ECON 3100
PROBLEM SET 6
Statistical investigation:
This exercise draws on the dataset “companies,” available in JMP under “sample data setsBusiness and Demographic” and on the course website. The goal is for you to learn to
incorporate qualitative variables into multiple regression analysis and to interpret the results
appropriately. We will analyze the profits of a set of companies in relationship to those
companies’ sales, number of employees, and industry.
1. Run a regression with profits as the dependent variable, sales and the number of employees as
the independent variables. Call this Model A, and include the regression output in your problem
set.
2. Conduct an F-test at a 5% significance level as to whether there is a useful relationship
between the dependent variable and the independent variables of Model A.
3. What are the r-squared and the adjusted r-squared of Model A? Interpret each of these values.
4. Create a dummy variable that that takes the value 1 if the company is in the computer
industry, 0 if the company is in the pharmaceutical industry.
5. Run a regression with profits as the dependent variable, sale, the number of employees, and
the dummy variable for “computer industry” as the independent variables. Call this Model B,
and include the regression output in your problem set.
6. Adjusted for the number of variables in the model, which model explains the greater share of
variation in profits, Model A or Model B?
7. Interpret the coefficient on the dummy variable for computer industry in model B.
8. Does industry have a statistically significant relationship to a company’s profits? Conduct a
t-test at the 5% significance level as to whether the coefficient on the dummy variable differs
from 0.
9. What is the predicted level of profits for a company in the computer industry with median
sales and a median number of employees for that industry?
10. What is the predicted level of profits for a company in the pharmaceutical industry with
median sales and a median level of employees for that industry?
1
11. Are there any outliers in the data set? Calculate the standardized (“studentized”) residual of
each observation and identify outliers as any observations with a studentized residual greater
than 3 in absolute value. Which observation has the largest standardized residual (in absolute
value).
12. Do any of the observations have unusual influence on the results (high leverage)? Use
Cook’s distance measure to identify variables with strong leverage.
Everyday statistics
The New Yorker article “Measure for Measure” that follows the problem set tells the story of
Francis Galton, the eccentric 19th century scholar who gave us the terms “correlation” and
“regression.”
1. Draw a rough sketch of Galton’s graph of children’s height (y) “regressed” on parental height
(x). What did Galton find to be the slope of the relationship between the two?
2. Interpret the slope coefficient in question one.
3. Explain carefully why a baseball player who had an extremely good year (batting better than
.300 for example), is likely to do worse the following year.
4. What is Galton’s fallacy? Does the author of the article believe that Galton himself
committed Galton’s fallacy?
5. Based on the concept of regression to the mean, suppose a student gets an extremely high
score on a midterm exam. Should he/she expect to do worse, the same, or better on the final
exam? Explain your answer.
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BOOKS
MEASURE FOR MEASURE
The strange science of Francis Galton.
by Jim Holt
JANUARY 24, 2005
I
n the eighteen-eighties, residents of cities across
Britain might have noticed an aged, bald,
bewhiskered gentleman sedulously eying every girl
he passed on the street while manipulating
something in his pocket. What they were seeing
was not lechery in action but science. Concealed in
the man’s pocket was a device he called a “pricker,”
which consisted of a needle mounted on a thimble
and a cross-shaped piece of paper. By pricking
holes in different parts of the paper, he could
surreptitiously record his rating of a female
passerby’s appearance, on a scale ranging from
attractive to repellent. After many months of
wielding his pricker and tallying the results, he
drew a “beauty map” of the British Isles. London
proved the epicenter of beauty, Aberdeen of its
opposite.
Such research was entirely congenial to Francis
Galton, a man who took as his motto “Whenever
you can, count.” Galton was one of the great Victorian innovators. He explored unknown
regions of Africa. He pioneered the fields of weather forecasting and fingerprinting. He
discovered statistical rules that revolutionized the methodology of science. Yet today he is most
often remembered for an achievement that puts him in a decidedly sinister light: he was the
father of eugenics, the science, or pseudoscience, of “improving” the human race by selective
breeding.
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A new biography, “Extreme Measures: The Dark Visions and Bright Ideas of Francis
Galton” (Bloomsbury; $24.95), casts the man’s sinister aspect right in the title. The author,
Martin Brookes, is a former evolutionary biologist who worked at University College London’s
Galton Laboratory (which, before a sanitizing name change in 1965, was the Galton Laboratory
of National Eugenics). Brookes is clearly impressed by the exuberance of Galton’s curiosity and
the range of his achievement. Still, he cannot help finding Galton a little dotty, a man gripped
by an obsession with counting and measuring that made him “one of the Victorian era’s chief
exponents of the scientific folly.” If Brookes is right, Galton was led astray not merely by
Victorian prejudice but by a failure to understand the very statistical ideas that he had
conceived.
Born in 1822 into a wealthy and distinguished Quaker family—his maternal grandfather
was Erasmus Darwin, a revered physician and botanist who wrote poetry about the sex lives of
plants—Galton enjoyed a pampered upbringing. As a child, he revelled in his own precocity: “I
am four years old and can read any English book. I can say all the Latin Substantives and
Adjectives and active verbs besides 52 lines of Latin poetry. I can cast up any sum in addition
and multiply by 2, 3, 4, 5, 6, 7, 8, 10. I can also say the pence table. I read French a little and I
know the Clock.” When Galton was sixteen, his father decided that he should pursue a medical
career, as his grandfather had. He was sent to train in a hospital, but was put off by the screams
of unanesthetized patients on the operating table. Seeking guidance from his cousin Charles
Darwin, who had just returned from his voyage on the H.M.S. Beagle, Galton was advised to
“read Mathematics like a house on fire.” So he enrolled at Cambridge, where, despite his
invention of a “gumption-reviver machine” that dripped water on his head, he promptly suffered
a breakdown from overwork.
This pattern of frantic intellectual activity followed by nervous collapse continued
throughout Galton’s life. His need to earn a living, though, ended when he was twenty-two, with
the death of his father. Now in possession of a handsome inheritance, he took up a life of
sporting hedonism. In 1845, he went on a hippo-shooting expedition down the Nile, then
trekked by camel across the Nubian Desert. He taught himself Arabic and apparently caught a
venereal disease from a prostitute—which, his biographer speculates, may account for a
noticeable cooling in the young man’s ardor for women.
The world still contained vast uncharted areas, and exploring them seemed an apt vocation
to this rich Victorian bachelor. In 1850, Galton sailed to southern Africa and ventured into parts
of the interior never before seen by a white man. Before setting out, he purchased a theatrical
crown in Drury Lane which he planned to place “on the head of the greatest or most distant
potentate I should meet with.” The story of his thousand-mile journey through the bush is
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grippingly told in this biography. Improvising survival tactics as he went along, he contended
with searing heat, scarce water, tribal warfare, marauding lions, shattered axles, dodgy guides,
and native helpers whose conflicting dietary superstitions made it impossible to settle on a
commonly agreeable meal from the caravan’s mobile larder of sheep and oxen. He became
adept in the use of the sextant, at one point using it to measure from afar the curves of an
especially buxom native woman—“Venus among Hottentots.” The climax of the journey was
his encounter with King Nangoro, a tribal ruler locally reputed to be “the fattest man in the
world.” Nangoro was fascinated by the Englishman’s white skin and straight hair, and
moderately pleased when the tacky stage crown was placed on his head. But when the King
dispatched his niece, smeared in butter and red ochre, to his guest’s tent to serve as a wife for
the night, Galton, wearing his one clean suit of white linen, found the naked princess “as
capable of leaving a mark on anything she touched as a well-inked printer’s roller . . . so I had
her ejected with scant ceremony.”
Galton’s feats made him famous: on his return to England, the thirty-year-old explorer was
celebrated in the newspapers and awarded a gold medal by the Royal Geographical Society.
After writing a best-selling book on how to survive in the African bush, he decided that he had
had enough of the adventurer’s life. He married a rather plain woman from an intellectually
illustrious family, with whom he never succeeded in having children, and settled down in South
Kensington to a life of scientific dilettantism. His true métier, he had always felt, was
measurement. In pursuit of it, he conducted elaborate experiments in the science of tea-making,
deriving equations for brewing the perfect cup. Eventually, his interest hit on something that
was actually important: the weather. Meteorology could barely be called a science in those days;
the forecasting efforts of the British government’s first chief weatherman met with such ridicule
that he ended up slitting his throat. Taking the initiative, Galton solicited reports of conditions
all over Europe and then created the prototype of the modern weather map. He also discovered a
weather pattern that he called the “anti-cyclone”—better known today as the high-pressure
system.
Galton might have puttered along for the rest of his life as a minor gentleman scientist had it
not been for a dramatic event: the publication of Darwin’s “On the Origin of Species,” in 1859.
Reading his cousin’s book, Galton was filled with a sense of clarity and purpose. One thing in it
struck him with special force: to illustrate how natural selection shaped species, Darwin cited
the breeding of domesticated plants and animals by farmers to produce better strains. Perhaps,
Galton concluded, human evolution could be guided in the same way. But where Darwin had
thought mainly about the evolution of physical features, like wings and eyes, Galton applied the
same hereditary logic to mental attributes, like talent and virtue.“If a twentieth part of the cost
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and pains were spent in measures for the improvement of the human race that is spent on the
improvements of the breed of horses and cattle, what a galaxy of genius might we not create!”
he wrote in an 1864 magazine article, his opening eugenics salvo. It was two decades later that
he coined the word “eugenics,” from the Greek for “wellborn.”
Galton also originated the phrase “nature versus nurture,” which still reverberates in debates
today. (It was probably suggested by Shakespeare’s “The Tempest,” in which Prospero laments
that his slave Caliban is “A devil, a born devil, on whose nature / Nurture can never stick.”) At
Cambridge, Galton had noticed that the top students had relatives who had also excelled there;
surely, he reasoned, such family success was not a matter of chance. His hunch was
strengthened during his travels, which gave him a vivid sense of what he called “the mental
peculiarities of different races.” Galton made an honest effort to justify his belief in nature over
nurture with hard evidence. In his 1869 book “Hereditary Genius,” he assembled long lists of
“eminent” men—judges, poets, scientists, even oarsmen and wrestlers—to show that excellence
ran in families. To counter the objection that social advantages rather than biology might be
behind this, he used the adopted sons of Popes as a kind of control group. His case elicited
skeptical reviews, but it impressed Darwin. “You have made a convert of an opponent in one
sense,” he wrote to Galton, “for I have always maintained that, excepting fools, men did not
differ much in intellect, only in zeal and hard work.” Yet Galton’s labors had hardly begun. If
his eugenic utopia was to be a practical possibility, he needed to know more about how heredity
worked. His belief in eugenics thus led him to try to discover the laws of inheritance. And that,
in turn, led him to statistics.
S
tatistics at that time was a dreary welter of population numbers, trade figures, and the like.
It was devoid of mathematical interest, save for a single concept: the bell curve. The bell
curve was first observed when eighteenth-century astronomers noticed that the errors in their
measurements of the positions of planets and other heavenly bodies tended to cluster
symmetrically around the true value. A graph of the errors had the shape of a bell. In the early
nineteenth century, a Belgian astronomer named Adolph Quetelet observed that this “law of
error” also applied to many human phenomena. Gathering information on the chest sizes of
more than five thousand Scottish soldiers, for example, Quetelet found that the data traced a
bell-shaped curve centered on the average chest size, about forty inches.
As a matter of mathematics, the bell curve is guaranteed to arise whenever some variable
(like human height) is determined by lots of little causes (like genes, health, and diet) operating
more or less independently. For Quetelet, the bell curve represented accidental deviations from
an ideal he called l’homme moyen—the average man. When Galton stumbled upon Quetelet’s
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work, however, he exultantly saw the bell curve in a new light: what it described was not
accidents to be overlooked but differences that revealed the variability on which evolution
depended. His quest for the laws that governed how these differences were transmitted from one
generation to the next led to what Brookes justly calls “two of Galton’s greatest gifts to
science”: regression and correlation.
Although Galton was more interested in the inheritance of mental abilities, he knew that
they would be hard to measure. So he focussed on physical traits, like height. The only rule of
heredity known at the time was the vague “Like begets like.” Tall parents tend to have tall
children, while short parents tend to have short children. But individual cases were
unpredictable. Hoping to find some larger pattern, in 1884 Galton set up an “anthropometric
laboratory” in London. Drawn by his fame, thousands of people streamed in and submitted to
measurement of their height, weight, reaction time, pulling strength, color perception, and so
on. Among the visitors was William Gladstone, the Prime Minister. “Mr. Gladstone was
amusingly insistent about the size of his head . . . but after all it was not so very large in
circumference,” noted Galton, who took pride in his own massive bald dome.
After obtaining height data from two hundred and five pairs of parents and nine hundred and
twenty-eight of their adult children, Galton plotted the points on a graph, with the parents’
heights represented on one axis and the children’s on the other. He then pencilled a straight line
though the cloud of points to capture the trend it represented. The slope of this line turned out to
be two-thirds. What this meant was that exceptionally tall (or short) parents had children who,
on average, were only two-thirds as exceptional as they were. In other words, when it came to
height children tended to be less exceptional than their parents. The same, he had noticed years
earlier, seemed to be true in the case of “eminence”: the children of J. S. Bach, for example,
may have been more musically distinguished than average, but they were less distinguished
than their father. Galton called this phenomenon “regression toward mediocrity.” Regression
analysis furnished a way of predicting one thing (a child’s height) from another (its parents’)
when the two things were fuzzily related. Galton went on to develop a measure of the strength
of such fuzzy relationships, one that could be applied even when the things related were
different in kind—like rainfall and crop yield. He called this more general technique
“correlation.”
The result was a major conceptual breakthrough. Until then, science had pretty much been
limited to deterministic laws of cause and effect—which are hard to find in the biological world,
where multiple causes often blend together in a messy way. Thanks to Galton, statistical laws
gained respectability in science. His discovery of regression toward mediocrity—or regression
to the mean, as it is now called—has resonated even more widely. Yet, as straightforward as it
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seems, the idea has been a snare even for the sophisticated. The common misconception is that
it implies convergence over time. If very tall parents tend to have somewhat shorter children,
and very short parents tend to have somewhat taller children, doesn’t that mean that eventually
everyone should be the same height? No, because regression works backward as well as
forward in time: very tall children tend to have somewhat shorter parents, and very short
children tend to have somewhat taller parents. The key to understanding this seeming paradox is
that regression to the mean arises when enduring factors (which might be called “skill”) mix
causally with transient factors (which might be called “luck”). Take the case of sports, where
regression to the mean is often mistaken for choking or slumping. Major-league baseball players
who managed to bat better than .300 last season did so through a combination of skill and luck.
Some of them are truly great players who had a so-so year, but the majority are merely good
players who had a lucky year. There is no reason that the latter group should be equally lucky
this year; that is why around eighty per cent of them will see their batting average decline.
To mistake regression for a real force that causes talent or quality to dissipate over time, as
so many have, is to commit what has been called “Galton’s fallacy.” In 1933, a Northwestern
University professor named Horace Secrist produced a book-length example of the fallacy in
“The Triumph of Mediocrity in Business,” in which he argued that, since highly profitable firms
tend to become less profitable, and highly unprofitable ones tend to become less unprofitable,
all firms will soon be mediocre. A few decades ago, the Israeli Air Force came to the conclusion
that blame must be more effective than praise in motivating pilots, since poorly performing
pilots who were criticized subsequently made better landings, whereas high performers who
were praised made worse ones. (It is a sobering thought that we might generally tend to overrate
censure and underrate praise because of the regression fallacy.) More recently, an editorialist for
the Times erroneously argued that the regression effect alone would insure that racial differences
in I.Q. would disappear over time.
Did Galton himself commit Galton’s fallacy? Brookes insists that he did. “Galton
completely misread his results on regression,” he argues, and wrongly believed that human
heights tended “to become more average with each generation.” Even worse, Brookes claims,
Galton’s muddleheadedness about regression led him to reject the Darwinian view of evolution,
and to adopt a more extreme and unsavory version of eugenics. Suppose regression really did
act as a sort of gravity, always pulling individuals back toward the average. Then it would seem
to follow that evolution could not take place through a gradual series of small changes, as
Darwin envisaged. It would require large, discontinuous changes that are somehow immune
from regression to the mean. Such leaps, Galton thought, would result in the appearance of
strikingly novel organisms, or “sports of nature,” that would shift the entire bell curve of ability.
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And if eugenics was to have any chance of success, it would have to work the same way as
evolution. In other words, these sports of nature would have to be enlisted to create a new
breed. Only then could regression be overcome and progress be made.
In telling this story, Brookes makes his subject out to be more confused than he actually
was. It took Galton nearly two decades to work out the subtleties of regression, an achievement
that, according to Stephen M. Stigler, a statistician at the University of Chicago, “should rank
with the greatest individual events in the history of science—at a level with William Harvey’s
discovery of the circulation of blood and with Isaac Newton’s of the separation of light.” By
1889, when Galton published his most influential book, “Natural Inheritance,” his grasp of it
was nearly complete. He knew that regression had nothing special to do with life or heredity. He
knew that it was independent of the passage of time. Regression to the mean held even between
brothers, he observed; exceptionally tall men tend to have brothers who are somewhat less tall.
In fact, as Galton was able to show by a neat geometric argument, regression is a matter of pure
mathematics, not an empirical force. Lest there be any doubt, he disguised the case of hereditary
height as a problem in mechanics and sent it to a mathematician at Cambridge, who, to Galton’s
delight, confirmed his finding.
Even as he laid the foundations for the statistical study of human heredity, Galton continued
to pursue many other intellectual interests, some important, some merely eccentric. He invented
a pair of submarine spectacles that permitted him to read while submerged in his bath, and
stirred up controversy by using statistics to investigate the efficacy of prayer. (Petitions to God,
he concluded, were powerless to protect people from sickness.) Prompted by a near-approach of
the planet Mars to Earth, he devised a celestial signalling system to permit communication with
Martians. More usefully, he put the nascent practice of fingerprinting on a rigorous basis by
classifying patterns and proving that no two fingerprints were exactly the same—a great step
forward for Victorian police work.
Galton remained restlessly active through the turn of the century. In 1900, eugenics received
a big boost in prestige when Gregor Mendel’s work on heredity in peas came to light. Suddenly,
hereditary determinism was the scientific fashion. Although Galton was now plagued by
deafness and asthma (which he treated by smoking hashish), he gave a major address on
eugenics in 1904. “What nature does blindly, slowly, and ruthlessly, man may do providently,
quickly, and kindly,” he declared. An international eugenics movement was springing up, and
Galton was hailed as its hero. In 1909, he was honored with a knighthood. Two years later, at
the age of eighty-eight, he died.
I
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when it comes to talent and virtue, nature dominates nurture. Yet he never doubted its truth, and
many scientists came to share his conviction. Darwin himself, in “The Descent of Man,” wrote,
“We now know, through the admirable labours of Mr. Galton, that genius . . . tends to be
inherited.” Given this axiom, there are two ways of putting eugenics into practice: “positive”
eugenics, which means getting superior people to breed more; and “negative” eugenics, which
means getting inferior ones to breed less. For the most part, Galton was a positive eugenicist.
He stressed the importance of early marriage and high fertility among the genetic élite,
fantasizing about lavish state-funded weddings in Westminster Abbey with the Queen giving
away the bride as an incentive. Always hostile to religion, he railed against the Catholic Church
for imposing celibacy on some of its most gifted representatives over the centuries. He hoped
that spreading the insights of eugenics would make the gifted aware of their responsibility to
procreate for the good of the human race. But Galton did not believe that eugenics could be
entirely an affair of moral suasion. Worried by evidence that the poor in industrial Britain were
breeding disproportionately, he urged that charity be redirected from them and toward the
“desirables.” To prevent “the free propagation of the stock of those who are seriously afflicted
by lunacy, feeble-mindedness, habitual criminality, and pauperism,” he urged “stern
compulsion,” which might take the form of marriage restrictions or even sterilization.
Galton’s proposals were benign compared with those of famous contemporaries who rallied
to his cause. H. G. Wells, for instance, declared, “It is in the sterilisation of failures, and not in
the selection of successes for breeding, that the possibility of an improvement of the human
stock lies.” Although Galton was a conservative, his creed caught on with progressive figures
like Harold Laski, John Maynard Keynes, George Bernard Shaw, and Sidney and Beatrice
Webb. In the United States, New York disciples founded the Galton Society, which met
regularly at the American Museum of Natural History, and popularizers helped the rest of the
country become eugenics-minded. “How long are we Americans to be so careful for the
pedigree of our pigs and chickens and cattle—and then leave the ancestry of our children to
chance or to ‘blind’ sentiment?” asked a placard at an exposition in Philadelphia. Four years
before Galton’s death, the Indiana legislature passed the first state sterilization law, “to prevent
the procreation of confirmed criminals, idiots, imbeciles, and rapists.” Most of the other states
soon followed. In all, there were some sixty thousand court-ordered sterilizations of Americans
who were judged to be eugenically unfit.
It was in Germany that eugenics took its most horrific form. Galton’s creed had aimed at the
uplift of humanity as a whole; although he shared the prejudices that were common in the
Victorian era, the concept of race did not play much of a role in his theorizing. German
eugenics, by contrast, quickly morphed into Rassenhygiene—race hygiene. Under Hitler, nearly
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four hundred thousand people with putatively hereditary conditions like feeblemindedness,
alcoholism, and schizophrenia were forcibly sterilized. In time, many were simply murdered.
The Nazi experiment provoked a revulsion against eugenics that effectively ended the
movement. Geneticists dismissed eugenics as a pseudoscience, both for its exaggeration of the
extent to which intelligence and personality were fixed by heredity and for its naïveté about the
complex and mysterious ways in which many genes could interact to determine human traits. In
1966, the British geneticist Lionel Penrose observed that “our knowledge of human genes and
their action is still so slight that it is presumptuous and foolish to lay down positive principles
for human breeding.”
S
ince then, science has learned much more about the human genome, and advances in
biotechnology have granted us a say in the genetic makeup of our offspring. Prenatal
testing, for example, can warn parents that their unborn child has a genetic condition like Down
syndrome or Tay-Sachs disease, presenting them with the agonizing option of aborting it. The
technique of “embryo selection” affords still greater control. Several embryos are created in
vitro from the sperm and the eggs of the parents; these embryos are genetically tested, and the
one with the best characteristics is implanted in the mother’s womb. Both of these techniques
can be subsumed under “negative” eugenics, since the genes screened against are those
associated with diseases or, potentially, with other conditions that the parents might regard as
undesirable, such as low I.Q., obesity, same-sex preference, or baldness.
There is a more radical eugenic possibility on the horizon, one beyond anything Galton
envisaged. It would involve shaping the heredity of our descendants by tinkering directly with
the genetic material in the cells from which they germinate. This technique, called “germline
therapy,” has already been used with several species of mammals, and its proponents argue that
it is only a matter of time before human beings can avail themselves of it. The usual
justification for germline therapy is its potential for eliminating genetic disorders and diseases.
Yet it also has the potential to be used for “enhancement.” If, for example, researchers identified
genes linked with intelligence or athletic ability, germline therapy could give parents the option
of souping up their children in these respects.
Galtonian eugenics was wrong because it was based on faulty science and carried out by
coercion. But Galton’s goal, to breed the barbarism out of humanity, was not immoral. The new
eugenics, by contrast, is based on a relatively sound (if still largely incomplete) science, and is
not coercive; decisions about the genetic endowment of children would be left up to their
parents. It is the goal of the new eugenics that is morally cloudy. If its technologies are used to
shape the genetic endowment of children according to the desires—and financial means—of
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their parents, the outcome could be a “GenRich” class of people who are smarter, healthier, and
handsomer than the underclass of “Naturals.” The ideal of individual enhancement, rather than
species uplift, is in stark contrast to the Galtonian vision.
“The improvement of our stock seems to me one of the highest objects that we can
reasonably attempt,” Galton declared in his 1904 address on the aims of eugenics. “We are
ignorant of the ultimate destinies of humanity, but feel perfectly sure that it is as noble a work to
raise its level . . . as it would be disgraceful to abase it.” Martin Brookes may be right to dismiss
this as a “blathering sermon,” but it possesses a certain rectitude when set beside the new
eugenicists’ talk of a “posthuman” future of designer babies. Galton, at least, had the excuse of
historical innocence. !
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big
small
small
small
small
small
medium
big
small
big
small
medium
big
big
medium
small
small
medium
small
small
small
small
big
medium
medium
medium
big
Sales ($M) Profits ($M) # Employ
5453.5
859.8 40929
2153.7
153.0 8200
6747.0 1102.2 50816
5284.0
454.0 12068
9422.0 747.0 54100
2876.1
333.3
9500
709.3
41.4
5000
2952.1 -680.4 18000
784.7
89.0
4708
1324.3 -119.7 13740
4175.6
939.5
28200
11899.0
829.0 95000
873.6
79.5
8200
9844.0 1082.0 83100
969.2 227.4
3418
6698.4 1495.4 34400
5956.0
412.0 56000
5903.7 681.1 42100
2959.3 252.8 31404
1198.3
8527
990.5
20.9
8578
3243.0
471.3 21300
1382.3
0.3 2900
1014.0
47.7
9100
1769.2
60.8
10200
1643.9
118.3
9548
1096.9 -639.3 82300
2916.3 176.0 20100
3078.4 -424.3 28334
4272.0 412.7
33000
63438.0 3758.0 383220
profit/
emp
21007.11
18658.54
21690.02
37620.15
13807.76
35084.21
8280.00
378000
18903.99
8711.79
33315.60
8726.32
9695.12
13020.46
66530.13
43470.93
7357.14
16178.15
8049.93
10144.25
2436.47
22126.76
103.45
5241.76
5960.78
12390.03
-7767.92
8756.22
14974.9
12506.06
9806.38
Assets %profit/sales
4851.6
15.77
2233.7
7.10
5681.5
16.34
2743.9
8.59
8497.0
2090.4
11.59
468.1
5.84
1860.7
-23.05
955.8
11.34
1040.2
-9.04
5848.0
22.50
10075.0
6.97
808.0
9.10
7919.0
10.99
784.0
23.46
6756.7
22.32
4500.0
6.92
8324.8
11.54
5611.1
8.54
1791.7
7.22
624.3
2.11
3613.5
14.53
1076.8
0.02
977.0
4.70
1269.1
3.44
1618.8
7.20
10751.0
-58.28
3246.9
6.04
2725.7
13.78
3051.6
9.66
77734.0
5.92
86.5
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File Edit Tables Rows Cols Analyze Graph Tools View Window Help
THE
Type
Companies
D
Notes Selected Data on the Fortunes
Size Co
small
big
small
big
small
big
Small
-680.4
Columns (870)
Type
BSize Co+
Sales (SM)
Profits (SM)
Employ
profit/emp +
Assets
%profit/sales +
1 Computer
2 Pharmaceutical
3 Computer
4 Pharmaceutical
5 Computer
6 Pharmaceutical
7 Computer
8 Computer
9 Computer
10 Computer
11 Computer
12 Pharmaceutical
13 Computer
14 Computer
15 Pharmaceutical
16 Pharmaceutical
17 Pharmaceutical
18 Computer
19 Pharmaceutical
20 Computer
21 Pharmaceutical
22 Computer
23 Pharmaceutical
24 Computer
25 Computer
26 Computer
27 Computer
28 Computer
29 Pharmaceutical
30 Computer
31 Pharmaceutical
small
small
small
small
medium
big
small
big
small
medium
big
big
medium
small
small
medium
small
small
small
small
big
medium
medium
medium
LI
Sales ($M) Profits ($M)
855.1
31.0
5453.5
859.8
2153.7
153.0
6747.0 1102.2
5284.0
454.0
9422.0
747.0
2876.1 333.3
709.3
41.4
2952.1
784.7
89.0
1324.3 119.7
4175.6
939.5
11899.0 829.0
873.6
79.5
9844.0 1082.0
969.2 227.4
6698.4 1495.4
5956.0 412.0
5903.7
681.1
2959.3
252.8
1198.3
86.5
990.5
20.9
3243.0 471.3
1382.3
0.3
1014.0
47.7
60.8
1643.9
118.3
1096.9 639.3
2916.3
176.0
3078.4 -424.3
4272.0 412.7
# Employ
7523
40929
8200
50816
12068
54100
9500
5000
18000
4708
13740
28200
95000
8200
83100
3418
34400
56000
42100
31404
8527
8578
21300
2900
9100
10200
9548
82300
20100
28334
33000
profit/
emp
4120.70
21007.11
18658.54
21690.02
37620.15
13807.76
35084.21
8280.00
-37800.0
18903.99
-8711.79
33315.60
8726.32
9695.12
13020.46
66530.13
43470.93
7357.14
16178.15
8049.93
10144.25
2436.47
22126.76
103.45
5241.76
5960.78
12390.03
-7767.92
8756.22
14974.9
12506.06
Assets
615.2
4851.6
2233.7
5681.5
2743.9
8497.0
2090.4
468.1
1860.7
955.8
1040.2
5848.0
10075.0
808.0
7919.0
784.0
6756.7
4500.0
8324.8
5611.1
1791.7
624.3
3613.5
1076.8
977.0
1269.1
1618.8
10751.0
3246.9
2725.7
3051,6
%profit/sales
3.63
15.77
7.10
16.34
8.59
7.93
11.59
5.84
23.05
11.34
-9.04
22.50
6.97
9.10
10.99
23.46
22.32
6.92
11.54
8.54
7.22
2.11
14.53
0.02
4.70
3.44
7.20
-58.28
6.04
13.78
9.66
can
1769.2
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