(#4) birthweight2.dta contains information, for a sample of 1,719 infants, on infant birth weight (in grams),
Apgar scores, demographic characteristics, and health behaviors of the mother.
For this problem, both the Stata code and output are given. You may reproduce it if you wish, but to receive
credit, you only need to answer the questions interpret the results. (You are NOT required to turn in a do-file,
log-file, or graphs with this question. You may write your answers concisely on a separate page to minimize
the number of pages in your upload file.)
(a) Consider the relationship between mother’s age (mage) and baby birthweight (bwght). To start, use Stata’s
twoway graph command to make a scatter plot along with the best fitting quadratic curve.
Stata notes. Recall that to graph a scatter plot combined with the OLS fitted line, you would type:
. twoway (scatter bwght mage) (lfit bwght mage)
To fit a quadratic model and graph it with the scatter plot, simply replace 1£it with qfit:
. twoway (scatter bwght mage) (qfit bwght mage)
XXXXXXXXXX
XXXXXXXXXX
1000
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mother's age, years
ted values
grams
(b) Suppose you were to estimate the model for birthweight that includes both mage and its square:
wght = Bo + P1 mage + B> magesq +u
Question: Based on the figure in (a), what sign would you expect to find for B 1? For Ba?
(c) Estimate the model and check your answer to (b). (You will first need to create the variable magesq.)
. gen magesq = mage“2
. reg bwght mage magesq
Source | ss af MS Number of obs 1,719
a mmm mmm mm mmm F(2, 1716) = 6.41
Model | XXXXXXXXXX XXXXXXXXXXProb > F 0.0017
Residual | XXXXXXXXXX, XXXXXXXXXXR-squared = 0.0074
-—- mmm -- Adj R-squared = 0.0063
XXXXXXXXXXRoot MSE 560.39
[95% Conf. Interval]
mage | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
magesq | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
cons
XXXXXXXXXX XXXXXXXXXX
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Question: Is the squared term statistically significant?
(d) To get a better visualization of the parabola, create the predicted values from your regression in (b).
Recall that the relevant command (following a regress command) is:
. predict yhat
(where yhat is the name of the variable that will contain the predicted or “fitted” values).
Then create a scatter plot of the fitted values (yhat) against mage.
. scatter yhat mage
Questions: Is the turning point in this parabola empirically relevant (are there observations in the range of
values above and below it)? What is the (approx..) mother’s age that “maximizes” birthweight (in a non-
causal sense)?
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mother's age, years
(e) Now consider the effect of maternal cigarette smoking and pre-natal doctor visits on the infant’s birthweight.
Estimate a model that includes the dummy variable for whether the mother smoked during pregnancy
(msmoke) and the dummy for mothers who had at least 10 prenatal doctor’s visits (prenat10). Also include the
interaction of these two dummy variables. (You will need to create the interaction variable msmokeXpn10.)
Report the results.
wght = Bo + B1 msmoke + Pz prenatl0 + Bs msmokeXpnl0 + u
. gen msmokeXpnl0 = msmoke*prenat10
. reg bught msmoke prenatl0 msmokeXpnl0
source | ss af Ms Number of obs = 1,719
———————— Hmmm mmm mmm mmm mmm mmm mmm mm F(3, XXXXXXXXXX
Model | XXXXXXXXXXProb > F 0.0000
Residual | XXXXXXXXXX, XXXXXXXXXXR-squared = 0.0224
+ Adj R-squared = 0.0207
|
P>|t| [95% Conf. Interval]
|
+ ———
msmoke | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
prenatl0 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
msmokeXpnl0 | XXXXXXXXXX XXXXXXXXXX397.886
_cons | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
(f) Use the coefficients from the model you estimated in (e) to calculate the following (round to nearest gram):
® The predicted infant birthweight for mothers who smoked and had >10 prenatal visits:
* The predicted infant birthweight for mothers who smoked and had <10 prenatal visits:
* The predicted infant birthweight for mothers who did not smoke and had <10 prenatal visits:
® The predicted effect of smoking on infant birthweight for mothers with >10 prenatal visits:
® The predicted effect of smoking on infant birthweight for mothers with <10 prenatal visits:
® The predicted difference in infant birthweights between mothers with >10 prenatal visits and those
with <10 prenatal visits (i.e. the predicted effect of prenat10) among mothers who smoke:
* Give two interpretations of the coefficient on msmokeXpnl10. What does it represent?
(g) Control linearly for mage in the regression from part (e).
. reg bwght mage msmoke prenatl0 msmokeXpnl0
Source | ss af MS Number of obs = 1,719
-— — — - F(4, 1714) = 10.07
Model | XXXXXXXXXX64 Prob > F = 0.0000
Residual | XXXXXXXXXX825 R-squared = 0.0230
————— —— - Adj R-squared = 0.0207
Total | XXXXXXXXXX Root MSE = 556.3
uwght | Coef. std. E
. tpt] [95% Conf. Interval]
mage | XXXXXXXXXX XXXXXXXXXX ~ XXXXXXXXXX
msmoke | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
prenatl0 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
msmokeXpnl0 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
cons | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
Question: Should we conclude that mother’s age has no significant effect on birthweight once we control fo
smoking and prenatal visits?
(h) Suppose you are interested in whether the effect of prenatal visits on birthweight differs by infant gender, and
you estimate the following regression:
. gen prenatlOXmale = prenatlO+male
. reg bught mage magesq prenatl0 prenatlOXmale
Source | ss af MS Number of obs = 1,719
_— -— — - F(4, 1714) = 8.33
Model | XXXXXXXXXX XXXXXXXXXXProb > F = 0.0000
Residual | XXXXXXXXXX038 R-squared = 0.0191
mmm — - Adj R-squared = 0.0168
XXXXXXXXXXRoot MSE = 557.41
std. E
. t >t] [95% Conf. Interval]
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
nage |
magesq | = XXXXXXXXXX = XXXXXXXXXX = XXXXXXXXXX
prenatl0 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
prenatlOXmale | XXXXXXXXXX XXXXXXXXXX143.553
cons | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
Question: Should you conclude that the effect of prenat10 is significantly larger for male babies?
‘Why or why not?
(i) Finally, consider the relationship between an infant's Apgar score at one minute (apgarlm) and the average
number of cigarettes the mother smoked per day (cigs). Suppose you estimate the following regression with cigs
in quadratic form:
. gen cigsq = cigs"2
. reg apgarlm cigs cigsq
Source | ss af MS Number of obs = 1,719
- F(2, 1716) = 3.99
Model | XXXXXXXXXX XXXXXXXXXXProb > F = 0.0186
Residual | XXXXXXXXXX, XXXXXXXXXXR-squared 0.0046
——— - - mmm Adj R-squared = 0.0035
Total | XXXXXXXXXX, XXXXXXXXXXRoot MSE = 1.1082
apgarim | Coef. Std. E
. tele] [95% Conf. Interval]
cigs | XXXXXXXXXX = XXXXXXXXXX004847
cigsq | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
_cons | XXXXXXXXXX
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Question: Should you conclude that there is no significant relationship between cigarette smoking and apgarIm?