### Stata Textbook Examples Applied Regression Analysis by John Fox Chapter 4: Transforming Data

Page 65, figure 4.2 This figure shows an example of a kernel density estimator (and is the same as page 41, figure 3.5, using the kdensity command. The width(800) option is used to specify the half-width of 800.
use http://www.ats.ucla.edu/stat/stata/examples/ara/prestige, clear

kdensity income, xlabel(0(5000)30000) ylabel(0(.00005).00015) width(800)
Page 66, table at top. You can download extrans from within Stata by typing findit extrans (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
extrans income

----> Variable income:

| Transformation      |    Q1    |    Q2    |    Q3    |(Q3-Q2)/(Q2-Q1)|
|_____________________|__________|__________|__________|_______________|
| income              |4075      |5930.5    |8206      |1.2263541
| SQRT(income)        |63.835728 |77.009518 |90.586975 |1.0306417
| LOG(income)         |8.3126259 |8.6878524 |9.0126209 |.86552668
| -1/SQRT(income)     |-.01566521|-.01298548|-.01103911|.72633104
Page 66, figure 4.3. Stata cannot quite make a graph just like figure 4.3.
generate lincome = log10(income)
kdensity lincome, ylabel(0 1 2)
On page 72, figure 4.7 repeats figure 2.7 from Chapter 2.
graph twoway (lowess prestige income, bwidth(.2) noweight mean) (scatter prestige income), ///
xlabel(0(5000)30000) ylabel(0(40)120)
Page 72, figure 4.8. This figure shows performing a cube root transformation on income, and then within graph twoway, combine the scatter plot, linear regression line and lowess regression line.
generate cr_inc = income^(1/3)
graph twoway (lowess prestige cr_inc, bwidth(.2) noweight mean) (lfit prestige cr_inc) ///
(scatter prestige cr_inc), xlabel(5(5)30) ylabel(0(40)120)
Page 73, figure 4.9 This shows a local regression and scatterplot of mortality by income. In the final scatter overlay, we only scatter observations with mortrate >= 250 and use mlabel(nation) option to portray the outlying nation names.
use http://www.ats.ucla.edu/stat/stata/examples/ara/leinhard, clear

graph twoway (lowess mortrate inc) (scatter mortrate inc) ///
(scatter mortrate inc if mortrate >= 250, mlabel(nation)), ///
xlabel(0(1000)6000) ylabel(0(250)750)
Page 74, figure 4.10 This graph shows the log of mortality by log of income. Like figure 4.8, this shows the results of a local regression using lowess and least squares regression using lfit.
generate linc = log10(inc)
generate lmort = log10(mortrate)
graph twoway (lowess lmort linc if nation ~="Saudi_Arabia" | nation ~="Libya", bwidth(.5)) ///
(lfit lmort linc if nation ~="Saudi_Arabia" | nation ~="Libya") ///
(scatter lmort linc if nation ~="Saudi_Arabia" | nation ~="Libya") ///
(scatter lmort linc if nation =="Saudi_Arabia" | nation =="Libya", mlabel(nation))
Page 75, figure 4.11 repeats figure 3.14 shown on page 52, as shown below.
use http://www.ats.ucla.edu/stat/stata/examples/ara/ornstein, clear

graph box intrlcks, over(nation) ylabel(0(50)150)
On page 75, the table in the center of the page can be produced using the table command in Stata. The lower hinge is p25, the median is p50, the upper hinge is p75 and the hinge spread is the interquartile range (iqr).
table nation, c(p25 intrlcks p50 intrlcks p75 intrlcks iqr intrlcks)

----------+-----------------------------------------------------------
Nation of |
Control   | p25(intrlcks)  med(intrlcks)  p75(intrlcks)  iqr(intrlcks)
----------+-----------------------------------------------------------
CAN |             5             12             29             24
OTH |             3           14.5             23             20
UK |             3              8             13             10
US |             1              5             12             11
----------+-----------------------------------------------------------
Page 76, figure 4.12, skipped for now.
Page 77, figure 4.13 skipped for now.
Page 78, figure 4.14. We convert the percent women to the proportion women, and make a stem and leaf plot of that.
use http://www.ats.ucla.edu/stat/stata/examples/ara/prestige, clear

gen propwomn = percwomn / 100
stem percwomn, round(1)

Stem-and-leaf plot for percwomn (% of incumbents who were women)

percwomn rounded to integers

0* | 00000111111111111222223334444444
0. | 555667788899
1* | 11112344
1. | 566777
2* | 0144
2. | 568
3* | 0134
3. | 599
4* |
4. | 778
5* | 22
5. | 567
6* | 3
6. | 889
7* | 12
7. | 56667
8* | 334
8. |
9* | 123
9. | 66678
Page 80, figure 4.16. This converts the proportion of women into the logit, and makes a stem and leaf plot. The Stata stem and leaf plot does not look the same as the one in Fox.
generate pprime  = .005 + .99*propwomn
generate lgtperc = ln(pprime / (1-pprime))
stem lgtperc, round(.1) lines(2)

Stem-and-leaf plot for lgtperc

lgtperc rounded to nearest multiple of .1
plot in units of .1

-5* | 33333
-4. | 65555
-4* | 4322210
-3. | 98765
-3* | 4332211000
-2. | 8887755
-2* | 4443210000
-1. | 988777655
-1* | 431111
-0. | 988776
-0* | 44111
0* | 11223
0. | 578899
1* | 11112
1. | 566
2* | 24
2. | 5
3* | 1112
3. | 5

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