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第二章 简单线性回归模型2.1
（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 Squares
Date: 12/23/15 Time: 14:37Sample: 1 22
Included observations: 22
Coefficien
tStd. Errort-Statistic56.647940.128360
1.9608200.027242
28.889924.711834
VariableCX1
R-squared
Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic
Prob(F-statistic)
Prob. 0.00000.000162.5000010.088896.8493246.9485106.8726890.629074
0.526082 Mean dependent var0.502386 S.D. dependent var
Akaike info
7.116881criterion
1013.000 Schwarz criterion
Hannan-Quinn
-73.34257criter.
22.20138 Durbin-Watson stat0.000134
有上可知，关系式为y=56.64794+0.128360x1
②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 Squares
Date: 12/23/15 Time: 15:01Sample: 1 22
Included observations: 22
Coefficien
tStd. Errort-Statistic38.794240.331971
3.5320790.046656
10.983407.115308
VariableCX2
R-squared
Adjusted R-squaredS.E. of regressionSum squared residLog likelihood
Prob. 0.00000.000062.5000010.088896.3343566.4335426.357721
0.716825 Mean dependent var0.702666 S.D. dependent var
Akaike info
5.501306criterion
605.2873 Schwarz criterion-67.67792 Hannan-Quinn
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F-statistic
Prob(F-statistic)
criter.
50.62761 Durbin-Watson stat0.000001
1.846406
由上可知，关系式为y=38.79424+0.331971x2
③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 Squares
Date: 12/23/14 Time: 15:20Sample: 1 22
Included observations: 22
Coefficien
tStd. Errort-Statistic31.799560.387276
6.5364340.080260
4.8649714.825285
VariableCX3
R-squared
Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic
Prob(F-statistic)
Prob. 0.00010.000162.5000010.088896.8240096.9231946.8473740.952555
0.537929 Mean dependent var0.514825 S.D. dependent var
Akaike info
7.027364criterion
987.6770 Schwarz criterion
Hannan-Quinn
-73.06409criter.
23.28338 Durbin-Watson stat0.000103
由上可知，关系式为y=31.79956+0.387276x3
（2）①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（β1）=4.711834>t0.025(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。
②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（β2）=7.115308>t0.025(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。
③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0.537929，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（β3）=4.825285>t0.025(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。
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2.2（1）
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 Squares
Date: 12/23/15 Time: 17:46Sample (adjusted): 1 33
Included observations: 33 after adjustments
Coefficien
tStd. Errort-Statistic0.176124-154.3063
0.00407239.08196
43.25639-3.948274
Variable
XC
R-squared
Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic
Prob(F-statistic)
Prob. 0.00000.0004902.51481351.00913.2288013.3194913.259310.100021
0.983702 Mean dependent var0.983177 S.D. dependent var
Akaike info
175.2325criterion
951899.7 Schwarz criterion
Hannan-Quinn
-216.2751criter.
1871.115 Durbin-Watson stat0.000000
②由上可知，模型的参数：斜率系数0.176124，截距为—154.3063
③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0.983702，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（β2）=43.25639>t0.025(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。④用规范形式写出检验结果如下：
Y=0.176124X—154.3063
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(0.004072) (39.08196)
t= (43.25639) （-3.948274）R2=0.983702 F=1871.115 n=33
⑤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，
①进行点预测，由上可知Y=0.176124X—154.3063，代入可得：Y= Y=0.176124*32000—154.3063=5481.6617②进行区间预测：先由Eviews分析：
X
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera Probability Sum Sum Sq. Dev. Observations 6000.441 2689.280 27722.31 123.7200 7608.021 1.432519 4.010515 12.69068 0.001755 198014.5 1.85E+09
33
Y 902.5148 209.3900 4895.410 25.87000 1351.009 1.663108 4.590432 18.69063 0.000087 29782.99 58407195 33
由上表可知，
∑x2=∑（Xi—X）2=δ2x(n—1)= 7608.0212 x (33—1)=1852223.473(Xf—X)2=(32000— 6000.441)2=675977068.2当Xf=32000时，将相关数据代入计算得到：
5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2即Yf的置信区间为（5481.6617—64.9649, 5481.6617+64.9649）
(3) 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 Squares
Date: 12/23/15 Time: 18:04Sample (adjusted): 1 33
Included observations: 33 after adjustments
Variable
CoefficienStd. Errort-Statistic
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Prob.
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t
LNXC
R-squared
Adjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic
Prob(F-statistic)
0.980275-1.918289
0.0342960.268213
28.58268-7.152121
0.00000.00005.5731201.6841890.6620280.7527260.6925450.096208
0.963442 Mean dependent var0.962263 S.D. dependent var
Akaike info
0.327172criterion
3.318281 Schwarz criterion
Hannan-Quinn
-8.923468criter.
816.9699 Durbin-Watson stat0.000000
①模型方程为：lnY=0.980275lnX-1.918289
②由上可知，模型的参数：斜率系数为0.980275，截距为-1.918289
③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（β2）=28.58268>t0.025(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。
④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 Squares
Date: 12/23/15 Time: 20:11Sample: 1 12
Included observations: 12
Coefficien
tStd. Errort-Statistic-64.184001845.475
4.80982819.26446
-13.3443495.79688
Variable
XC
Prob. 0.00000.0000
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计量经济学第三版课后习题答案解析
