Sociology 362
data exercise 1
1. The following table shows, for a period of 14 months, gasoline lead sales (metric tons) in Massachusetts
and the mean lead (ug/dl) concentrations in umbilical-cord blood of babies born at a Boston hospital.
month leaded gas cord lead
1 141 6.4
2 166 6.1
3 161 5.7
4 170 6.9
5 148 7.0
6 136 7.2
7 169 6.6
8 109 5.7
9 117 5.7
10 87 5.3
11 105 4.9
12 73 5.4
13 82 4.5
14 75 6.0
a. Use the input varlist command to input these data into Stata, and then use save filespec to create a
.dta file in Stata internal format.
b. Find the usual univariate summary statistics for all the variables. One way to do this is with the
command summarize month cordld ldgas, where the words in italics are the names I gave to the
variables.
c. Find the covariance and correlation between all three variables. Try correlate month cord ldgas and the
same command tihe the option ,cov added after the variable names. What do these quantities tell us
about the relationships?
d. Graph the gas and cord series against month (”time plots”), and graph the cord series against the gas
series. Are these about what you would expect based on the correlations? How do these graphs manifest
the relative magnitudes of the correlations?
For the following problems, first do them “by hand,” that is, without using Stata’s regress or predict
commands. You can use Stata’s other commands to generate the five fundamental quantities needed to
find the least-squares solutions, or to produce vectors of fitted values, residuals, etc. In other words, you
can use Stata as a calculator. Once you’re done, then use regress and predict to check your answers.
e. Let ˆ
Yi=a+bXibe the line expressing cord (Y) as a linear function of ldgas (X). Find the
least-squares values of a and b.
f. Use the least-squares line (and perhaps Stata’s gen and list commands) to find all the fitted values ˆ
Yi
generated by the observed values of X.
g. Suppose you have done gen yhat = a + b*(ldgas), where yhat is the name you chose for the fitted Y’s
and ldgas is the name you gave to the lead gas series when you input the data. To see how the fitted line
looks on the scatterplot of cord lead against gas lead, try graph cordld yhat ldgas,two.
h. Find the average of the fitted ˆ
Yi(i.e., fitted cord lead values that we called yhat) and compare them to
the average of the observed Ys given above. This command will work: summarize cordld yhat.
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