20*0.399911=7.998223 dw=1.7388 因为)1(201.0 =6.635
假设 0...2 1 0 nh :
:1h 至少一个n 不等于 0。
9982.72 tr lm , 与)1(201.0 相 比,)1(201.0 =6.635,2tr lm >)1(201.0 =6.635,所以拒绝0h,接受1h,所以该误差项存在一阶自相关。
(4)已知 dw=0.7347,若给定 05.0 ,查表得 dw 检验临界值20.1 ld,41.1 ud。因为 dw=0.7347<1.20,依据判别规则,认为 误 差 项tu 存 在 严 重 的 自 相 关。
估 计 得 自 相 关 系 数63265.021 ˆ dw。
对原变量做广义差分变换。令 163265.0 t t ty y gdy 163265.0 t t tx x gdx 以tgdy、tgdx,(1976~1994 年)为样本再次回归,得 dependent variable: y1 method: least squares date: 12/06/13 time: 16:09 sample(adjusted): 1976 1994 included observations: 19 after adjusting endpoints variable coefficient t-statistic prob.c-0.391467 0.167101-2.342704 0.0316 x1 0.173740 0.002966 58.57989 0.0000 r-squared 0.995070 mean dependent var 9.355585 adjusted r-squared 0.994780 ent var 0.929364 regression 0.067143 akaike info criterion-2.464684 sum squared resid 0.076639 schwarz criterion-2.365269 log likelihood 25.41450 f-statistic 3431.603 durbin-watson stat 1.651928 prob(f-statistic)0.000000 t tgdx gdy 174.0 39.0 (-2.34)(58.58))(,,1994 ~ 1976 19 652.1 067.0 e.s 995.02 t dw r dw=1.65,查临界值表,若给定 05.0 ,查表得 dw 检验临界值18.1 ld,40.1 ud。因为 dw=1.65>1.18,依据判别规则,认为误差项tu 不存在自相关。残差图如下:
残差图 0657.1)63265.0 1 /(3915.0)1 /(*0 0 t tx y 174.0 0657.1ˆ 经济含义是该公司的年销售额占该行业的年销售额的 17.4%。
实验十 p159 第六章第 4 题 dependent variable: y method: least squares date: 12/09/13 time: 08:41 sample: 1960 2001 included observations: 42 variable coefficie t-statistic c-3028.563 655.4268-4.620749 0.0000 gdp 0.697492 0.019060 36.59467 0.0000 r-squared 0.970997 mean dependent var 10765.23 adjusted r-squared 0.970272 ent var 20154.12 regression 3474.938 akaike info criterion 19.19099 sum squared resid 4.83e+08 schwarz criterion 19.27373 log likelihood-401.0108 f-statistic 1339.170 durbin-watson stat 0.178439 prob(f-statistic)0.000000(1)线性回归模型 tgdp y 6975.0 56.3028ˆ (-4.6207)(36.5947)97.02 r s.e=3474.94 dw=0.1784 t=42
所以回归方程拟合效果较好,但是 dw 值比较低。
(2)lm 检验:
breusch-godfrey serial correlation lm test: f-statistic 327.3780 probability 0.000000 obs*r-squared 37.52921 probability 0.000000 test equation: dependent variable: resid method: least squares date: 12/09/13 time: 08:51
presample missing value lagged residuals set to le coefficient t-statistic prob.c-425.8114 217.8406-1.954693 0.0578 gdp 0.034728 0.006584 5.274762 0.0000 resid(-1)1.109597 0.061325 18.09359 0.0000 r-squared 0.893553 mean dependent var-3.29e-12 adjusted r-squared 0.888094 ent var 3432.299 regression 1148.186 akaike info criterion 16.99850 sum squared resid 51414932 schwarz criterion 17.12262 log likelihood-353.9686 f-statistic 163.6890 durbin-watson stat 1.408348 prob(f-statistic)0.000000 假设 0...2 1 0 nh :
:1h 至少一个n 不等于 0。
5292.372 tr lm , 与)1(201.0 相 比,)1(201.0 =6.635,2tr lm >)1(201.0 =6.635,所以拒绝0h,接受1h,所以该误差项存在一阶自相关。
(4)已知 dw=0.1784,若给定 05.0 ,查表得 dw 检验临界值46.1 ld,55.1 ud。因为 dw=0.7347<1.46,依据判别规则,认为误差项tu 存在严重的自相关。估计得自相关系数 9108.021 ˆ dw。
对原变量做广义差分变换。令 1 19108.0 t ty y y 1 19108.0 t tgdp gdp gdp 以1y、tgdp,(1961~2001 年)为样本再次回归,得 dependent variable: y1 method: least squares date: 12/09/13 time: 09:23 sample(adjusted): 1961 2001 included observations: 41 after adjusting endpoints variable coefficient t-statistic prob.c-421.5539 280.8946-1.500755 0.1415 gdp1 0.779526 0.042995 18.13047 0.0000 r-squared 0.893939 mean dependent var 2620.667 adjusted 0.891220 ent 4373.39
r-squared var 9 regression 1442.428 akaike info criterion 17.43359 sum squared resid 81143297 schwarz criterion 17.51718 log likelihood-355.3887 f-statistic 328.7140 durbin-watson stat 0.836300 prob(f-statistic)0.000000 t tgdx gdy 7795.0 55.421 (-1.50)(18.13))(,,001 2 ~ 1961 41 8363.0 43.1442 e.s 894.02 t dw r dw=0.8363,查临界值表,若给定 05.0 ,查表得 dw 检验临界值 45.1 ld,54.1 ud。因为 dw=0.8363<1.45,依据判别规则,认为误差项tu 存在严重的自相关。残差图如下:
08.513)1784.0 1 /(55.421)1 /(*0 0 t tx y 7795.0 08.513ˆ 经济含义是中国储蓄存款总额占 gdp 的 77.95% 回归检验 dependent variable: e method: least squares date: 12/09/13 time: 09:53 sample(adjusted): 1961 2001 included observations: 41 after adjusting endpoints variable coefficient t-statistic prob.e(-1)1.009174 0.074755 13.49981 0.0000 r-squared 0.819979 mean dependent-50.6979
var 8 adjusted r-squared 0.819979 ent var 3458.980 regression 1467.608 akaike info criterion 17.44474 sum squared resid 86154890 schwarz criterion 17.48654 log likelihood-356.6172 durbin-watson stat 0.755836 ,给定的,1.68<13.49981,所以存在一阶自相关。
dependent variable: e method: least squares date: 12/09/13 time: 10:19 sample(adjusted): 1962 2001 included observations: 40 after adjusting endpoints variable coefficient t-statistic prob.e(-1)1.649051 0.156003 10.57065 0.0000 e(-2)-0.718464 0.160362-4.480266 0.0001
r-squared 0.880898 mean dependent var-107.7910 adjusted r-squared 0.877764 ent var 3483.425 regression 1217.887 akaike info criterion 17.09633 sum squared resid 56363443 schwarz criterion 17.18077 log likelihood-339.9266 durbin-watson stat 1.674695 给定的,所以存在二阶自相关。
dependent variable: e method: least squares date: 12/09/13 time: 10:41 sample(adjusted): 1963 2001 included observations: 39 after adjusting endpoints variable coefficient t-statistic prob.e(-1)1.332544 0.253901 5.248284 0.0000 e(-2)-0.05780 0.449331-0.128638 0.8984
1 e(-3)-0.413896 0.263149-1.572860 0.1245 r-squared 0.887189 mean dependent var-168.7096 adjusted r-squared 0.880921 ent var 3507.310 regression 1210.295 akaike info criterion 17.10892 sum squared resid 52733319 schwarz criterion 17.23689 log likelihood-330.6239 durbin-watson stat 1.687480,给定的,所以不存在三阶自相关。
实验十一 第七章第 8 题 p171 dependent variable: y method: least squares date: 12/09/13 time: 10:54 sample: 1 10
included observations: 10 variable coefficient t-statistic prob.c 3.914451 1.952440 2.004902 0.1013 x1 0.060263 0.048378 1.245671 0.2681 x2 0.089090 0.037168 2.396978 0.0619 x3-0.012598 0.018171-0.693309 0.5190 x4 0.007406 0.017612 0.420498 0.6916 r-squared 0.979655 mean dependent var 7.570000 adjusted r-squared 0.963379 ent var 1.233829 regression 0.236114 akaike info criterion 0.257851 sum squared resid 0.278750 schwarz criterion 0.409144 log likelihood 3.710743 f-statistic 60.18950 durbin-watson stat 2.213879 prob(f-statistic)0.000204 4 3 2 10074.0 0126.0 0890.0 0602.0 915.3ˆx x x x y
(2.0049)(1.2457)(2.3970)(-0.6933)(0.4205)1895.60 , 2139.2 , 9634.0 , 9797.02 2 f dw r r 括号内的表示 t 值,给定显著水平05.0 ,回归系数估计值都没有显著性。查 f 分布表,的临界值为 19.5)5 , 4(05.0 f,故 f=60.1895>5.19,回归方程显著。
分别计算4 3 2 1, , , x x x x 的两两相关系数,得 x1 x2 x3 x4 x1 1.000000 0.879363-0.338876 0.956248 x2 0.879363 1.000000-0.304705 0.760764 x3-0.338876-0.304705 1.000000-0.413541 x4 0.956248 0.760764-0.413541 1.000000 414.0 , 761.0 , 305.0 , 956.0 , 339.0 , 879.034 24 23 14 13 12 r r r r r r 可见,解释变量之间不是高度相关的。为了检验和处理多重共线性,采用修正法 frisch 法。对 y 分别关于4 3 2 1, , , x x x x 作最小二乘回归,得(1)dependent variable: y method: least squares date: 12/09/13 time: 11:11 sample: 1 10 included observations: 10
variable coefficient t-statistic prob.c 0.942307 0.572960 1.644630 0.1387 x1 0.122124 0.010405 11.73672 0.0000 r-squared 0.945112 mean dependent var 7.570000 adjusted r-squared 0.938251 ent var 1.233829 regression 0.306599 akaike info criterion 0.650305 sum squared resid 0.752024 schwarz criterion 0.710822 log likelihood-1.251524 f-statistic 137.7507 durbin-watson stat 1.683709 prob(f-statistic)0.000003 11221.0 9423.0ˆx y 751.137 , 684.1 , 938.0 , 945.02 2 f dw r r(2)dependent variable: y method: least squares date: 12/09/13 time: 11:15
sample: 1 10 included observations: 10 variable coefficient t-statistic prob.c 5.497455 0.307504 17.87768 0.0000 x2 0.205406 0.026933 7.626515 0.0001 r-squared 0.879088 mean dependent var 7.570000 adjusted r-squared 0.863974 ent var 1.233829 regression 0.455057 akaike info criterion 1.440070 sum squared resid 1.656618 schwarz criterion 1.500587 log likelihood-5.200350 f-statistic 58.16373 durbin-watson stat 0.612996 prob(f-statistic)0.000062 22054.0 4975.5ˆx y 164.58 , 613.0 , 864.0 , 879.02 2 f dw r r(3)dependent variable: y
method: least squares date: 12/09/13 time: 11:17 sample: 1 10 included observations: 10 variable coefficient t-statistic prob.c 17.09021 7.986587 2.139864 0.0648 x3-0.095107 0.079695-1.193386 0.2669 r-squared 0.151119 mean dependent var 7.570000 adjusted r-squared 0.045009 ent var 1.233829 regression 1.205743 akaike info criterion 3.388925 sum squared resid 11.63052 schwarz criterion 3.449442 log likelihood-14.94462 f-statistic 1.424170 durbin-watson stat 0.647123 prob(f-statistic)0.266905 30951.0 0902.17ˆx y
424.1 , 647.0 , 045.0 , 151.02 2 f dw r r(4)dependent variable: y method: least squares date: 12/09/13 time: 11:20 sample: 1 10 included observations: 10 variable coefficient t-statistic prob.c 2.017807 0.898099 2.246752 0.0548 x4 0.055027 0.008741 6.295432 0.0002 r-squared 0.832047 mean dependent var 7.570000 adjusted r-squared 0.811053 ent var 1.233829 regression 0.536321 akaike info criterion 1.768688 sum squared resid 2.301120 schwarz criterion 1.829205 log likelihood-6.843439 f-statistic 39.63246 durbin-watson 0.596061 prob(f-statistic)0.00023
stat 4 3055.0 018.2ˆx y 632.39 , 596.0 , 811.0 , 832.02 2 f dw r r 其中括号内的数字值是 t 值,根据经济理论分析和回归结果,易知观测值中1x 是最重要的解释变量,所以选取第一个回归方程为基本回归方程。
1.加入 x2,对 y 关于 x1,x2 做最小二乘回归,得 dependent variable: y method: least squares date: 12/10/13 time: 09:01 sample: 1 10 included observations: 10 variable coefficient t-statistic prob.c 2.322897 0.626102 3.710092 0.0076 x1 0.081826 0.015677 5.219553 0.0012 x2 0.079919 0.027340 2.923182 0.0222 r-squared 0.975284 mean dependent var 7.570000 adjusted r-squared 0.968222 ent var 1.233829
regression 0.219948 akaike info criterion 0.052476 sum squared resid 0.338641 schwarz criterion 0.143252 log likelihood 2.737618 f-statistic 138.1058 durbin-watson stat 2.264141 prob(f-statistic)0.000002 2 107991.0 0818.0 322.2ˆx x y (3.71009)(5.21955)(2.9231)1058.138.2641.2 , 96822.0 , 97528.02 2 f dw r r 92.2 45.2)1 3 10(, 01.5 45.2)1 3 10(2 025.0 1 025.0 t t t t 可以看出,加入2x后,拟合优度2r和2r均有所增加,参数估计值的符号也正确,并且没有影响1x系数的显著性,所以在模型中保留2x。
2.加入 x3,对 y 关于 x1,x2,x3 做最小二乘回归,得 dependent variable: y method: least squares date: 12/10/13 time: 09:12 sample: 1 10 included observations: 10
variable coefficient t-statistic prob.c 4.037285 1.793154 2.251500 0.0653 x1 0.079302 0.015827 5.010578 0.0024 x2 0.079503 0.027265 2.915951 0.0268 x3-0.015716 0.015410-1.019885 0.3471 r-squared 0.978935 mean dependent var 7.570000 adjusted r-squared 0.968403 ent var 1.233829 regressio...
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