实验三.docx

1、实验三实 验（实训）报 告项 目 名 称 多元线性回归模型 所属课程名称 应用回归分析 项 目 类 型 验证性实验 实验(实训)日期 11年11月12 日 班 级 09统计1 学 号 姓 名 指导教师 浙江财经学院教务处制一、实验（实训）概述：【目的及要求】目的: 掌握多元线性回归模型估计、检验、预测，标准化回归方程的估计,残差的性质等。要求: 运用软件进行多元线性回归模型的相关计算,按具体的题目要求完成实验报告。并及时上传到给定的FTP！【基本原理】 t 检验, F检验, OLS的残差的各种性质等. 【实施环境】（使用的材料、设备、软件）STATA软件或SPSS 软件二、实验（实训）内容：【

2、项目内容】多元线性回归模型估计、回归系数和回归方程检验、标准化回归方程、预测。【方案设计】共含2道题目,第一题为英文题目来自北大的中级计量经济学的练习,该题目设计地很好,从一元到多元,特别是一些理论上的知识通过具体的计算来加深理解和掌握. 第二题为中文题目来自课本,强调对课本涉及的基础知识的掌握.【实验（实训）过程】（步骤、记录、数据、程序等）附后【结论】（结果、分析）附后三、指导教师评语及成绩：评语：成绩： 指导教师签名： 批阅日期：12年11月实验三 报告多元线性回归模型（验证性实验）实验类型：验证性实验实验目的：掌握多元线性回归模型估计、检验、预测，标准化回归方程的估计等。实验内容：多元

3、线性回归模型估计、回归系数和回归方程检验、标准化回归方程、预测。实验要求：运用软件进行多元线性回归模型的相关计算,按具体的题目要求完成实验报告。并及时上传到给定的FTP！实验题目一： 来源于北大的中级计量经济学的相关题目。In this exercise we study the effect of smoking during pregnancy on infant health. One measure of infant health is birth weight; a too low birth weight puts the infant at the risk of variou

4、s illnesses. The dataset bwght.dta contains the data on 1388 infants birth weight, measured in ounces, and other factors that could affect their weights. After reading in the data, use command describe to see the labels for all the variables.1. If we believe that the single most important factor for

5、 birth weight is the number of cigarettes the mother smokes during pregancy,where bwght measures birth weight in ounces, and cigs is the number of cigerattes smoked per day during preganancy.(a) Find out the mean, minimum and maximum for bwght and cigs.(b) Provide scatter plots for bwght (at the y a

6、xis) against cigs (at the x axis). What can you observe from this plot?(c) Regress bwght on an intercept and cigs. Report the estimated oefficients and standard errors for 0 and 1. What is the sign of 1? What does it tell us?(d) Save the residuals, ,from the above regression. Calculate. What are the

7、 differences of these values from zero? Regress (1) on cigs, and (2) on bwght. Report the estimated coefficients and the related t statistics. Report R-squared and adjust R-squared and comment on these results.(e) What are the Total sum of squares, explained sum of squares, and residual sum of squar

8、es of regressing model (1)? Report the R-squared and describe how R-squared explains the fit of model (1). (f) Calculate the correlation coefficient of bwght and cigs. What is the relation of this value with R-squared?(g) Show how the standard error of is calculated.2. Since factors other than smoki

9、ng 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 prenatalcare, as well as better nutrition for the mother. An equation that recognize this is(a) Plot family income, faminc

10、, against cigs, and calculate the correlation coefficient among these two.(b) Regress faminc on cigs. Report the results in equation form with standard errors, and discuss what information does R-squared deliver.(c) Regress model (2), report the results in equation form, including the sample size an

11、d the R-squared.Discuss your results, focusing on whther adding faminc substantially changes the estimated effect of cigs on bwght.(d) It is said that there is a linear relation between the mean of bwght and the means of cigs and faminc. Without any calculation can you tell us what is the exact line

12、ar relationship between these two based on the regression on model (2)?(e) Verify thatwhere is estimated from model (1), and are estimated from model (2), and is the slope coefficients from regressing faminc on cigs.(f) Regress cigs on faminc, and save the residuals, name them rcigs. Then regress bw

13、ght on rcigs. Compare the estimated slope coefficients for rcigs with the coefficients on cigs obtained from model (2). Compare also the estimated standard errors. What conclusions can you draw?(g) There is another variable called packs. It measures the number of packs of cigerattes smoked during pr

14、egnancy. Now regress bwght to cigs, f aminc, and packs. Can you get estimated coefficients for this model? Why not? 3. It is suspected that family income may have nonlinear effect on the birth weight of the babies. In particular, one may think fit the following modelDenote the fitted model as(a) Per

15、form OLS regression to get the estimated coefficients (b) State the null hypothesis that only linear wealth effect matters, and also write out the alternative hypothesis for a two-sided test. Report the t statistics at 5% significance level, will we reject the nullin this case.(c) Report the p value

16、 for H0 :. What does p value exactly tell us?(d) If we are interested in testing H0 :, perform this test using 5% significance level. Can we reject the null that cigarette smoking during preganancy has no partial effect on birth weight?(e) Report the 5% confidence interval for H0 :.(f) Test the hypo

17、thesis that.实验题目二：研究货运总量y（万吨）与工业总产量x1(亿元)，农业总产值x2（亿元），居民非商品支出x3（亿元）的关系。数据如表：.计算y,x1,x2,x3的相关系数矩阵；.求y关于x1,x2,x3的三元线性回归方程；.对所求得的方程作拟合度检验.对每个回归系数作显著性检验；.对回归方程作显著性检验；.如果有的回归系数没有通过显著性检验，将其剔除，重新建立回归方程，再作回归方程的显著性检验和回归系数的显著性检验；.求出新回归方程的每一个回归系数的置信水平为的置信区间；.求新回归方程的标准化回归方程；.求当x1=75, x2=42时的y的预测值，给定的置信水平，计算其置信区

18、间？数据如下：y x1 x2 x3 160 70 35 1.0 260 75 40 2.4 210 65 40 2.0 265 74 42 3.0 240 72 38 1.2 220 68 45 1.5 275 78 42 4.0 160 66 36 2.0 275 70 44 3.2 250 65 42 3.0题目来源于何晓群第3章 习题3.11实验题目一分析报告：1:(a). su bwght Variable | Obs Mean Std. Dev. Min Max-+- bwght | 1388 118.6996 20.35396 23 271. su cigs Variable |

19、Obs Mean Std. Dev. Min Max-+- cigs | 1388 2.087176 5.972688 0 50(b) (c) . reg bwght cigs Source | SS df MS Number of obs = 1388-+- F( 1, 1386) = 32.24 Model | 13060.4194 1 13060.4194 Prob F = 0.0000 Residual | 561551.3 1386 405.159668 R-squared = 0.0227-+- Adj R-squared = 0.0220 Total | 574611.72 13

20、87 414.283864 Root MSE = 20.129- bwght | Coef. Std. Err. t P|t| 95% Conf. Interval-+- cigs | -.5137721 .0904909 -5.68 0.000 -.6912861 -.3362581 _cons | 119.7719 .5723407 209.27 0.000 118.6492 120.8946 均方误为0.572和0.0904 sig=0.000，所以回归方程显著(d) =0 =0 , =0 Source | SS df MS Number of obs = 1388-+- F( 1, 1

21、386) = 32.24 Model | 13060.4194 1 13060.4194 Prob F = 0.0000 Residual | 561551.3 1386 405.159668 R-squared = 0.0227-+- Adj R-squared = 0.0220 Total | 574611.72 1387 414.283864 Root MSE = 20.129(e) sst=574611.72 ssr=561551.3 sse=13060.4194 r2=0.0227,所以不能很好的解释吸烟量与孩子体重的关系，解释平方和只占了2.27%。(f) . corr bwght

22、 cigs(obs=1388) | bwght cigs-+- bwght | 1.0000 cigs | -0.1508 1.0000相关系数为-0.1508(g) 的标准误=-0.513772/-5.68=0.09052:(a) | bwght faminc cigs-+- bwght | 1.0000 faminc | 0.1089 1.0000 cigs | -0.1508 -0.1730 1.0000(b) Source | SS df MS Number of obs = 1388-+- F( 1, 1386) = 42.78 Model | 14584.7911 1 14584.

23、7911 Prob F = 0.0000 Residual | 472475.223 1386 340.891214 R-squared = 0.0299-+- Adj R-squared = 0.0292 Total | 487060.014 1387 351.160789 Root MSE = 18.463- faminc | Coef. Std. Err. t P|t| 95% Conf. Interval-+- cigs | -.5429278 .0830042 -6.54 0.000 -.7057551 -.3801004 _cons | 30.15984 .524988 57.45

24、 0.000 29.12999 31.1897R2=0.0299，解释平方和只占2.99%，不能很好地解释吸烟与家庭收入的关系(c) Source | SS df MS Number of obs = 1388-+- F( 2, 1385) = 21.27 Model | 17126.2088 2 8563.10442 Prob F = 0.0000 Residual | 557485.511 1385 402.516614 R-squared = 0.0298-+- Adj R-squared = 0.0284 Total | 574611.72 1387 414.283864 Root M

25、SE = 20.063- bwght | Coef. Std. Err. t P|t| 95% Conf. Interval-+- faminc | .0927647 .0291879 3.18 0.002 .0355075 .1500219 cigs | -.4634075 .0915768 -5.06 0.000 -.6430518 -.2837633 _cons | 116.9741 1.048984 111.51 0.000 114.9164 119.0319R2=0.0298，家庭收入与孩子的体重正相关，吸烟与孩子的体重负相关，且解释平方和只占2.98%(d) (e) =-0.514

26、， = 0.0928 ， =-0.4634， =-0.543，所以有(f) 系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)118.700.542219.164.000Unstandardized Residual-.463.092-.134-5.031.000a. 因变量: bwght系数标准为与（2）中的斜率相等(g) Source | SS df MS Number of obs = 1388-+- F( 1, 1386) = 32.24 Model | 13060.4194 1 13060.4194 Prob F = 0.0000 Residual | 561551

27、.3 1386 405.159668 R-squared = 0.0227-+- Adj R-squared = 0.0220 Total | 574611.72 1387 414.283864 Root MSE = 20.129- bwght | Coef. Std. Err. t P|t| 95% Conf. Interval-+- cigs | -.5137721 .0904909 -5.68 0.000 -.6912861 -.3362581 packs | (dropped) _cons | 119.7719 .5723407 209.27 0.000 118.6492 120.8946-