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

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 sizeParameters = 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 testF[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. |

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

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

|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

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 sizeParameters = 3 |

| Degreesof freedom = 13 |

| Residuals Sumof squares = 2067.257 |

| Standard error of e= 12.61030 |

| Fit R-squared = .7263530 |

| Adjusted R-squared = .6842534 |

| Model testF[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 |

| AutocorrelDurbin-Watson Stat.=1.3385152 |

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

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

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

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

Variable| Coefficient| Standard Error |t-ratio |P[|T|>t]| Mean of X|

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

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