Critique of image/~$itique.docx Critique of image/critique.docx I want critique for each image. No Plagiarism plzz  How has the artist used colors in the work(s)?  - What sort of effect do the colors have on the artwork?  - How as the artist used shapes within the work of art?  - How have lines been used in the work(s)? Has the artist used them as an  important or dominant part of the work, or do they play a different roll?  - What role does texture play in the work(s)? Has the artist used the illusion of texture or has the artist used actual texture? How has texture been used within the work(s)?  - How has the artist used light in the work(s)? Is there the illusion of a scene with lights and shadows, or does the artist use light and dark values in a more abstracted way?  - How has the overall visual effect or mood of the work(s)? Been achieved by the use of elements of art and principles of design.  - How were the artists design tools used to achieve a particular look or focus?  Critique of image/golden retriever 1 5x7.jpg Critique of image/marilyn.jpg Assignment 2 The goal of the next few questions is to help you intuitively understand omitted variable bias and too-many variables bias, multicollinearity, and heteroskedasticity using a simulation in Stata. Introduction. There's an important debate over how we can get more children to be able to read by 3rd grade. I have heard anecdotal evidence that the state government plans the number of prisons to build based on regressions that use current-year 3rd grade reading scores on the RHS, which might be suggestive of the importance of this goal. But we won't worry about the causal e�ect of literacy on crime in this assignment. As we saw in class, children from poor families are already behind in terms of reading ability in fall of Kinder- garten. This is a problem. Local governments have two main policies to try to solve this problem: free full-day preschool, and family income supports. Omitted variable & too-many variables bias. Question 1. Suppose the process that determines child test score in Kindergarten is given by test scorei = β0 + β1preschooli + β2incomei + �i where β1,β2 > 0 and preschooli is a continuous measure of �preschool quality.� Preschool quality can be purchased with cash, and is purchased in cash according to the linear model preschooli = α0 + α1incomei + ηi You should interpret both of these linear models as structural models of human behavior. In other words, if you gave a random family another dollar, the family would indeed purchase α1 more units of preschool quality, and the family would purchase other children's stu� that has β2 additional e�ect on test scores. This means that the total e�ect on test scores of giving the family another dollar is: (a) α0β1 (b) α1 (c) β2 + β1α1 (d) α1β1 + β2 Question 2. Let's try to simulate this model in Stata. Run Part I in the �le �assignment2.do.� This will generate a fake dataset of 1000 students for this problem a.

1. Critique of image/~$itique.docx
Critique of image/critique.docx
I want critique for each image. No Plagiarism plzz
How has the artist used colors in the work(s)?
- What sort of effect do the colors have on the artwork?
- How as the artist used shapes within the work of art?
- How have lines been used in the work(s)? Has the artist used
them as an
important or dominant part of the work, or do they play a
different roll?
- What role does texture play in the work(s)? Has the artist used
the illusion of texture or has the artist used actual texture? How
has texture been used within the work(s)?
- How has the artist used light in the work(s)? Is there the
illusion of a scene with lights and shadows, or does the artist
use light and dark values in a more abstracted way?
- How has the overall visual effect or mood of the work(s)?
Been achieved by the use of elements of art and principles of
design.
- How were the artists design tools used to achieve a particular
look or focus?
Critique of image/golden retriever 1 5x7.jpg
Critique of image/marilyn.jpg
Assignment 2

2. The goal of the next few questions is to help you intuitively
understand omitted variable bias and too-many
variables bias, multicollinearity, and heteroskedasticity using a
simulation in Stata.
Introduction. There's an important debate over how we can get
more children to be able to read by 3rd
grade. I have heard anecdotal evidence that the state
government plans the number of prisons to build based on
regressions that use current-year 3rd grade reading scores on the
RHS, which might be suggestive of the importance
of this goal. But we won't worry about the causal e�ect of
literacy on crime in this assignment.
As we saw in class, children from poor families are already
behind in terms of reading ability in fall of Kinder-
garten. This is a problem. Local governments have two main
policies to try to solve this problem: free full-day
preschool, and family income supports.
Omitted variable & too-many variables bias.
Question 1. Suppose the process that determines child test score
in Kindergarten is given by
test scorei = β0 + β1preschooli + β2incomei + �i
where β1,β2 > 0 and preschooli is a continuous measure of
�preschool quality.�
Preschool quality can be purchased with cash, and is purchased
in cash according to the linear model
preschooli = α0 + α1incomei + ηi
You should interpret both of these linear models as structural
models of human behavior. In other words, if you

3. gave a random family another dollar, the family would indeed
purchase α1 more units of preschool quality, and the
family would purchase other children's stu� that has β2
additional e�ect on test scores. This means that the total
e�ect on test scores of giving the family another dollar is:
(a) α0β1
(b) α1
(c) β2 + β1α1
(d) α1β1 + β2
Question 2. Let's try to simulate this model in Stata. Run Part I
in the �le �assignment2.do.� This will
generate a fake dataset of 1000 students for this problem
assuming that α0 = β0 = 0, α1 = 0.5, and β1 = β2 = 1.
(You can easily play around by modifying these parameter
assumptions.)
Regress testscore on preschool. As an estimator for β1, this
regression's coe�cient is
(a) biased upward
(b) biased downward
Question 3. A big city government is thinking about
implementing a program that will raise a family's
preschool quality by 1 unit. An analyst uses the regression you
ran in the previous question to make the case that
this program is a highly e�ective way to improve student test
scores�in particular it is better than direct income
supports.
You counter that students who go to good preschools probably
come from wealthier backgrounds, so at the very
least the analyst should be controlling for family income. The
analyst retorts: �these kinds of families wouldn't
spend a dime of their own income on preschool!�

4. The analyst is proposing the testable null hypothesis that at
least for the families he is considering,
(a) β2 = 0
(b) β1 = 0
(c) α1 = 0
(d) α0 = 0
Question 4. Were the analyst's claim true, his estimator for β1
would be
(a) unbiased and consistent
(b) biased and inconsistent
Question 5. You gather appropriate data and show that even in
the analyst's population, α1 is signi�cantly
positive. The analyst then suggests that now that we have the
nice data you collected, why don't we run the
regression
test scorei = β0 + β1preschooli + β2incomei + �i
and then check whether β1 exceeds β2c, where c is the cost of a
unit of government-provided preschool in dollars?
He reasons that if β1 > β2c, the government should provide
preschool since the test score return per dollar for
preschool exceeds that for income supports; otherwise the
government should provide income supports.
1
Why might the analyst be wrong?
(a) The estimator for β1 is inconsistent because of the inclusion
of income on the RHS of the regression
(b) One e�ect of income supports may be to increase family
preschool purchases, thus the e�ect of income

5. supports is probably greater than β2 (too-many variables bias).
Multicollinearity.
Question 6. Now we want to know whether income supports
during preschool or before preschool are better.
We consider the model
test scorei = β0 + β1income_beforei + β2income_duringi + �i
Try part II of the simulation. There, income_during is
income_before plus a very small income change.
Regress test score on income_before and income_during. You'll
notice that at N = 100 observations, the
con�dence intervals for these parameters are very loose. Try N
= 1000 observations by changing the -set obs 100-
code to -set obs 1000-. Then try N = 10000. Notice that you
need a ton of observations before the con�dence
intervals really start to tighten. Why?
(a) Hard to distinguish income_before from income_during.
(b) The OLS estimators for β1 and β2 are ine�cient.
(c) The OLS estimators for β1 and β2 are biased.
(d) Hard to distinguish income_during from the constant.
Heteroskedasticity and weighted least squares.
The above analysis assumed that you could get individual-level
data on income, preschool enrollment, and
Kindergarten test scores. You might be able to do this in a
survey dataset like the ECLS-K, but more generally
you might �nd yourself working with averages at the school
district level for instance.
Run part III of assignment2.do. This part simulates data for
school districts of various sizes. The simulated

6. data includes �population,� a variable that gives you the total
number of kids in the district. There's one really big
district�this is supposed to help you have some empathy for me
since oftentimes I'm studying New York State and,
you know, New York City is a single school district...
Try the regression
reg avgtestscore avgincomebefore avgincomeduring, robust
And then try the weighted regressions
reg avgtestscore avgincomebefore avgincomeduring
[w=population], robust
and
reg avgtestscore avgincomebefore avgincomeduring
[w=sqrtpop], robust
Make sure you understand what these weighted regressions are
doing�review the lecture slides if need be.
For me, all three approaches work reasonably well. Weighting
by the square root of population seems to have
the tightest con�dence intervals around the true parameter
values (because this is a simulation we all know the
true parameter values�inspect the code to �nd them). I think
there are theoretical reasons to justify the square
root of population as the �best� weights in this case. Maybe
I'll give you the chance to explore this deeper on your
midterm exam.
For now let's make this simulation more realistic. Imagine that
each district has some measurement error for
average test scores. Thus run the regressions
reg avgtestscorewithdistrictshock avgincomebefore
avgincomeduring, robust
reg avgtestscorewithdistrictshock avgincomebefore
avgincomeduring [w=pop], robust
and

7. reg avgtestscorewithdistrictshock avgincomebefore
avgincomeduring [w=sqrtpop], robust
I generally �nd that with district-level shocks regular
unweighted OLS works better, followed by weighting by
the square root of population. My intuition was that if there are
district-level errors in measuring the dependent
variable, then we don't want to put a ton of weight on New York
City, because then our OLS regression will be
driven mostly by whether New York City happens to have a
high or low error and high or low RHS variables.
(In some analysis I was undertaking last fall, I was using
teacher employment data and New York City had the
unfortunate problem of �losing� all of its guidance counselors
for a few years... wouldn't have been such a big deal
if I wasn't weighting by district enrollments! It's tough when
your analysis rests on a some 9-to-5er not making a
coding mistake.)
Question 7. We might consider weighting by total district
population/enrollment in the previous regressions
because
(a) larger school districts are more important than smaller
school districts
2
(b) the dependent and independent variables, which are
averages, will be estimated more precisely for larger
school districts
(c) population is an omitted variable
(d) all of the above

8. Question 8. In the regression following this question, r_1 is fall
K reading test score, incthous_1 is household
income in thousands in fall K, and age_1 is the child's age in
months at the time of taking the test.
Richard's friend Kyle is 3 months younger than him, but
attended the same school and was in the same cohort,
and their families have about the same total household income.
If they took this exam on the same day in
Kindergarten, what do you expect Kyle's score would be
relative to Richard's? (For your information, a standard
deviation of r_1 is about 10.)
(a) about 1.14 scaled points more (or 11.4% of a standard
deviation)
(b) about 0.38 scaled points less (or 3.8% of a standard
deviation)
(c) about 0.38 scaled points more (or 3.8% of a standard
deviation)
(d) about 1.14 scaled points less (or 11.4% of a standard
deviation)
. reg r_1 incthous_1 age_1
Source | SS df MS Number of obs = 16 ,747
−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
− F(2 , 16744) = 794.64
Model | 152935.97 2 76467.9852 Prob > F = 0.0000
Residual | 1611276.4 16 ,744 96.2300764 R−squared = 0.0867
−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
− Adj R−squared = 0.0866
Total | 1764212.37 16 ,746 105.35127 Root MSE = 9.8097

9. −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
r_1 | Coef . Std . Err . t P>|t | [95% Conf . Interval ]
−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
incthous_1 | .0451514 .0013383 33.74 0.000 .0425283 .0477745
age_1 | .3830728 .017546 21.83 0.000 .3486807 .4174649
_cons | 6.671546 1.208196 5.52 0.000 4.303354 9.039738
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
Question 9. Download the dataset kindergarten_version2.dta
from the course website.
Generate a new variable being a child's growth on the math
exam score from Fall K to Spring K, m_2 minus
m_1. Generate a new variable equal to the child's age growth in
month, age_2 minus age_1. Regress math growth
on age growth and enroll_1. Use robust standard errors.
Let βE be the coe�cient for enroll_1 in this regression.
Consider the hypothesis test
H0 : βE = 0
HA : βE < 0
What's the smallest signi�cance level at which you can reject
the null hypothesis? (Careful�this is a one-tailed
test!)
(a) about 1.2%
(b) about 11.8%

10. (c) about 5.9%
(d) about 4.1%
Question 10. The ECLS-K uses a complicated sampling scheme,
and to account for this the National Center for
Education Statistics (NCES) includes sampling weights
sample_weight which they recommend we use in estimation.
Re-run your previous regression using these sample weights
(put �[w=sample_weight]� before the comma in your
regression.)
With this new speci�cation, what's the smallest signi�cance
level at which you can reject the null hypothesis?
(a) about 0.1%
(b) about 10.4%
(c) about 5.2%
(d) about 3.4%
3
Question 11. Finally, the ECLS-K is a clustered sample. This
means that the NCES �rst samples schools and
then samples students within schools. This sampling approach
violates OLS assumption 2: simple random sample,
since the NCES is not �shaking up the whole country� and
drawing children at random. Because child outcomes
are probably positively correlated within school, the standard
errors are likely overstated.
One very general (and in many ways �hands-free�) way to
control for this is to use �cluster-robust� standard
errors. As the name implies, these standard errors are robust to
heteroskedasticity, and also take into account
within-cluster correlation.

11. Try it: replace the �robust� option in your current regression
with �vce(cluster schlid)�. This will tell Stata to
calculate cluster-robust standard errors, where the clusters are
school IDs.
With this new speci�cation, what's the smallest signi�cance
level at which you can reject the null hypothesis?
(a) about 100%
(b) about 15%
(c) about 30%
(d) about 10%
Question 12. Open the kindergarten_version2.dta dataset, and
plot a histogram of income_1. There are
some crazily large incomes. We know that OLS and other
expectation-based analyses do not behave well when
there are very large outliers. What to do?
One approach is to log very right-skewed variables like this.
Apparently the income_1 variable is never less than
1, so this will work in this case: gen logincome_1 =
log(income_1). A histogram of logincome_1 is much closer to
normal, especially in the upper tail (you can assess this using -
qnorm-, as you learned in the last assignment.)
Recall that the test scores were also very right-skewed. Log the
math test score, creating a new variable logm_1.
Then regress log reading score on log income. In other words,
�t the model
log(math score) = β0 + β1log(income) + �
The standard approach to interpret this regression is to
di�erentiate both sides w.r.t. income, treating math
score as a function of income:

12. d
dincome
log(math score) = β
d
dincome
log(income)
I'm guessing it makes sense to assume � is not a function of
income under OLS assumption 1.
If you play around with this expression you'll get
%∆math score = β1%∆income
or
%∆math score
%∆income
= β1
thus β1 is interpreted as an elasticity. Which is lovely and very
economic.
This approach (using di�erentiation) has for some reason never
confronted me as intuitive, because I cannot
see it with discrete changes in income using the original
conditional expectations model. Nevertheless, you should
remember that in a log-log regression like this, we give β1 the
interpretation of an elasticity: it's the % change in
the outcome variable expected from a 1% increase in the RHS
variable. For example if β1 = 3, then a 3% increase
in math score is expected from a 1% increase in income.

13. According to your estimates, a 1% increase in income is
associated with about a
(a) 0.12% increase in math test score
(b) 1.2% increase in math test score
(c) 12% increase in math test score
(d) 1.9% increase in math test score
4