第一题一、实验目的（1）将数据输入并建立工作文件（2）估计参数（3）进行假设检验（4）进行点预测和区间预测（5）对简单的问题进行分析二、实验要求（1） 掌握一元线性回归模型的估计方法（2） 掌握一元线性回归模型的检验方法（3） 掌握一元线性回归模型的预测方法三、实验原理普通最小二乘法四、实验内容1A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth rate that is too low can put an infant at risk for contracting various illnesses. Since factors other than cigarette smoking that affect birth weight are likely to be correlated with smoking, we should take those factors into account. For example, higher income generally results in access to better prenatal care, as well as better nutrition for the mother. An equation that recognizes this is(i) What is the most likely sign for?(ii) Do you think cigs and faminc are likely to be correlated? Explain why the correlation might be positive or negative.(iii) Now estimate the equation with and without faminc, using the data in BWGHT.RAW. Report the results in equation form, including the sample size and R-squared. Discuss your results, focusing on whether adding faminc substantially changes the estimated effect of cigs on bwght.(i)估计的值为正数。(ii)实验得：Covariance Analysis: OrdinaryDate: 05/13/13 Time: 19:19Sample: 1 1388Included observations: 1388Correlationt-StatisticProbabilityCIGSFAMINCCIGS1.000000-FAMINC-0.1730451.000000-6.540971-0.0000-1.由实验数据得，二者相关系数为-0.173045，可知，二者负相关。2.T值为-6.540971，不等于0，可知二者相关。3.本题中，假设cigs与faminc的相关系数为0，即二者不相关，试验数据得，p值为0.00000.05，拒绝原假设，所以二者相关。(iii) Dependent Variable: BWGHTMethod: Least SquaresDate: 05/13/13 Time: 19:39Sample: 1 1388Included observations: 1388VariableCoefficientStd. Errort-StatisticProb.CIGS-0.4634080.091577-5.0603150.0000FAMINC0.0927650.0291883.1781950.0015C116.97411.048984111.51180.0000R-squared0.029805Mean dependent var118.6996Adjusted R-squared0.028404S.D. dependent var20.35396S.E. of regression20.06282Akaike info criterion8.837772Sum squared resid557485.5Schwarz criterion8.849089Log likelihood-6130.414Hannan-Quinn criter.8.842005F-statistic21.27392Durbin-Watson stat1.921690Prob(F-statistic)0.000000Dependent Variable: BWGHTMethod: Least SquaresDate: 05/13/13 Time: 19:40Sample: 1 1388Included observations: 1388VariableCoefficientStd. Errort-StatisticProb.CIGS-0.5137720.090491-5.6776090.0000C119.77190.572341209.26680.0000R-squared0.022729Mean dependent var118.6996Adjusted R-squared0.022024S.D. dependent var20.35396S.E. of regression20.12858Akaike info criterion8.843598Sum squared resid561551.3Schwarz criterion8.851142Log likelihood-6135.457Hannan-Quinn criter.8.846420F-statistic32.23524Durbin-Watson stat1.924390Prob(F-statistic)0.000000分析：当增加变量faminc后，cigs前的系数由-0.513772变为-0.463408，其变化很小，因此是否加入变量faminc对cigs影响很小。五、实验步骤（1）输入数据（2）输入方程bwght=c(1)+c(2)*cigs+c(3)*faminc（3） 估计参数Dependent Variable: BWGHTMethod: Least SquaresDate: 05/13/13 Time: 19:48Sample: 1 1388Included observations: 1388VariableCoefficientStd. Errort-StatisticProb.CIGS-0.4634080.091577-5.0603150.0000FAMINC0.0927650.0291883.1781950.0015C116.97411.048984111.51180.0000R-squared0.029805Mean dependent var118.6996Adjusted R-squared0.028404S.D. dependent var20.35396S.E. of regression20.06282Akaike info criterion8.837772Sum squared resid557485.5Schwarz criterion8.849089Log likelihood-6130.414Hannan-Quinn criter.8.842005F-statistic21.27392Durbin-Watson stat1.921690Prob(F-statistic)0.000000方程为：bwght=116.9741-0.463408*cigs+0.092765*faminc （111.5118）（-5.060315）（3.178195） N=1388 R2=0.029805 F-statistic=21.27392（4） 假设检验变量cigs的t-statistic=-5.060315，p值为0.00000.05，参数显著；变量faminc的t-statistic=3.178195，p值为0.00150.05，参数显著；方程整体检验： F-statistic=21.27392，p值为0.0000000.05，方程整体显著。 (5)预测（点预测和区间预测）点预测：obsBWGHTBWGHTF1109.0000118.22652133.0000117.66993129.0000117.02054126.0000118.41205134.0000119.52526118.0000117.66997140.0000123.0038886.00000119.52529121.0000119.525210129.0000120.452811101.0000119.525212133.0000119.52521361.00000117.577114104.0000117.94821592.