计量的实验，本人刚学习不是很懂，望高手指点下

wangyanse

1756

收藏 2013-05-18

悬赏 50 个论坛币未解决

小弟初学计量。不是很懂。刚做的作业有点问题。

希望高手给解决下。可给稿酬

数据在附件中

airline.xls
大小:(3.06 KB)

马上下载

Q=出售机票量 P=航空公司票价 P0=竞争对手的票价 Y=收入

假设模型为 Q= β1P + β2P0 + β3Y + e.

a) 给出结果并加以说明

b) Arethere any signs of miss specification?
不是很懂。。

c) Analyse ifthe model should include a constant term or not.
解释这个模型需不需要一个常数项

d) Test H0:β3 = 2 againstH1: β3 1 2.

测试H0: β3 = 2 against H1: β3 1 2.

e) Computethe price elasticity, the cross-price elasticity and the income elasticity.

算出各个量的弹性。1价格2corss价格3收入

输出为
--> REGRESS;Lhs=Q;Rhs=P,P0,Y$

+----------------------------------------------------+

| Ordinary leastsquares regression |

| Model was estimated May 16, 2013 at 08:53:01PM |

| LHS=Q Mean = 87.24375 |

| Standard deviation = 27.93562 |

| WTS=none Number of observs. = 16 |

| Model size Parameters = 3 |

| Degrees of freedom = 13 |

| Residuals Sumof squares = 2622.326 |

| Standard error of e = 14.20273 |

| Fit R-squared = .7759840 |

| Adjusted R-squared = .7415200 |

| Model test F[ 2, 13] (prob) = 22.52 (.0001) |

| Diagnostic Loglikelihood = -63.49684 |

| Restricted(b=0) = -75.46515 |

| Chi-sq [ 2] (prob) = 23.94 (.0000) |

| Info criter. LogAmemiya Prd. Crt. = 5.478718 |

| Akaike Info. Criter. = 5.474228 |

| Autocorrel Durbin-WatsonStat. = 1.0998728 |

| Rho= cor[e,e(-1)] = .4500636 |

| Not using OLS or no constant. Rsqd & F may be <0. |

+----------------------------------------------------+

+--------+--------------+----------------+--------+--------+----------+

+--------+--------------+----------------+--------+--------+----------+

P | -2.11839990 .32605643 -6.497 .0000 239.687500

P0 | 1.10188791 .21812294 5.052 .0002 243.125000

Y | 3.19929914 .71632554 4.466 .0006 102.237500

a）模型 Q = -2.1P + 1.1P0 + 3.2Y + e.

So,β1:每增加一个单位的P,Q将会减少2.1个单位

β2:每增加一个单位的PO,Q将会增加1.1个单位

β3: 每增加一个单位的Y,Q将会减少3.2个单位

b)不会 c)不会
BC两题希望会的高手指导

d) Test H0: β3 = 2 against H1: β3 1 2.
--> calc;list;tstat1=(b(3)-2)/0.72$

+------------------------------------+

| Listed Calculator Results |

+------------------------------------+

TSTAT1 = 1.665693
13个变量

在B等于0.05时。临界值为2.160和-2.160数据结果为 1.666 并且在飞拒绝区域内。

所以假设被接受在5%B等于0.1和0.01时。

临界值分别为1.771和-1.7713.012和-3.012

所以在b等于0.1和0.01时。假设也被接受

e)命令界面输入

--> CREA;qstar=q-rho*q[-1]$

--> CREA;pstar=p-rho*p[-1]$

-->CREA;p0star=p0-rho*p0[-1]$

--> CREA;ystar=y-rho*y[-1]$

--> SAMPLE;1-1$-->CREA;qstar=q*sqr(1-rho^2)$

-->CREA;pstar=p*sqr(1-rho^2)$

-->CREA;p0star=p0*sqr(1-rho^2)$

--> CREA;ystar=y*sqr(1-rho^2)$

重置数据，启用新数据

--> REGRESS;Lhs=QSTAR;Rhs=PSTAR,P0STAR,YSTAR$

+----------------------------------------------------+

| Ordinary leastsquares regression |

| Model was estimated May 16, 2013 at 08:39:04PM |

| LHS=QSTAR Mean = 50.41993 |

| Standard deviation = 22.44172 |

| WTS=none Number of observs. = 16 |

| Model size Parameters = 3 |

| Degreesof freedom = 13 |

| Residuals Sumof squares = 2067.257 |

| Standard error of e = 12.61030 |

| Fit R-squared = .7263530 |

| Adjusted R-squared = .6842534 |

| Model test F[ 2, 13] (prob) = 17.25 (.0002) |

| Diagnostic Loglikelihood = -61.59413 |

| Restricted(b=0) = -71.96146 |

| Chi-sq [ 2] (prob) = 20.73 (.0000) |

| Info criter. LogAmemiya Prd. Crt. = 5.240879 |

| Akaike Info. Criter. = 5.236389 |

| Autocorrel Durbin-Watson Stat. = 1.3385152 |

| Rho= cor[e,e(-1)] = .3307424 |

| Not using OLS or no constant. Rsqd & F may be <0. |

+----------------------------------------------------+

+--------+--------------+----------------+--------+--------+----------+

+--------+--------------+----------------+--------+--------+----------+

PSTAR | -1.88031580 .33750451 -5.571 .0001 136.751256

P0STAR | 1.12732312 .24288748 4.641 .0005 138.782307

YSTAR | 2.57014923 .78685350 3.266 .0061 58.5946562

--> calculate;list;pelast = b(1)*(136.751256/50.41993)$

+------------------------------------+

| Listed Calculator Results |

+------------------------------------+

P的弹性 PELAST = -5.099879

--> calculate;list;p0elast =b(2)*(138.782307/50.41993)$

+------------------------------------+

| Listed Calculator Results |

+------------------------------------+

P0的弹性 P0ELAST = 3.102989

--> calculate;list;yelast =b(3)*(58.5946562/50.41993)$

+------------------------------------+

| Listed Calculator Results |

+------------------------------------+

Y的弹性 YELAST = 2.986855

各个结果为 P的弹性为5.09, P0的弹性为3.10 ， Y的弹性为2.99

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全部回复

ermutuxia

2013-5-21 15:47:35

stata软件的结果

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wangyanse

2013-5-23 00:00:32

ermutuxia 发表于 2013-5-21 15:47
stata软件的结果

limdep

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h3327156

2013-5-23 00:59:01

b)  貌似问β1  β2  β3的正负符号有无违反或错误设定，
   建议楼主想想经济学告诉您的概念…【但这很容易见人见智】
   如果是我来答，我觉得β2在 a)中估出为正，对手票价高，我们就卖地比较好？
   不见得吧！对手票价高，消费者不一定就转而买咱机票…
   我想这个和两家机票是不是替代财货有关，此外，和竞争型态也有关，对手订票价提高，
   咱到底是要跟著提高…还是降价？？？这都进而影响出售机票量。

c)  您可以先执行个没有放constant term的回归阿！

--> REGRESS;Lhs=Q;Rhs=ONE,P,P0,Y$

+----------------------------------------------------+
| Ordinary least squares regression             |
| Model was estimated May 23, 2013 at 00:16:29AM    |
| LHS=Q       Mean                = 87.24375    |
|             Standard deviation = 27.93562    |
| WTS=none    Number of observs. =       16    |
| Model size Parameters          =       4    |
|             Degrees of freedom =       12    |
| Residuals Sum of squares    = 2616.380    |
|             Standard error of e  = 14.76590    |
| Fit       R-squared          = .7764920    |
|             Adjusted R-squared = .7206150    |
| Model test F[  3, 12] (prob) =  13.90 (.0003) |
| Diagnostic Log likelihood    =  -63.47868    |
|             Restricted(b=0)    =  -75.46515    |
|             Chi-sq [  3]  (prob) =  23.97 (.0000) |
| Info criter. LogAmemiya Prd. Crt. = 5.607784    |
|             Akaike Info. Criter. = 5.596958    |
| Autocorrel Durbin-Watson Stat.  =  1.1114092    |
|             Rho = cor[e,e(-1)] = .4442954    |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
Constant| 28.8437673    174.665253    .165 .8716
P    | -2.12350124    .34038998 -6.238 .0000 239.687500
P0    | 1.03456093    .46652664    2.218 .0466 243.125000
Y    | 3.08936605    .99889316    3.093 .0093 102.237500

就一般常见的Adjusted R-squared来看，好像摆了constant term没有比较高【反而下降】，
而且，从constant term那项的p-value看，此系数与零无异，所以貌似constant term可省略。
坦白说，摆不摆差异不大啦！【如果硬要两模型检定，也必支持两者无异】

结论：不需要。其实需要不需要不重要，因为摆不摆都没关系。

不过这里是EViews专版，怎么在问Limdep? 通常爱用Limdep的，都是挺支持Greene的，
楼主如果有最新的Limdep 10，可否发一个上来？

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wangyanse

2013-5-24 22:41:34

h3327156 发表于 2013-5-23 00:59
b) 貌似问β1 β2 β3的正负符号有无违反或错误设定，
建议楼主想想经济学告诉您的概念…【但这很 ...

哈哈，多谢。讲解的比较详细。。我也想要比较新的limdep。目前还在用论坛上的的limdep9.。。另外第二个问题您懂吗

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h3327156

2013-6-4 07:10:16

楼主另外问的 F test，请参考
R11.4.2 F Tests in Linear Models

/*以楼主资料为主的Limdep执行 */
--> REGRESS; Lhs=Q;Rhs=P,P0,Y
; CLS: b(1)+b(2)+b(3)=0$

+----------------------------------------------------+
| Ordinary least squares regression             |
| Model was estimated Jun 04, 2013 at 06:17:47AM    |
| LHS=Q       Mean                = 87.24375    |
|             Standard deviation = 27.93562    |
| WTS=none    Number of observs. =       16    |
| Model size Parameters          =       3    |
|             Degrees of freedom =       13    |
| Residuals Sum of squares    = 2622.326    |
|             Standard error of e  = 14.20273    |
| Fit       R-squared          = .7759840    |
|             Adjusted R-squared = .7415200    |
| Model test F[  2, 13] (prob) =  22.52 (.0001) |
| Diagnostic Log likelihood    =  -63.49684    |
|             Restricted(b=0)    =  -75.46515    |
|             Chi-sq [  2]  (prob) =  23.94 (.0000) |
| Info criter. LogAmemiya Prd. Crt. = 5.478718    |
|             Akaike Info. Criter. = 5.474228    |
| Autocorrel Durbin-Watson Stat.  =  1.0998728    |
|             Rho = cor[e,e(-1)] = .4500636    |
| Not using OLS or no constant. Rsqd & F may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
P    | -2.11839990    .32605643 -6.497 .0000 239.687500
P0    | 1.10188791    .21812294    5.052 .0002 243.125000
Y    | 3.19929914    .71632554    4.466 .0006 102.237500

+----------------------------------------------------+
| Linearly restricted regression                   |
| Ordinary least squares regression             |
| Model was estimated Jun 04, 2013 at 06:17:47AM    |
| LHS=Q       Mean                = 87.24375    |
|             Standard deviation = 27.93562    |
| WTS=none    Number of observs. =       16    |
| Model size Parameters          =       2    |
|             Degrees of freedom =       14    |
| Residuals Sum of squares    = 8279.932    |
|             Standard error of e  = 24.31920    |
| Fit       R-squared          = .2926750    |
|             Adjusted R-squared = .2421518    |
| Model test F[  1, 14] (prob) = 5.79 (.0305) |
| Diagnostic Log likelihood    =  -72.69503    |
|             Restricted(b=0)    =  -75.46515    |
|             Chi-sq [  1]  (prob) = 5.54 (.0186) |
| Info criter. LogAmemiya Prd. Crt. = 6.500316    |
|             Akaike Info. Criter. = 6.499001    |
| Autocorrel Durbin-Watson Stat.  = .5162647    |
|             Rho = cor[e,e(-1)] = .7418677    |
| Restrictns.  F[  1, 13] (prob) =  28.05 (.0001) |
| Not using OLS or no constant. Rsqd & F may be < 0. |
| Note, with restrictions imposed,  Rsqd may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
P    | -.82206760    .36882579 -2.229 .0441 239.687500
P0    | 1.41389310    .35960884    3.932 .0017 243.125000
Y    | -.59182550    .04457795 -13.276 .0000 102.237500

--> REGRESS; Lhs=Q;Rhs=P,P0,Y
; CLS: b(1)+b(2)+b(3)=0,
b(1)+b(2)=1$

+----------------------------------------------------+
| Ordinary least squares regression             |
| Model was estimated Jun 04, 2013 at 06:39:14AM    |
| LHS=Q       Mean                = 87.24375    |
|             Standard deviation = 27.93562    |
| WTS=none    Number of observs. =       16    |
| Model size Parameters          =       3    |
|             Degrees of freedom =       13    |
| Residuals Sum of squares    = 2622.326    |
|             Standard error of e  = 14.20273    |
| Fit       R-squared          = .7759840    |
|             Adjusted R-squared = .7415200    |
| Model test F[  2, 13] (prob) =  22.52 (.0001) |
| Diagnostic Log likelihood    =  -63.49684    |
|             Restricted(b=0)    =  -75.46515    |
|             Chi-sq [  2]  (prob) =  23.94 (.0000) |
| Info criter. LogAmemiya Prd. Crt. = 5.478718    |
|             Akaike Info. Criter. = 5.474228    |
| Autocorrel Durbin-Watson Stat.  =  1.0998728    |
|             Rho = cor[e,e(-1)] = .4500636    |
| Not using OLS or no constant. Rsqd & F may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
P    | -2.11839990    .32605643 -6.497 .0000 239.687500
P0    | 1.10188791    .21812294    5.052 .0002 243.125000
Y    | 3.19929914    .71632554    4.466 .0006 102.237500

+----------------------------------------------------+
| Linearly restricted regression                   |
| Ordinary least squares regression             |
| Model was estimated Jun 04, 2013 at 06:39:14AM    |
| LHS=Q       Mean                = 87.24375    |
|             Standard deviation = 27.93562    |
| WTS=none    Number of observs. =       16    |
| Model size Parameters          =       1    |
|             Degrees of freedom =       15    |
| Residuals Sum of squares    = 57864.94    |
|             Standard error of e  = 62.11008    |
| Fit       R-squared          =  -3.943195    |
|             Adjusted R-squared =  -3.943195    |
| Diagnostic Log likelihood    =  -88.24924    |
|             Restricted(b=0)    =  -75.46515    |
| Info criter. LogAmemiya Prd. Crt. = 8.318441    |
|             Akaike Info. Criter. = 8.318278    |
| Autocorrel Durbin-Watson Stat.  = .1290264    |
|             Rho = cor[e,e(-1)] = .9354868    |
| Restrictns.  F[  2, 13] (prob) = 136.93 (.0000) |
| Not using OLS or no constant. Rsqd & F may be < 0. |
| Note, with restrictions imposed,  Rsqd may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
P    |    .07155080    .90838782    .079 .9384 239.687500
P0    |    .92844920    .90838782    1.022 .3254 243.125000
Y    | -1.00000000 ......(Fixed Parameter).......

*为验证_楼主的资料拿到Stata_执行相同的检验*
. reg q p p0 y, noc

   Source |    SS    df    MS             Number of obs =    16
-------------+------------------------------          F(  3, 13) =  216.26
   Model |  130867.202    3  43622.4008          Prob > F    =  0.0000
Residual |  2622.32575 13  201.717365          R-squared    =  0.9804
-------------+------------------------------          Adj R-squared =  0.9758
   Total |  133489.528 16  8343.09551          Root MSE    =  14.203

------------------------------------------------------------------------------
         q |    Coef. Std. Err.    t P>|t|    [95% Conf. Interval]
-------------+----------------------------------------------------------------
         p | -2.1184 .3260564 -6.50 0.000 -2.822802 -1.413998
      p0 | 1.101888 .2181229    5.05 0.000    .6306619 1.573114
         y | 3.199299 .7163255    4.47 0.001    1.651772 4.746826
------------------------------------------------------------------------------
. test  p+p0+y=0

( 1)  p + p0 + y = 0

   F(  1, 13) = 28.05
         Prob > F = 0.0001

. test  (p+p0+y=0) (p+p0=1)

( 1)  p + p0 + y = 0
( 2)  p + p0 = 1

   F(  2, 13) =  136.93
         Prob > F = 0.0000

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