这个作业是用R语言统计各个国家的增长模型
Homework 2 Due
1.您已经收集了104个国家/地区的数据，以解决决定因素的难题
世界各国之间生活水平的差异。你从你的回忆中
宏观经济学讲座认为，新古典增长模型表明人均产出（人均
人均收入水平取决于储蓄率和人口增长
率。要测试此增长模型的预测，请运行以下回归：
= 0.339 – 12.894×n + 1.397×SK，= 0.621，SER = 0.177
其中RelPersInc是相对于美国的人均GDP，n是平均人口
1980-1990年的增长率，SK是1960年至1990年GDP的平均投资份额
（记住投资等于储蓄）。
（a）解释结果。这些迹象是否符合您的预期？
说明。
（b）您还记得，人力资本除物质资本外，在
确定一个国家的生活水平。因此，您收集有关的其他数据
1985年的平均受教育程度，并将此变量（Educ）添加到
以上回归。结果是修改后的回归输出：
= 0.046 – 5.869×n + 0.738×SK + 0.055×Educ，= 0.775，SER = 0.1377
加入Educ对您以前的成绩有何影响？
（c）检查回归输出后，您会发现只有86个观测值，
由于您的样本中并非所有104个国家都提供Educ数据。你一定要吗
比较两个之间的系数时，修改（b）中的某些语句
楷模？
（d）您的样本中巴西具有以下值：RelPersInc = 0.30，n = 0.021，SK =
0.169，Educ = 3.5。您的方程式是高估还是低估了相对GDP
工人？如果巴西设法使平均水平提高一倍，结果将会怎样？
受教育程度？
2.假设您已经收集了平均时薪（ahe）的横截面数据，
受教育年限（educ）和个人性别（您已编码个人
如果是女性，则为“ 1”；如果是男性，则为“ 0”；结果变量的名称为DFemme）。
面对您大学最近的学费上涨，您对恢复教育感兴趣，
也就是说，在您所在的机构工作一年，您将获得多少收入。至
调查此问题，运行以下回归：
= -4.58 + 1.71×educ
N = 14,925，R
2 = 0.18，SER = 9.30
一个。解释回归输出。
b。作为女性，您想知道如果输入二进制文件会如何影响这些结果
变量（DFemme），如果个人是女性，则取值为“ 1”，为“ 0”
对于男性。结果如下：
= -3.44-4.09×DFemme + 1.76×educ
N = 14,925，R
2 = 0.22，SER = 9.08
SE（?ி）= 2.06
SE（? ௗ௨）= 0.24
回归的标准误差（SER）降低而
回归R2增加了吗？
C。您是否认为您首先估计的回归遭受了遗漏的变量偏差？
（对FDemme进行t检验，看是否可以将其视为ahe的决定因素）
3.您想找到性别和婚姻状况对收入的影响。结果，你
考虑运行以下回归：
ahei =β0+β1×DFemmei +β2×DMarri
+β3×DSinglei
+β4×educi + … +用户界面
如果ahe是平均每小时收入，则DFemme是一个二元变量，其取值为
如果个人是女性，则为“ 1”，否则为“ 0”，则DMarr是一个二进制变量，采用
如果个人已婚，则为“ 1”，否则为“ 0”，DSingle将采用
如果个人未结婚，则为“ 1”，否则为“ 0”。您是的回归程序
使用或返回消息无法估计方程式或丢弃其中一个
系数。你为什么这么认为呢？
4. In the process of collecting weight and height data from 29 female and 81 male students at
your university, you also asked the students for the number of siblings they have. Although it
was not quite clear to you initially what you would use that variable for, you construct a new
theory that suggests that children who have more siblings come from poorer families and will
have to share the food on the table. Although a friend tells you that this theory does not pass the
“straight-face” test, you decide to hypothesize that peers with many siblings will weigh less, on
average, for a given height. In addition, you believe that the muscle/fat tissue composition of
male bodies suggests that females will weigh less, on average, for a given height. To test these
theories, you perform the following regression:
= –229.92 – 6.52 × Female + 0.51 × Sibs+ 5.58 × Height,
(44.01) (5.52) (2.25) (0.62)
R2 = 0.50, SER = 21.08
where Studentw is in pounds, Height is in inches, Female takes a value of 1 for females and is 0
otherwise, Sibs is the number of siblings (heteroskedasticity-robust standard errors in
parentheses).
(a) Carrying out hypotheses tests using the relevant t-statistics to test your two claims
separately (claims shown with bold font above), is there strong evidence in favor of your
hypotheses? Is it appropriate to use two separate tests in this situation?
(b) You also perform an F-test on the joint hypothesis that the two coefficients for
females and siblings are zero. The calculated F-statistic is 0.84. Find the relevant p-value.
Can you reject the null hypothesis? Is it possible that one of the two parameters is zero in
the population, but not the other?
(c) You are now a bit worried that the entire regression does not make sense and therefore
also test for the height coefficient to be zero. The resulting F-statistic is 57.25. Does that
prove that there is a relationship between weight and height?
5. Use the leadmort data set that you used in Homework 1. Again, you want to analyze the impact of lead
on infant mortality rate. But this time you want to control for a bunch of related variables. You end up
running the following regression:
??????? = ? + ?ଵ???? + ?ଶ?ℎ + ?ଷℎ??????? + ?
a. Run this regression and report the coefficients and standard errors, and R2.
b. Interpret your coefficient on lead (?ଵ).
c. Now you want to test the hypothesis that both lead and hardness are irrelevant in explaining
infrate. Write a single hypothesis to check these two variables simultaneously.
d. Let’s assume that homoscedasticity holds in our data. To test hypothesis above, write down
your restricted model. Run the restricted model, and report the coefficients, standard errors
and R2.
e. Using your results so far, find the F-statistic for your test.
f. Find the p-value of your test. What does this p-value tell us? Explain.
g. Test the same hypothesis using heteroscedasticity-robust variance-covariances. What is the
new F-statistic? P-value? Your decision to reject or not?