4.1 Quantitative Data Analysis Prof. Treiman Exercise 4: Illustrative ...

Quantitative Data Analysis
Prof. Treiman
Exercise 4: Illustrative Answer
A. Direct Standardization via Stata
Here is the table called for in the assignment.
Premarital sex is...
Education
< H.S. grad H.S. grad Some coll. College +
Observed percentages
Always wrong 37.4 32.2 26.5 19.7
Almost always wrong 12.1 7.5 8.8 10.0
Sometimes wrong 10.1 16.4 14.7 20.5
Not wrong at all 40.4 43.9 50.0 49.8
Total 100.0 100.0 100.0 100.0
N (99) (214) (238) (239)
Percentages adjusted for age
Always wrong 25.8 31.4 26.4 19.5
Almost always wrong 15.8 6.9 10.2 10.4
Sometimes wrong 10.3 16.2 15.3 20.8
Not wrong at all 48.1 45.5 48.1 49.3
The top panel of the table shows a modest association between education and attitudes regarding
premarital sex, with the better educated less likely to think that premarital sex is wrong. About
37 per cent of those lacking high school education think that premarital sex is always wrong,
compared to less than 20 per cent of those with college degrees. At the other extreme, only
about 40 per cent of those with less than high school think that premarital sex is not wrong at all
compared to about half of those with at least some college.
We might suspect that these results simply reflect the tendency of older people both to be more
poorly educated and to have less liberal attitudes regarding premarital sex than younger people.
Indeed, both of these associations hold for late 20 th century Americans. [I have estimated but
4.1

have not presented the tables, but you can easily make them. In a full analysis, you would want
to show these tables.] But standardizing for age reveals that the association between education
and acceptance of premarital does not arise simply from their joint dependence on age. Indeed,
standardizing for age has virtually no impact on the coefficients in the table, except for those
with less than a high school education—the disapproval of premarital sex by those with less than
a high school education is apparently due in part to the fact that the poorly educated are
disproportionately elderly since there is a noticeable shift toward greater acceptance of
premarital sex in this group after standardizing for age.
The -do- file that created these computations is shown in the Appendix.
B. Simple Correlation and Regression
1. Correlation ratios
a) Table 1A shows a strong relationship between religious affiliation and tolerance of those
opposed to religion, among Americans queried in 1974. Nearly three quarters of the
Jews, nearly two thirds of those without religion, but only two fifths of the Catholics and
hardly more than a quarter of the Protestants are in the highest tolerance category,
endorsing the right of those “against religion” to speak at a public meeting, teach in a
college or university, and have their books included in public library collections.
b) On a three point tolerance scale (the number of endorsements of the rights mentioned in
answer to (1a)), the means (and standard deviations) for the four religious categories are
as follows:
Mean
S.D.
Protestants 1.44 1.40
Catholics 1.83 1.36
Jews 2.36 1.30
No religion 2.34 1.21
Total 1.63 1.42
From visual inspection ("eye balling the data") we are led to a similar conclusion from
the means as from the percentage distributions. Jews and those without religion are
substantially more tolerant than are Catholics, who are in turn substantially more tolerant
than are Protestants.
c. The correlation ratio, 0 2 , is a measure of the ratio of the sum of squared standard deviations
of observations from subgroup means (the within-group sum of squares) to the sum of
squared deviations of observations from the grand mean for the entire sample. It tells us
what proportion of the variance in the dependent variable can be explained by knowledge of
4.2

which of several categories of the independent variable an observation falls into. In the
present case, the correlation ratio tells us how much of the variance in tolerance of antireligionists
we can explain by knowing the religious affiliation of respondents. The easiest
way to compute 0 2 is to compute sums of squares separately for each subgroup and then add
them up to find the “within group sum of squares.” Then compute the sum of squares for the
total column. This, obviously, is the “total sum of squares.” Then simply make the
computation indicated in the assignment. Recall from the assignment that:
2
η = 1−
Within group sum of squares
Total sum of squares
This can be tabulated by hand. But it is possible to exploit Stata to shorten your hand
computations and improve the accuracy. The trick is to read the data into Stata, treating the
tolerance score, the frequencies for each religious group, and the total frequency as variables
and the four rows (excluding the total) as observations. The -do- file I used to get the
correlation ratio is shown as the second section of the Appendix.
For this problem, 0 2 = .056. This indicates that about six per cent of the variance in tolerance
of anti-religionists can be accounted for by the religious affiliations of the population. The
apparent inconsistency between the small percentage of variance explained by religious
affiliation and the large differences in the tolerance levels of the religious groups indicated
by the percentage tables is due to the fact that the more tolerant groups, Jews and those
without religion, are very small, and hence cannot contribute much to the total variance in
the population. Put differently, religious affiliation cannot explain much of the variance in
tolerance because most people have the same religion (65 per cent of the sample is
Protestant). This is an important point, which will recur repeatedly in our subsequent
discussion. Be sure you understand it.
2. Correlation and regression
The Stata do file that generates the output for Part B.2 of the exercise is shown as the third
section of the Appendix. I have extensively documented my do file.
2.a.
2.b.
See the do file.
See the do file.
2.b.1. As we see from the R-squared, 15.9 per cent of the variance in income is explained by
variance in education.
2.b.2. To get predicted levels of income for particular levels of education, we substitute the
level of education into the equation:
4.3

For high school graduates: = - 24,846 + 5141(12) = 36,846
For someone with a B.A.: = - 24,846 + 5141(16) = 57,410
For someone with 4 years after B.A.: = - 24,846 + 5141(20) = 77,974
Yˆ
Yˆ
Yˆ
2.c.
2.d.
2.e.
The correlation ratio is .188. This is three percentage points larger than the squared
product moment correlation (.159). The correlation ratio will always be larger (or, at the
limit, equal to) the squared product moment correlation, since the squared product
moment correlation gives 1 minus the ratio of the sum of squared deviations around a
straight regression line to the sum of squared deviations around the mean of the
dependent variable while the correlation ratio gives 1 minus the ratio of the sum of
squared deviations around the subgroup means to the sum of squared deviations around
the mean of the dependent variable. Recall from your elementary statistics course that
the mean is the point that minimizes the sum of squared deviations. If the means do not
increase in an exactly linear fashion, the sum of squares around the subgroup means
necessarily will be smaller than the sum of squares around the regression line.
See the do file.
The graph is shown as Fig. 1. The relationship between education and income appears to
be curvilinear. First, no one (in these data) has negative income and so the points for
those with little education are uniformly above the regression line (although we should be
cautious since there are relatively few cases in this part of the graph; very few men in the
sample have less than 8 years of schooling). 1 [I know this not only from inspecting the
scatter plot but also from a tabulation of education that I made but haven’t shown; see the
do file. In the course of your work, you should make many such tabulations to check
whether the data are behaving as expected, even if you never include them in your final
paper.] Second, it is probable that the presence of very high (arbitrarily coded at
$130,000) incomes among some of those with high amounts of education would pull the
line up on the right side were it not constrained to be linear. A better fit to the data might
be found by positing a curvilinear relationship between education and income, which we
will learn how to do shortly. The relatively large variance in income at each level of
education tells us why the squared correlation is so low: while average income tends to
increase with education, there is a great deal of individual variation in the incomes of
equally well educated men. Note finally that the mean for those with 19 years of school
is higher than for those with 20 or more years of school, which probably reflects the fact
that lawyers are better paid than professors.
1 When estimating correlation ratios, one should be cautious about the possibility of “over-fitting” the data
by capitalizing on sampling variation. When the subgroups are small, the subgroup means may reflect sampling
variability rather than true non-linearity in the population. Because of the danger of over-fitting data, it usually is
preferable to estimate r 2 rather than 0 2 when both variables are measured at the interval level—or to fit a smooth
curve if the relationship is curvilinear. An alternative is to collapse small categories into a single larger category. In
the present case, each year of schooling less than eight has fewer than 10 cases, so the estimated means are highly
subject to sampling variability. I might, therefore, have collapsed years 0-8 into a single category to get a more
reliable estimate of the mean for this group.
4.4

3. Individual and aggregate correlations
I ˆ = a+
b ( E )
3.a. We wish to estimate an equation of the form where I = the mean annual
income of white males in each occupation and E = the years of schooling of white males
in each occupation. Our problem is to solve for a and b. We get these from Table 2 by
making use of the relationship and the
b = r ( s / s ) = .72(2153/ 2.3) = 674
YX YX Y X
Y = a+ b( X)
a = Y −b( X)
relationship , which implies that . Thus, a = 5,311 -
674(10.2) = -1,564.
2
3.b. r = .72 2 IE
= .5184. So 52 per cent of the variance over occupations in mean annual
income can be attributed to variance in the average years of school completed by
incumbents.
3.c.
Recall from Part 2 that 16 per cent of the variance in the income of individuals can be
explained by variance in their education, compared to 52 per cent of the variance in the
average income of occupations explained by variance in their average income. It will
almost always be the case that aggregated data will show higher correlations than
disaggregated data involving the same variables, because most of the random
variability is removed when summary characteristics of central tendency (medians,
means, per cent above a certain level, etc.) are correlated. Be sure you understand this
point. In the present case, this is easy to see by thinking about specific occupations. For
example, while an occasional truck driver might be well educated and a few truck drivers
(not necessarily the well educated ones) might make a good deal of money, truck drivers
on the whole neither are very well educated nor make much money.
4.5

150000
Observed
Linear fit
Mean|Yrs. of School
Annual Income in 1993
100000
50000
0
0 4 8 12 16 20
Years of Schooling
Fig. 1. Annual Income in 2003 by Years of School Completed, U.S. Males, 2004 (Open-ended
Upper Category Coded to $150,000); N=855.
Appendix - Log File for the Computations
--------------------------------------------------------------------------------------
log: d:\teach\soc212ab\2007-2008\computing\ex05.log
log type: text
opened on: 2 Nov 2007, 22:07:26
. version 10.0
. #delimit;
delimiter now ;
. clear;
. set more 1;
. program drop _all;
. set mem 100m;
Current memory allocation
current
memory usage
settable value description (1M = 1024k)
--------------------------------------------------------------------
set maxvar 5000 max. variables allowed 1.909M
set memory 100M max. data space 100.000M
set matsize 500 max. RHS vars in models 1.949M
-----------
103.858M
. *EX05.DO (DJT 8/31/03, last modified 11/2/06);
4.6

. ***********************************************
> This -do- file does the computations for Ex. 5.
> ***********************************************;
. ********************************
> *Part A: Direct standardization.
> ********************************;
. use c:\e_old\data\gss\gssy2004.dta,replace;
. *Create a categorical variable for education.;
. recode educ
> (0/11=1 "Some H.S. or less")
> (12=2 "H.S. grad")
> (13/15=3 "Some college")
> (16/20=4 "Coll.grad.or more")
> (*=.),gen(edcat) label(edcat);
(2809 differences between educ and edcat)
. *Create a categorical variable for age.;
. recode age
> (25/34=1 "25-34")
> (35/44=2 "35-44")
> (45/54=3 "45-54")
> (55/64=4 "55-64")
> (65/89=5 "65+")
> (*=.),gen(agecat) label(agecat);
(2803 differences between age and agecat)
. *Convert the missing data codes for premarital sex to the Stata missing
> value.;
. recode premarsx 0 8 9=.;
(premarsx: 18 changes made)
. tab premarsx;
sex before |
marriage | Freq. Percent Cum.
-----------------+-----------------------------------
always wrong | 238 26.95 26.95
almst always wrg | 79 8.95 35.90
sometimes wrong | 157 17.78 53.68
not wrong at all | 409 46.32 100.00
-----------------+-----------------------------------
Total | 883 100.00
. *Mark the "good"--that is, non-missing--data to ensure that all
> analysis is based on the same data set.;
. mark good if premarsx~=. & agecat~=. & edcat~=.;
. *Get the necessary cross-tabs to understand the relationships among
> the three variables.;
. tab premarsx edcat if good==1,col;
4.7

+-------------------+
| Key |
|-------------------|
| frequency |
| column percentage |
+-------------------+
| RECODE of educ (highest year of school
sex before |
completed)
marriage | Some H.S. H.S. grad Some coll Coll.grad | Total
-----------------+--------------------------------------------+----------
always wrong | 37 69 63 47 | 216
| 37.37 32.24 26.47 19.67 | 27.34
-----------------+--------------------------------------------+----------
almst always wrg | 12 16 21 24 | 73
| 12.12 7.48 8.82 10.04 | 9.24
-----------------+--------------------------------------------+----------
sometimes wrong | 10 35 35 49 | 129
| 10.10 16.36 14.71 20.50 | 16.33
-----------------+--------------------------------------------+----------
not wrong at all | 40 94 119 119 | 372
| 40.40 43.93 50.00 49.79 | 47.09
-----------------+--------------------------------------------+----------
Total | 99 214 238 239 | 790
| 100.00 100.00 100.00 100.00 | 100.00
. tab premarsx agecat if good==1,col;
+-------------------+
| Key |
|-------------------|
| frequency |
| column percentage |
+-------------------+
sex before |
RECODE of age (age of respondent)
marriage | 25-34 35-44 45-54 55-64 65+ | Total
-----------------+-------------------------------------------------------+----------
always wrong | 41 49 38 33 55 | 216
| 22.78 25.39 24.84 27.05 38.73 | 27.34
-----------------+-------------------------------------------------------+----------
almst always wrg | 11 14 13 11 24 | 73
| 6.11 7.25 8.50 9.02 16.90 | 9.24
-----------------+-------------------------------------------------------+----------
sometimes wrong | 31 29 23 20 26 | 129
| 17.22 15.03 15.03 16.39 18.31 | 16.33
-----------------+-------------------------------------------------------+----------
not wrong at all | 97 101 79 58 37 | 372
| 53.89 52.33 51.63 47.54 26.06 | 47.09
-----------------+-------------------------------------------------------+----------
Total | 180 193 153 122 142 | 790
| 100.00 100.00 100.00 100.00 100.00 | 100.00
. tab agecat edcat if good==1,row;
+----------------+
| Key |
|----------------|
| frequency |
| row percentage |
+----------------+
4.8

RECODE of |
age (age |
of | RECODE of educ (highest year of school
respondent |
completed)
) | Some H.S. H.S. grad Some coll Coll.grad | Total
-----------+--------------------------------------------+----------
25-34 | 22 32 57 69 | 180
| 12.22 17.78 31.67 38.33 | 100.00
-----------+--------------------------------------------+----------
35-44 | 16 61 71 45 | 193
| 8.29 31.61 36.79 23.32 | 100.00
-----------+--------------------------------------------+----------
45-54 | 7 39 48 59 | 153
| 4.58 25.49 31.37 38.56 | 100.00
-----------+--------------------------------------------+----------
55-64 | 19 32 38 33 | 122
| 15.57 26.23 31.15 27.05 | 100.00
-----------+--------------------------------------------+----------
65+ | 35 50 24 33 | 142
| 24.65 35.21 16.90 23.24 | 100.00
-----------+--------------------------------------------+----------
Total | 99 214 238 239 | 790
| 12.53 27.09 30.13 30.25 | 100.00
. *Convert the premarital sex variable to a set of dichotomous variables,
> necessary to get directly standardized percentages.;
. tab premarsx if good==1,gen(pm);
sex before |
marriage | Freq. Percent Cum.
-----------------+-----------------------------------
always wrong | 216 27.34 27.34
almst always wrg | 73 9.24 36.58
sometimes wrong | 129 16.33 52.91
not wrong at all | 372 47.09 100.00
-----------------+-----------------------------------
Total | 790 100.00
. *Create the "popvar" variable, here called "tot," required by Stata's
> "dstdize" command. Note that the way to make dstdize work on unit
> rather than tabular data is to set the popvar variable = 1 for each
> case.;
. gen tot=1 if good==1;
(2022 missing values generated)
. *Do the direct standardization.;
. for num 1/4:dstdize pmX tot agecat if good==1,by(edcat);
-> dstdize pm1 tot agecat if good==1,by(edcat)
----------------------------------------------------------
-> edcat= 1
-----Unadjusted----- Std.
Pop. Stratum Pop.
Stratum Pop. Cases Dist. Rate[s] Dst[P] s*P
----------------------------------------------------------
25-34 22 4 0.222 0.1818 0.228 0.0414
35-44 16 2 0.162 0.1250 0.244 0.0305
45-54 7 0 0.071 0.0000 0.194 0.0000
55-64 19 9 0.192 0.4737 0.154 0.0732
65+ 35 22 0.354 0.6286 0.180 0.1130
----------------------------------------------------------
4.9

Totals: 99 37 Adjusted Cases: 25.6
Crude Rate: 0.3737
Adjusted Rate: 0.2581
95% Conf. Interval: [0.1878, 0.3284]
----------------------------------------------------------
-> edcat= 2
-----Unadjusted----- Std.
Pop. Stratum Pop.
Stratum Pop. Cases Dist. Rate[s] Dst[P] s*P
----------------------------------------------------------
25-34 32 9 0.150 0.2813 0.228 0.0641
35-44 61 21 0.285 0.3443 0.244 0.0841
45-54 39 13 0.182 0.3333 0.194 0.0646
55-64 32 6 0.150 0.1875 0.154 0.0290
65+ 50 20 0.234 0.4000 0.180 0.0719
----------------------------------------------------------
Totals: 214 69 Adjusted Cases: 67.1
Crude Rate: 0.3224
Adjusted Rate: 0.3136
95% Conf. Interval: [0.2507, 0.3765]
----------------------------------------------------------
-> edcat= 3
-----Unadjusted----- Std.
Pop. Stratum Pop.
Stratum Pop. Cases Dist. Rate[s] Dst[P] s*P
----------------------------------------------------------
25-34 57 16 0.239 0.2807 0.228 0.0640
35-44 71 18 0.298 0.2535 0.244 0.0619
45-54 48 11 0.202 0.2292 0.194 0.0444
55-64 38 12 0.160 0.3158 0.154 0.0488
65+ 24 6 0.101 0.2500 0.180 0.0449
----------------------------------------------------------
Totals: 238 63 Adjusted Cases: 62.8
Crude Rate: 0.2647
Adjusted Rate: 0.2640
95% Conf. Interval: [0.2062, 0.3218]
----------------------------------------------------------
-> edcat= 4
-----Unadjusted----- Std.
Pop. Stratum Pop.
Stratum Pop. Cases Dist. Rate[s] Dst[P] s*P
----------------------------------------------------------
25-34 69 12 0.289 0.1739 0.228 0.0396
35-44 45 8 0.188 0.1778 0.244 0.0434
45-54 59 14 0.247 0.2373 0.194 0.0460
55-64 33 6 0.138 0.1818 0.154 0.0281
65+ 33 7 0.138 0.2121 0.180 0.0381
----------------------------------------------------------
Totals: 239 47 Adjusted Cases: 46.7
Crude Rate: 0.1967
Adjusted Rate: 0.1952
95% Conf. Interval: [0.1438, 0.2466]
Summary of Study Populations:
edcat N Crude Adj_Rate Confidence Interval
--------------------------------------------------------------------------
1 99 0.373737 0.258100 [ 0.187773, 0.328426]
2 214 0.322430 0.313598 [ 0.250660, 0.376536]
3 238 0.264706 0.263981 [ 0.206202, 0.321759]
4 239 0.196653 0.195220 [ 0.143805, 0.246635]
-> dstdize pm2 tot agecat if good==1,by(edcat)
4.10

[Log omitted for pm2-pm4 to save space.]
. *****************************
> Part B.1: Correlation ratios.
> *****************************;
. preserve;
. *Read in the frequencies from Table 1 in the assignment and confirm correct.;
. clear;
. infile score p c j n tot using ex6b.raw;
(4 observations read)
. list;
+-----------------------------------+
| score p c j n tot |
|-----------------------------------|
1. | 3 265 151 32 65 513 |
2. | 2 212 93 3 18 326 |
3. | 1 155 50 2 5 212 |
4. | 0 322 82 7 13 424 |
+-----------------------------------+
. *Get the within-group sum of squared deviations.;
. for var p c j n: sum score [aw=X] \ gen sdX=X*((score-r(mean))^2)
> \ gen ssX=sum(sdX);
-> sum score [aw=p]
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
score | 4 954 1.440252 1.403347 0 3
-> gen sdp=p*((score-r(mean))^2)
-> gen ssp=sum(sdp)
-> sum score [aw=c]
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
score | 4 376 1.832447 1.355896 0 3
-> gen sdc=c*((score-r(mean))^2)
-> gen ssc=sum(sdc)
-> sum score [aw=j]
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
score | 4 44 2.363636 1.304791 0 3
-> gen sdj=j*((score-r(mean))^2)
-> gen ssj=sum(sdj)
-> sum score [aw=n]
4.11

Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
score | 4 101 2.336634 1.208083 0 3
-> gen sdn=n*((score-r(mean))^2)
-> gen ssn=sum(sdn)
. egen wgss=rsum(ssp ssc ssj ssn) in 4;
(3 missing values generated)
. *Get the total sum of squared deviations.;
. sum score [aw=tot];
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
score | 4 1475 1.629153 1.416017 0 3
. gen gmean=r(mean);
. for var p c j n: gen tdX=X*((score-gmean)^2) \ gen tsX=sum(tdX);
-> gen tdp=p*((score-gmean)^2)
-> gen tsp=sum(tdp)
-> gen tdc=c*((score-gmean)^2)
-> gen tsc=sum(tdc)
-> gen tdj=j*((score-gmean)^2)
-> gen tsj=sum(tdj)
-> gen tdn=n*((score-gmean)^2)
-> gen tsn=sum(tdn)
. egen tss=rsum(tsp tsc tsj tsn) in 4;
(3 missing values generated)
. *Get eta-squared.;
. gen etasq=1 - wgss/tss;
(3 missing values generated)
. list etasq;
+----------+
| etasq |
|----------|
1. | . |
2. | . |
3. | . |
4. | .0558446 |
+----------+
. restore;
. **************************************
> *Part B.2: Correlation and Regression.
> **************************************;
. *Recode income;
4.12

. recode rincom98 1=500 2=2000 3=3500 4=4500 5=5500 6=6500 7=7500 8=9000
> 9=11250 10=13750 11=16250 12=18750 13=21250 14=23750 15=27500
> 16=32500 17=37500 18=45000 19=55000 20=67500 21=82500
> 22=100000 23=150000 *=.,gen(inc);
(1849 differences between rincom98 and inc)
. *Mark complete data for Problem 2.;
. replace educ=. if educ>20;
(0 real changes made)
. mark good2 if sex==1;
. markout good2 inc educ;
. *Get the regression of income on education.;
. reg inc educ if good2==1;
Source | SS df MS Number of obs = 855
-------------+------------------------------ F( 1, 853) = 161.61
Model | 2.0172e+11 1 2.0172e+11 Prob > F = 0.0000
Residual | 1.0647e+12 853 1.2482e+09 R-squared = 0.1593
-------------+------------------------------ Adj R-squared = 0.1583
Total | 1.2664e+12 854 1.4829e+09 Root MSE = 35329
------------------------------------------------------------------------------
inc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ | 5141.039 404.4016 12.71 0.000 4347.3 5934.778
_cons | -24846.61 5824.733 -4.27 0.000 -36279.1 -13414.12
------------------------------------------------------------------------------
. *Get the correlation ratio of income on education.;
. anova inc educ if good2==1;
Number of obs = 855 R-squared = 0.1881
Root MSE = 35068.8 Adj R-squared = 0.1707
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 2.3826e+11 18 1.3237e+10 10.76 0.0000
|
educ | 2.3826e+11 18 1.3237e+10 10.76 0.0000
|
Residual | 1.0281e+12 836 1.2298e+09
-----------+----------------------------------------------------
Total | 1.2664e+12 854 1.4829e+09
. *Now get the mean income for each year of schooling. It is a
> good idea to make a tabulation of mean income by year of schooling,
> to determine how many cases there are in each category.;
. tab educ if good2==1,s(inc) mean freq;
highest | Summary of RECODE of
year of | rincom98 (respondents
school |
income)
completed | Mean Freq.
------------+------------------------
1 | 37500 1
2 | 50000 2
3 | 36875 2
5 | 24375 2
4.13

6 | 27750 5
7 | 17583.333 3
8 | 16250 6
9 | 21973.684 19
10 | 28009.615 26
11 | 25481.25 40
12 | 36769.9 201
13 | 40492.308 65
14 | 43408.397 131
15 | 42310 50
16 | 56506.494 154
17 | 65546.875 32
18 | 72534.091 44
19 | 86650 25
20 | 84984.043 47
------------+------------------------
Total | 47590.936 855
. egen avginc = mean(inc) if good2==1, by(educ);
(1957 missing values generated)
. *Graph the relationship between actual income, mean income given
> education, predicted income from the linear regression of income
> on education, and education.;
. *Note: The graphics commands in Stata 8.0 and 9.0 are completely rewritten
> from previous versions. They are much more powerful, but take some
> studying to figure out. The thing to do is first to make a simple
> graph, without labels, and then to successively add refinements.
> This is what I did here. We will discuss graphics many times in class.
> But the commands are too complicated for a simple exposition here to be
> very helpful. One way you can take advantage of my work is to study my
> command and compare it to the graph, to see how I have achieved various
> labeling.;
. label var inc "Observed";
. label var avginc "Mean|Yrs. of School";
. *I strongly prefer the "lean1" scheme programmed by Juul (see the article
> posted on the course web page). The most important reason for this is that
> the y-axis labels are shown horizontally rather than vertically. But there
> are other improvements as well, discussed in the article. Thus, I set "lean1"
> (which I have downloaded from Stata's web page) as my permanent graphics
> scheme.;
. set scheme lean1,permanent;
(set scheme preference recorded)
. graph twoway
> (scatter inc educ,msymbol(Oh) mcolor(black) jitter(5))
> (lfit inc educ,sort clwidth(thick) clpattern(solid) clcolor(red))
> (line avginc educ,sort clwidth(thick) clpattern(solid) clcolor(blue))
> if good2==1,
> legend(label(2 "Linear fit") cols(1) ring(0) position(11))
> ylab(0(50000)150000)
> ymtick(0(10000)150000)
> xlab(0(4)20)
> xmtick(0(1)20)
> ytitle("Annual Income in 1993")
> xtitle("Years of Schooling")
> saving(ex05.gph,replace);
(file ex05.gph saved)
4.14

. *A note on getting graphs into your word processor document. The
> simplest way to do this (there may be others) is, when the graph
> is on the screen, to click on "edit" and then "copy graph" and then
> toggle to your word processor and paste the graph into it. (When
> I tried this in MS Word, it didn't work for me but an alternative
> did: simply click cntrl-c (the standard Windows copy command) with
> your cursor on the graph, then toggle to MS Word and click cntrl-v
> (the standard Windows paste command).
>
> You should always save your graphs so that you can access them without
> having to rerun the do file that created them---a useful time saving
> when one has a complex do file that takes a long time to execute. A
> new and happy feature of Stata 8.0 and 9.0 is that you can edit saved graphs.;
. log close;
log: d:\teach\soc212ab\2007-2008\computing\ex05.log
log type: text
closed on: 2 Nov 2007, 22:07:39
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4.15