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 various 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 birth weight is the number of cigarettes the mother smokes during pregancy,)1(10ucigs bwght ++=ββwhere 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 axis) 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 β0 and β1. What is the sign of β1? What does it tell us?(d) Save the residuals, i uˆ ,from the above regression. Calculate ∑∑∑===⋅⋅ni in i in i iu bwght u cigs u111ˆ,ˆ,ˆ. What are the differences of these valuesfrom zero?Regress (1) i uˆ on cigs, and (2) i u ˆon 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 squares 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 1ˆβ is calculated.2. Since factors other than smoking that affect birth weight are likelyto 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 recognize this is)2(min 210uc fa cigs bwght +++=βββ(a) Plot family income, faminc, 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 and 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 linear relationship between these two based on theregression on model (2)? (e) Verify that 1211~ˆˆ~δβββ+=where 1~βis estimated from model (1), 1ˆβ and 2ˆβare estimated from model (2), and 1~δ is the slope coefficients from regressing faminc on cigs . (f) Regress cigs on faminc , and save the residuals, name them rcigs . Then regress bwght 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 pregnancy. 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 model)3(min min 22210uc fa c fa cigs bwght ++++=ββββDenote the fitted model asu c fa c fa cigs wght b ++++=23210min ˆmin ˆˆˆˆββββ (a) Perform OLS regression to get the estimated coefficients .3,2,1,ˆ=j j β (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 null in this case.(c) Report the p value for H0 :03=β. What does p value exactly tell us? (d) If we are interested in testing H 0 :01=β, perform this test using5% 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 H 0 : 02=β. (f) Test the hypothesis that 21ββ-=.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。