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

= 0.339 – 12.894×n + 1.397×SK，= 0.621，SER = 0.177

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？

（b）您还记得，人力资本除物质资本外，在

1985年的平均受教育程度，并将此变量（Educ）添加到

= 0.046 – 5.869×n + 0.738×SK + 0.055×Educ，= 0.775，SER = 0.1377

（c）检查回归输出后，您会发现只有86个观测值，

（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

2.假设您已经收集了平均时薪（ahe）的横截面数据，

= -4.58 + 1.71×educ
N = 14,925，R
2 = 0.18，SER = 9.30

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

= -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

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

ahei =β0+β1×DFemmei +β2×DMarri
+β3×DSinglei
+β4×educi + … +用户界面

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.
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?

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