Business Memo Technically, this refers to the following.docx

Business Memo
Technically, this refers to the following format (such as in
email):
TO:
FROM:
SUBJECT: (should be informative) (“Assignment 1” isn’t
informative.)
DATE:
In addition, business memos are short (generally a page or less,
but sometimes two
pages). In our course, we stretch this limit. This makes our
reports a compromise between a
business memo and a business report.
They are informal. Not written in jargon. And, right to the
point.
I recommend one more thing. Begin with an Executive Summary
of a short to middle
length paragraph.
The Executive Summary communicates the findings,
conclusions or recommendations,
and whatever else is needful to a decision-maker. In practice,
decision-makers only read the
complete report as necessary. This is because they’re busy.

Internal organization. If the communicate is short, there is no
need for subheadings.
With middle-sized and longer
What a business memo is not: It’s not a mystery novel. Readers
of business reports want
to know the conclusion immediately. Like I said, readers might
not even read the entire report.
While the conclusion is put first, the conclusion should be based
on the information
gathered for the assignment and its analysis. With this in mind,
you might write the conclusion
last, but then copy and place it at the beginning. You may want
to then edit the rest of the
report.
Time is a consideration. Business decisions are made in real
time. A conclusion that
“more research” is needed sounds like an academic paper, not a
business report. The following
is an illustration of how to draw a conclusion when the data
isn’t clear: “No conclusion can be
drawn.” Or, “While the data suggests conclusion X, no strong
conclusion can be drawn.”
Some odds and ends: Business communications often involve
quantitative information,
often organized into tables and charts. If possible, these should
be able to stand alone
(meaning, could be read without reading the text).
With regard to lists: up to four or five items in a list: think of
using bullet points. More
than that, think of numbering the items.

With regard to numbers in the flow of the text, try to avoid long
numbers. Say 2.3
million. Don’t say 2,289,411. With regard to numbers in tables:
as much as possible, use a
uniform format.
Page numbers: 1 page – don’t use page numbers. 2 or more
pages – use page numbers.
C.F. Thies 6/21/19
Hind Aljohani
Hind Aljohani
Hind Aljohani
Ex5Average IncomeAverage Expenditure552651Dependent
Variable =
Expenditure777851IncomeConstant1,0651,110Coeff.0.8875162.
61631,3521,371Std. Error0.00326.60341,6411,624R-
sqr99.99%9.13289509711,9371,86976072.898949922982,2522,1
606345223.22181716667.27818283822,5292,414t-
stat.275.813224.62602,8812,7043,4683,251
Ex6Average IncomeDummy Variable = 0 for white families and
1 for black familiesAverage Charitable
Contributions55505Dependent Variable = Charitable
Contributions78106BlackIncomeConstant1,068013Coeff.12.662
60.0318-23.36931,351017Std.
Error4.21980.00245.09831,642026R-
sqr93.1%7.6985880273ERROR:#N/A1,93503587.162593999313

ERROR:#N/A2,25304610331.9501510101770.4873489899ERR
OR:#N/A2,530052t-stat.3.000713.1196-
4.58372,8800633,466091549167581101,0311151,3331311,5921
322,315183
ChartCars
Price versus Age of Ford Taurus Cars
0.5 0.5 1 1 1 2 3 3 4 5 14992
13900 11 875 9992 11900 8990 10300 7999
6990 4990
Age (in years)
ChartHouses
Price versus Square Feet of House
830 1050 1124 1378 1518 1700 1904 1969 2070 2078 2350 2439
2448 2467 2490 2550 2708 2800 2843 2927 3100 3171 3400
3400 3400 3470 3600 3600 3800 4200 98000 77000
84000 104650 150500 90300 142300 185500
147000 192500 195650 166600 179200 185500
202300 244650 269500 192500 195600 202650
241500 255500 301000 273000 244650 269500
265650 245000 262500 300300
Square Feet of House
ChartSchooling
Earnings versus Years of Schooling

(Males, 25 to 35 years old)
8 10 12 14 14 16 17714 24517 28772
32354 34670 48688
Years of Schooling
ChartLN
LN( Earnings ) versus Years of Schooling
(Males, 25 - 34)
8 10 12 14 14 16 9.7820999999999998
10.107100000000001 10.267200000000001
10.384499999999999 10.4536 10.793200000000001
Years of Schooling
DataEducational Attainment, Males, 25-34, '97Earnings, Full-
Educational Attainment, Males, 25-34, '97Earnings, Full-
Educational Attainment, Males, 25-34, '97LN( Earnings), Full-
Age (years)Asking PricePriceSquare FeetTime WorkersTime
WorkersTime WorkersAsking Price of Ford
Taurus0.514,992$98,000830less than 9th
grade$17,7148$17,71489.7821Age (in
Years)Intercept0.513,900$77,00010509th-12th
grade$24,51710$24,5171010.1071Coefficient-
1787.8913947.38111,875$84,0001124H.S.
graduate$28,77212$28,7721210.2672Std.
Error285.00734.9419,992$104,6501378Some

College$32,35414$32,3541410.3845R-
sqr83.1%1348.8593395374111,900$150,5001518Assoc.
Degree$34,67014$34,6701410.453639.3547964308828,990$90,
3001700Bach. Degree or
more$48,68816$48,6881610.793271602963.457142914555372.1
428571310,300$142,3001904t-stat-
6.2718.9837,999$185,500196946,990$147,0002070Price of
House54,990$192,5002078Square
FeetIntercept$195,6502350Coefficient69.4021190.20$166,6002
439Std. Error5.4114615.79$179,2002448R-
sqr85.4%25498.3899121507$185,5002467164.372691659528$2
02,3002490106869845799.52918204700867.1379$244,6502550t
-stat12.821.45$269,5002708$192,5002800Earnings, Males, 25-
34$195,6002843Schooling (in
Years)Intercept$202,6502927Coefficient3384.73-
10625.85$241,5003100Std. Error564.067120.04$255,5003171R-
sqr90.0%3713.1294648957$301,000340036.00726811554$273,0
003400496444103.14102655149321.6923077$244,6503400t-
stat6.00-1.49$269,5003470$265,6503600LN( Earnings ), Males,
25-34$245,0003600Schooling (in
Years)Intercept$262,5003800Coefficient0.118.90$300,3004200
Std. Error0.010.15R-
sqr95.9%0.077470659592.716030026940.55645408270.0240068
123t-stat9.6359.91Intercept in natural numbers:7335
1
Performing Regression in Excel
A Tutorial
Simple Regression using the eye-ball method

Before
proceeding
to
using
Excel
to
perform
multiple
regression,
it
is
useful
as
a
refresher
(or,
as
an
introduction)
to
perform
some
simple
regressions
using
the
eye-‐
ball
method.
Simple
regression
–

involves
one
“X”
or
independent
variable
Multiple
regression
–
involves
two
or
more
“X”
or
independent
variables
In
simple
regression,
a
“Y”
variable
(or
dependent
variable
or
response
variable)
is

assumed
to
be
caused
by
an
“X”
variable
(or
independent
variable).
(In
multiple
regression,
the
“Y”
variable
is
assumed
to
be
caused
by
a
set
of
X
variables.)
For
example,
if
“X”
is
the

amount
of
rainfall
during
the
day,
and
“Y”
is
the
number
of
car
accidents,
then
we
might
assume
that
“X”
causes
“Y.”
Assuming
the
relationship
is
linear,
we
would
have

Yt
=
α
+
βXt
+
et
• Yt
is
the
number
of
car
accidents
on
day
t,
• Xt
is
the
amount
of
rainfall
on
day

t,
• α
is
the
expected
number
of
car
accidents
when
it
doesn’t
rain,
• β
is
the
additional
number
of
car
accidents
for
each
unit
of
rainfall,
and
• et
is
the
random
variation
of

auto
accidents
about
its
expected
value.
2
Question:
How
do
we
know
which
variable
is
the
dependent
variable
and
which
is
the
independent
variable?

Answer:
We
often
do
not
know.
We’ll
simply
call
it
an
assumption.
Question:
Why
is
there
an
error
term,
et?
Answer:
Possible
reasons
include
(1)
other
“X”
variables
not
included

in
the
regression,
(2)
the
relationship
isn't
well
approximated
by
a
straight
line,
(3)
there
are
errors
in
measuring
the
variables
that
are
included
in
the
regression,
and
(4)
there
is
true

unpredictability
in
the
"Y"
variable.
Question:
Must
the
relationship
between
the
“Y”
and
“X”
variables
be
linear?
Answer:
No.
In
fact,
we
will
explore
a
particular
non-‐linear
relationship
later

in
this
section.
Exercise 1. Age and Price of Ford Taurus Cars.
Asking Price and Age of Ford Taurus Cars
Age (years) Asking Price
0.5 $14,992.00
0.5 $13,900.00
1.0 $11,875.00
1.0 $9,992.00
1.0 $11,900.00
2.0 $8,990.00
3.0 $10,300.00
3.0 $7,999.00
4.0 $6,990.00
5.0 $4,990.00
3
In this exercise, the Asking Price of Ford Taurus cars is plotted
against the age of the car
in years. Notice that the trend is downward.
Take a straight-edge (the best would be a tinted, see-through

plastic ruler). Orient the
edge so that it aligns with the trend of the scatter of points.
Then, mark this trend with a
line, being sure to project the line northwestward through the
vertical axis and
southeastward to at least where 5 years is on the horizontal axis.
Put a small open circle around the point where the line goes
through the vertical axis.
This is the predicted value of a new Ford Taurus, i.e., the
predicted value of a Ford
Taurus with zero years of age. We’ll call this value “A.”
Carefully identify the point on the trend line directly above 5
years on the horizontal axis,
and mark this point with another small open circle. We’ll call
the height of this second
point “C.” It is the predicted value of a Ford Taurus that is 5
years old. Compute B = (A-
C) / 5. “B” is the slope of the line. It is how much the predicted
value of a Ford Taurus
will fall per year.
We now have a regression equation: Y = A + BX + e, where Y
is the value of a Ford
Taurus, X is its age in years, A and B are the parameters we just
estimated, and e is a
random number representing factors we have not taken into
account.
Asking Price and Age of Ford Taurus
$0
$2,000

$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Age (Years)
A
sk
in
g
P
ri
ce
4
Exercise 2. Price and Square Feet of Homes.

Price and Square Feet of Homes
Price Square Feet Price Square Feet
$98,000 830 $244,650 2550
$77,000 1050 $269,500 2708
$84,000 1124 $192,500 2800
$104,650 1378 $195,600 2843
$150,500 1518 $202,650 2927
$90,300 1700 $241,500 3100
$142,300 1904 $255,500 3171
$185,500 1969 $301,000 3400
$147,000 2070 $273,000 3400
$192,500 2078 $244,650 3400
$195,650 2350 $269,500 3470
$166,600 2439 $265,650 3600
$179,200 2448 $245,000 3600
$185,500 2467 $262,500 3800
$202,300 2490 $300,300 4200
Following the same procedure in Exercise 1, mark the trend line
of the scatterplot above.
Notice, this trend line slopes upward. Mark the vertical
intercept, “A.” In this case, select
2500 square feet to mark the point “C.” Then, estimate B = (A –
C) / 2500.
Price and Square Feet of Homes
$0

$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
$350,000
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Square Feet
P
ri
ce
5
Question: In the above exercise, A is (or should be)
approximately zero. Does this make
sense?
Answer: The expected price of an infinitely small house might
indeed be approximately
zero.

Question: What do you get for B, and does this make sense?
Answer: B would be the expected change in price for another
square foot in the size of a
house. This might be compared to engineering-type estimates of
the construction
cost per square foot of homes. Unfortunately, the data of this
example are quite
old, and construction costs have risen a lot since then.
Exercise 3. Income versus Education.
Education and Income
Educational Attain-
ment, Males, 25-34, '97
Earnings, Full-
Time Workers
less than 9th grade $17,714
9th-12th grade $24,517
H.S. graduate $28,772
Some College $32,354
Assoc. Degree $34,670
Bach. Degree or more $48,688
Earnings versus Educational Attainment (in years)
Males, 25-34 years old, in 1997
$0

$10,000
$20,000
$30,000
$40,000
$50,000
$60,000
0 2 4 6 8 10 12 14 16 18
Educational Attainment (in years)
A
nn
ua
l E
ar
ni
ng
s
6
From the Statistical Abstract of the United States, I obtained the
data in the above table.
These data show that the annual earnings of Males, 26 to 34
years old, in 1997, who

worked full-time during the year, tended to rise with education.
Of course, these earnings
figures are averages, and therefore average-out differences in
earnings among individuals
due to the quality of an individual’s education, the kind of
education, how many hours
the individual worked (other than categorized as “full-time” by
the census department),
how hard the individual worked, and the many other factors that
contribute to an
individual’s earnings.
In order to conduct a statistical analysis of the relationship
between earnings and
education, I first had to quantify the categories of “less than 9th
grade,” “9th to 12th
grade,” etc. Somewhat arbitrarily, I assumed that “less than 9th
grade” meant 8 years of
schooling (on average), “9th to 12th grade” meant 10 years of
schooling (on average), etc.
I then constructed the scatterplot shown above.
Proceeding, for the moment, in the usual way, mark the trend
line through this scatterplot.
Question: Notice that the vertical intercept, “A,” is negative.
Does this make sense?
Answer: A negative intercept makes little sense since people
with zero years of schooling
have positive (but low) productivity. Their wage is low, not
negative.
The strange intercept is a clue that the regression line is not
exactly correct. A second

clue that the regression line is inaccurate is that the vertical
increment from the next-to-
the-last point to the last point appears greater than the vertical
increment from one point
to the next among the first several points. These clues indicate
that the relationship
between earnings and education is non-linear.
In cases like this, it is often useful to convert to the data to
logarithms. Indeed, this is so
often the case that Excel allows you to convert charts to
logarithms by one click. The
reason why logarithms are so useful, we believe, is because they
preserve equal
percentage changes. Therefore, if something is growing at a
roughly constant rate, the
trend line will appear to be a straight line if the numbers are
converted to logarithms.
By converting the vertical scale to logarithms, I produced the
scatterplot show below.
Now, the points appear to lie on an approximately straight line.
We can mark the trend
line of these points using the “eye-ball” method. The vertical
intercept is now a positive
number, something like $6,000; meaning, that a person with no
years of schooling
working full-time will make something like $6,000 per year.
With the vertical scale converted to logarithms, the slope of the
trend line, i.e., the “B” of
the regression equation, is interpreted as the percentage change
in earnings per year of
schooling. Another way of interpreting this parameter is the rate
of return to schooling;
i.e., by what percentage will your future earnings tend to

increase for each additional year
of investment in education. It is unnecessarily difficult to
estimate “B” via the “eyeball”
7
method when you are using logarithms, but it is relatively easy
to do once you learn how
to estimate regression equations using Excel.
Calculating a regression in Excel
In this section, we move from the eyeball method to Excel. With
Excel we will be able to
calculate the regression, including multiple as well as simple
regressions, use samples
that can be very, very large, and obtain several descriptive and
test statistics that enable
us to measure the precision of our model and each of its parts.
We will kind of start over again, and approach regression using
Excel step by step.
1. Formulate a regression.
For example … Yi = α + β1X1t + β2X2t + et
Where Yt is the dependent variable, and X1t and X2t and the
independent variables. The
variables X1t and X2t are the causes, and the variable Yt is the
effect.

2. Collect the data.
Below, I’ve entered some data from the Statistical Almanac of
the United States into
Excel. (This exercise is taken from my exercise on “eye-ball
regressions.”)
Earnings versus Educational Attainment (in years)
Males, 25-34 years old, in 1997
$1,000
$10,000
$100,000
0 2 4 6 8 10 12 14 16 18
Educational Attainment (in years)
A
nn
ua
l E
ar
ni
ng
s

8
Educational Attainment,
Males, 25-34, '97
Earnings,
Full-time
Workers
less than 9th grade $17,714
9th-12th grade $24,517
H.S. graduate $28,772
Some College $32,354
Assoc. Degree $34,670
Bach. Degree or more $48,688
3. Transform the data, as may be necessary.
Here, I’ve transformed the category “Educational Attainment”
into “Years of Schooling,”
and the Earnings of Full-Time Workers into the Natural Log of
Earnings of Full-Time
Workers.
Years of
Schooling Ln(Earnings)
8 9.7821
10 10.1071
12 10.2672
14 10.3845
12 10.4536

16 10.7932
4. Invoke …. Tools, Data Analysis, Regression
5. Invoke … Input Y range and then highlight the range of
numbers giving
ln(earnings).
6. Invoke … Input X range and then highlight the range of
numbers giving years of
schooling.
7. Invoke … New Worksheet Ply and give the ply a
recognizable name, e.g.,
RegressionHumanCapital.
8. Hit … OK and a new ply will show with the regression
output.
9. I suggest annotating this ply with the names of the dependent
and independent
variables (or, Y and X variables).
9

ALTERNATE INSTRUCTIONS
4.Highlight a matrix that is 1+ the number of X variables wide
in terms of
columns; and, 5 rows high.
5.Type =linest(“. Some helps should appear.
6.Highlight the array of the Y variable, from the first to the last
observation (when
you observe both the Y and the X variable or the set of X
variables). Then, type a
comma.
7.Highlight the array of the X variable or the matrix of the set
of X variables (if
you have more than one X variable, they all have to adjacent),
also from the first
to the last observation. Then, type a comma.
8.Now type “1,1)”.
9.Now use two fingers of your left hand to hold down the
“shift” and the “control”
buttons;” and, while holding down these two buttons, use a
finger of your right
hand to depress the “Return” button.
10.A matrix of number should appear.
11.In the cell above the right-most column of the matrix, input
“Constant.”
12.In the cell or cells to the left of the one just marked
“Constant,” input the name

of the X variable or the names of the X variables (putting the
name of the X1
variable in the first cell to the left of the cell marked
“Constant,” the name of the
X2 variable in the next cell to the left, and so on).
13.In the cell to the left of the top row of the matrix, input
“Coefficient.”
14.In the cell below the cell just marked “Coefficient,” input
“Std. Error.”
15.In the cell below the cell just marked “St. Error,” input “R-
square.”
16.In the cell three rows below the cell just marked “R-square,”
input “t-statistic.”
17.In the cell to the left of the cell just marked “t-statistic,”
input as a formula the
amount in the cell in the top cell of the first column of the
matrix divided by the
amount in the cell in the second to the top cell of the first
column of the matrix.
18.Copy and paste this formula across all the other cells in the
row below the
matrix.
10
“X variable” or, as I have renamed it, “Yrs of Sch,” refers to the

one X variable in this
regression. Its coefficient, 0.11, is the regression’s estimate of
the parameter β. In
general, it is interpreted as the expected change in the Y
variable for a 1 unit change in
the X variable. In this case, since the Y variable is the natural
logarithm of earnings, the
coefficient gives the percentage change for a 1 unit change in
the X variable. Thus, an
additional year of schooling is predicted to increase earnings by
11 percent.
“Intercept” is the regression’s estimate of the parameter α. In
general, it is interpreted as
the expected value of the Y variable when the X variable is
equal to zero. In this case, it
is the expected value of the natural logarithm of earnings for
full-time workers with zero
years of schooling. To convert this figure, 8.92, into units, take
its exponential, viz.,
7,497 = e8.92 [ or, in Excel, = exp(8.92) ]
Regression Output: R2 (“R-squared”)
R2, pronounced “R Square,” is the percent of the variation in
the Y variable explained by
the X variable (or, by the set of X variables in the case of a
multiple regression). In the
above case, we have explained 91 percent of the variation in the
average earnings of men
grouped by educational attainment.
In the following chart, I show three hypothetical regressions. In

the bottom regression,
there is perfect positive correlation between the X and Y
variables. In this regression, R2
is 100 percent. In the middle regression, there is a strong but
less than perfect positive
correlation. The Y values are close to their predicted values. In
this case, R2 is shown to
be 78 percent, indicating that percent of the variation in the Y
variable is explained by the
X variable. In the top regression, there is only a weak positive
correlation. R2 is shown to
be 12 percent.
11
As pleasing as R2 is, it is merely a descriptive statistic. One
regression might have an R2
of 78 percent and be considered unacceptable. Another
regression might have an R2 of 12
percent and be considered acceptable. For example, in the above
case, which deals with
data grouped by educational attainment, 91 percent is obtained
for R2. But, if I were to
calculate the regression with the original data – the earnings
and educational attainment
of individual men aged 25 to 34, who worked full-time – it is
likely R2 would be
something like 12 percent. At this time, all that can be said
about how big R2 should be is
that it depends on the situation.

Regression output: the t-statistic
The estimates of α and β are merely statistics, and are subject –
among other things – to
sampling error. This error is given by the numbers in the
column marked “Standard
Error” in the Excel output.
The “t-Stat.” indicates the significance of the X variable. The t-
statistic is calculated as
the estimated parameter divided by its standard error. With a
large sample, if the absolute
value of t > 1.96, we can say, with 95 confidence, that the Y
variable is correlated with
the X variable.1 (If we had more than one X variable, we would
say that the Y variable is
correlated with that particular X variable, holding the other X
variables in the regression
constant.)
1 In the first eye-ball regression (the one involving Ford Taurus
cars), we see a negative relationship and
should expect to obtain a negative t statistic in Excel.
12
The t-statistic deals with the problem of a small sample. A
sample is “small” first because
it has a limited size and second because a bit of information is
used in estimating each
parameter that is estimated. So, if we are simply estimating the

unconditional mean, it is
like we are using up the information in one observation. If we
are estimating two
parameters, e.g., the constant and x-coefficient of a straight
line, then we are using up the
information in two observations. The sample size minus the
number of parameters being
estimated gives the “degrees of freedom” (or, “df” in the
associated chart). As the degrees
of freedom gets large, the t-statistic approximates the normal
curve. But, even with small
degrees of freedom, the t-statistic is approximately normal.
It is the t-statistic (and not the R2) that tells us whether the
relation between an X variable
and the Y variable is statistically significant. Meaning, probably
not due to chance. What
is more, each X variable and the constant term gets its own t-
statistic.
Exercise 4. Income and Expenditure – simple regression.
From the 1934-1935 study of the budgets of 14,469 families, the
U.S. Bureau of Labor
Statistics developed the table below.
Average
Income
Average
Expenditure
552 651
777 851

1,065 1,110
1,352 1,371
1,641 1,624
1,937 1,869
2,252 2,160
2,529 2,414
2,881 2,704
3,468 3,251
Question: Do these data support or contradict the hypothesis
that as income rises,
expenditure tends to rise?
Answer: The estimated β coefficient is 0.89, meaning, that for
each additional dollar of
income, expenditure rises by 89 cents.
Question: Is the relationship between income and expenditure
statistically significant?
Answer: The t-statistic of the β coefficient is 275.81, which is
larger than 1.96; so, the
relationship is statistically significant.
Question: What is the 95 percent confidence interval for the
true parameter b?
Answer: Adding and subtracting 1.96 standard errors to the
estimated coefficient of
income, it can be said that the true amount of each additional
dollar of income that

is expended is between 88.1 and 89.3 cents
13
Exercise 5. Income and Expenditure – multiple regression.
Also, from the 1934-1935 study of the budgets of 14,469
families, the U.S. Bureau of
Labor Statistics developed the data of the table below.
Average
Income
Dummy Variable = 0 for white
families and 1 for black
families
Average
Charitable
Contributions
555 0 5
781 0 6
1,068 0 13
1,351 0 17
1,642 0 26
1,935 0 35
2,253 0 46
2,530 0 52

2,880 0 63
3,466 0 91
549 1 6
758 1 10
1,031 1 15
1,333 1 31
1,592 1 32
2,315 1 83
that charitable contributions
rise as income rises:
Answer: In a multiple regression, Yi = α + β1X1i + β2X2i + ei,
where Yi is charitable
contributions, X1i is income, and X2i is a dummy variable
identifying black
families, the estimated coefficient β1 is 0.0318, indicating that
for each additional
dollar of income, 3.18 cents tends to be contributed to charity.
Question: Is the relationship between income and charitable
contributions statistically
significant when you hold the other independent variables of the
regression
constant?
Answer: The t-statistic of the X1 variable is 13.12, which is

greater than 1.96. Therefore,
yes, the relationship is statistically significant holding the other
independent
variables of the regression constant.
that, during the 1930s,
blacks were “exaggerated Americans”2 because, for the income
that they had, they
tended to make larger charitable contributions than whites?
2 The expression “exaggerated American” was developed by the
Swedish economist and politician Gunner
Myrdal (An American Dilemma: The Negro Problem and
Modern Democracy, 1944). The expression was
designed to capture the greater dedication of African Americans
to work, family and charity, which he
considered to be strong traits among all Americans. (Things
may have changed since then.) The “dilemma”
facing America, Myrdal said, was the high ideals on which this
country was founded, of freedom and
equality, which were not being realized by all of its people.
14
Answer: The estimated coefficient β2 is 12.66, indicating that a
black family tended to
give an additional $12.66 to charity when compared to a white
family with the

same income.
Question: Is the relationship between race and charitable
contributions statistically
significant when you hold the other independent variables of the
regression
constant?
Answer: The t-statistic of the X2 variable is 3.00, which is
greater than 1.96. Therefore,
yes, the relationship is statistically significant holding the other
independent
variables of the regression constant.
The chart below illustrates the multiple regression, compressing
three dimensions ("Y"
and two "X" variables) into two dimensions using color. You
can see that the dots
representing black households tend to lie above those
representing white households, and
that both sets of dots have an upward slope.
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6277.1138.456.4%189.4105.660.131.7%96.9131.765.067.1%227
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150.9210.1110.973.5%470.0138.7113.424.1%186.3184.1117.16
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833-
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720.9%240.6189.3155.764.7%1893101893.103.083-
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616.1%188.0134.7128.468.3%1893111893.113.167-
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948.6%265.142.646.117.4%288.1150.0132.746.1%353.022.118.
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46.8%263.338.435.113.3%273.0141.4127.046.5%133.613.411.1
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11.2%181.6133.7109.460.3%175.317.016.09.1%233.7125.7104.
044.5%227.157.947.721.0%346.6148.1141.440.8%69.616.714.0
20.1%203.6133.7120.959.4%189421894.023.417-
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27.1%213.167.763.029.6%259.4139.6120.046.3%102.714.913.6
13.2%169.6104.697.357.4%189431894.033.500-
15.25%305.643.343.314.2%410.9219.7219.753.5%214.734.726.
912.5%168.3162.9104.662.1%260.633.031.011.9%298.7122.197
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38.4%179.4150.4131.373.2%189441894.043.583-
14.30%313.638.038.012.1%357.7257.0238.666.7%232.459.739.
717.1%183.6178.3115.162.7%253.921.018.07.1%263.3171.7123
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416.3%166.7163.1134.980.9%189451894.053.667-
15.48%267.028.928.910.8%321.9242.4191.759.6%234.458.956.
624.1%180.4163.1119.166.0%285.757.941.914.7%302.1165.013
0.643.2%329.174.774.722.7%271.7229.7171.963.2%195.028.92
6.313.5%180.0130.7119.966.6%189461894.063.750-
15.39%268.017.317.36.4%263.6186.7144.054.6%238.445.639.6
16.6%163.4150.3110.967.8%248.316.313.35.4%272.4102.378.4
28.8%286.750.353.618.7%290.1232.0159.054.8%200.435.330.6
15.3%157.9148.3106.367.3%189471894.073.833-
17.25%269.618.918.97.0%244.4158.1128.152.4%219.129.120.7
9.5%189.3131.0111.458.9%241.010.09.43.9%261.775.168.726.3
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%149.1124.990.060.3%189481894.083.917-
15.53%238.118.318.37.7%235.7122.6109.446.4%258.752.135.7
13.8%210.9156.6114.054.1%193.917.617.18.8%260.185.680.33

0.9%286.049.150.917.8%342.0197.4168.049.1%143.735.925.61
7.8%153.7160.9126.482.2%189491894.094.000-
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025.8%187.9215.1126.767.5%199.630.728.714.4%262.1136.111
3.043.1%310.379.376.024.5%316.3238.3183.057.9%248.034.63
3.613.5%186.7191.3136.473.1%1894101894.104.083-
12.35%275.918.418.46.7%296.0148.0139.147.0%229.687.159.6
25.9%217.6188.6130.359.9%245.635.935.914.6%268.0141.4125
.046.6%327.684.386.326.3%315.3236.6179.356.9%295.9127.98
8.129.8%167.1137.9122.073.0%1894111894.114.167-
10.96%224.917.917.97.9%262.7117.7120.745.9%230.065.646.4
20.2%193.6122.3103.053.2%243.921.419.48.0%272.997.484.03
0.8%341.169.473.721.6%361.4180.1159.744.2%324.134.628.38.
7%128.1100.981.663.7%1894121894.124.250-
11.25%97.114.04.04.1%191.9112.797.350.7%272.639.330.111.1
%190.1153.6119.963.0%243.614.314.35.9%235.392.077.132.8%
331.955.156.116.9%293.6181.6158.654.0%294.729.626.69.0%1
07.4148.092.385.9%189511895.014.333-
10.32%136.615.914.910.9%226.1124.6114.050.4%268.147.125.
49.5%209.7169.0126.360.2%210.028.028.013.3%345.6187.6188
.754.6%302.939.047.615.7%401.1244.4212.753.0%250.333.322.
18.8%162.7124.6101.162.2%189521895.024.417-
11.12%66.415.615.623.4%184.1134.9107.958.6%209.645.130.3
14.5%162.3148.3104.764.5%178.631.430.617.1%222.4160.4119
.053.5%219.448.643.019.6%288.7196.7181.462.8%238.015.917.
07.1%120.792.684.970.3%189531895.034.500-
9.98%85.022.020.724.4%209.3249.4147.370.4%211.746.427.61
3.0%198.1225.4151.476.4%220.027.126.011.8%233.6168.4125.
453.7%279.678.678.628.1%355.7335.3254.371.5%343.949.340.
711.8%152.1136.4119.978.8%189541895.044.583-
9.33%83.641.135.942.9%191.1308.4137.371.8%271.693.360.12
2.1%196.9270.4145.673.9%236.736.334.714.7%239.9197.6146.
661.1%360.0101.787.424.3%309.0329.1229.374.2%326.462.052
.616.1%134.4163.094.770.5%189551895.054.667-
8.73%81.333.432.039.4%169.4287.0119.370.4%254.452.743.41
7.1%187.9248.3145.177.3%251.138.938.415.3%235.3185.0137.

158.3%351.3130.0125.335.7%346.9358.9246.771.1%197.763.04
3.021.7%94.6166.479.183.7%189561895.064.750-
9.07%116.727.721.718.6%170.3229.4112.065.8%259.155.938.1
14.7%190.1207.0145.676.6%209.923.622.610.8%199.7131.693.
646.9%335.762.352.915.7%356.0294.0224.062.9%227.932.431.
413.8%121.7157.0101.483.3%189571895.074.833-
8.52%329.942.142.112.8%241.7245.7176.673.0%285.773.960.4
21.2%179.0169.4123.769.1%233.916.016.06.8%213.1124.698.7
46.3%305.172.968.322.4%382.9223.3178.646.6%190.723.923.9
12.5%134.7124.3113.984.5%189581895.084.917-
6.66%255.943.943.917.1%282.0286.3226.980.4%259.445.932.1
12.4%174.9171.4129.474.0%180.425.323.312.9%195.0128.0121
.662.3%300.671.167.122.3%397.0238.9213.153.7%228.337.035.
015.3%147.3154.0110.975.3%189591895.095.000-
6.50%280.0110.4110.439.4%270.6305.7246.090.9%231.482.962
.126.9%167.7209.9128.676.7%163.618.318.311.2%225.3212.41
61.671.7%308.077.972.123.4%428.9307.0265.361.9%383.1177.
7118.330.9%207.7206.9146.070.3%1895101895.105.083-
6.19%188.340.740.721.6%262.1285.0232.488.7%219.793.952.0
23.7%179.0220.9141.178.9%193.135.335.318.3%250.1198.4153
.961.5%334.793.091.027.2%441.6272.4244.355.3%276.660.372.
626.2%133.9147.3106.379.4%1895111895.115.167-
5.60%201.344.044.021.9%302.7281.4233.177.0%228.948.439.4
17.2%175.1157.7122.670.0%172.130.030.017.4%215.4176.3129
.360.0%325.677.971.321.9%394.7222.6205.652.1%256.963.363.
424.7%118.791.086.773.0%1895121895.125.250-
7.03%167.025.625.615.3%232.7251.1179.677.2%190.936.426.9
14.1%169.7158.9126.174.3%201.315.115.17.5%192.6125.1108.
056.1%272.155.060.422.2%351.3177.0169.648.3%250.032.432.
413.0%124.198.097.078.1%189611896.015.333-
7.63%168.032.632.619.4%300.9353.3227.475.6%209.930.922.9
10.9%197.4175.9144.973.4%211.722.420.49.6%223.7157.6123.
455.2%325.164.053.916.6%434.7225.9199.645.9%206.642.042.
020.3%125.9102.698.978.5%189621896.025.417-
9.08%83.026.926.932.4%262.9292.0188.371.6%217.127.022.91
0.5%195.7151.9127.965.3%201.938.927.913.8%201.6158.3123.

361.2%223.067.172.332.4%397.9235.1209.752.7%168.625.025.
014.8%81.493.988.4100.0%189631896.035.500-
11.59%76.720.620.626.8%291.7281.7208.371.4%215.064.764.3
29.9%197.0180.4127.164.5%173.118.918.910.9%192.0163.4120
.162.6%280.478.373.426.2%375.0286.0239.063.7%181.434.634.
619.1%82.788.776.392.2%189641896.045.583-
12.68%90.133.633.637.2%330.6317.7237.671.9%191.158.759.6
31.2%197.1198.3137.769.9%161.739.938.924.0%192.7190.3141
.973.6%301.1105.990.730.1%369.0352.9255.769.3%238.9117.1
105.344.1%80.3151.394.1100.0%189651896.055.667-
13.99%106.942.042.039.3%382.9407.0283.774.1%195.644.936.
718.8%177.7207.4131.974.2%151.033.028.018.5%196.3184.413
7.770.2%397.0131.6101.625.6%380.3325.6260.968.6%175.721.
421.312.1%110.3166.3104.394.6%189661896.065.750-
14.98%115.326.426.422.9%337.0386.4262.377.8%215.764.327.
912.9%208.1161.9136.765.7%135.918.318.313.5%169.4138.710
9.664.7%354.786.373.720.8%356.9255.0203.957.1%142.114.61
3.69.5%77.398.673.695.2%189671896.075.833-
16.00%87.023.623.627.1%253.0299.1191.975.8%333.482.464.7
19.4%261.3214.1156.760.0%135.421.116.111.9%194.0123.997.
450.2%323.742.939.312.1%465.0239.4240.951.8%211.371.361.
329.0%78.087.375.396.5%189681896.085.917-
18.41%106.421.321.320.0%237.1251.0208.187.8%444.960.344.
910.1%220.7248.7191.086.5%125.118.118.114.5%178.492.674.
041.5%299.792.076.025.4%425.0234.3211.649.8%209.966.660.
628.9%118.9112.9104.087.5%189691896.096.000-
18.90%121.727.727.722.8%285.0301.1234.482.3%424.470.357.
013.4%246.9260.7246.699.9%123.317.016.013.0%143.4103.985
.159.4%237.468.654.422.9%445.1280.9236.353.1%195.474.970.
936.3%278.1239.7232.183.5%1896101896.106.083-
17.86%117.429.029.024.7%308.1316.3251.481.6%334.052.350.
915.2%230.1197.3185.180.4%130.113.613.610.4%165.196.081.
949.6%182.046.944.924.6%488.9239.1227.346.5%173.758.356.
132.3%307.7268.3241.378.4%1896111896.116.167-
18.15%105.418.618.617.6%254.9261.0208.982.0%304.382.369.
622.9%166.3186.1176.3100.0%122.912.712.710.3%160.074.766

.341.4%314.442.745.114.4%450.9233.3198.644.0%401.0284.32
81.470.2%268.0249.9218.981.7%1896121896.126.250-
16.90%89.917.117.119.1%199.4212.9167.684.0%305.159.161.0
20.0%152.7147.7146.996.2%118.97.37.36.1%137.366.755.040.1
%300.448.357.719.2%319.1165.0177.055.5%220.959.754.924.8
%296.1227.4191.064.5%189711897.016.333-
16.78%282.341.339.614.0%302.6301.6240.979.6%330.447.641.
012.4%147.0215.7196.7100.0%115.08.17.16.2%119.174.160.95
1.1%270.038.148.718.0%407.0224.6239.958.9%202.6127.1107.
653.1%400.3392.6335.483.8%189721897.026.417-
16.05%323.965.059.418.4%290.4267.1214.073.7%233.752.029.
012.4%115.0205.4174.1100.0%102.69.09.08.8%122.762.951.64
2.0%230.340.655.324.0%335.3251.9285.385.1%220.7145.1130.
058.9%330.3408.3350.0100.0%189731897.036.500-
15.29%207.183.674.936.1%331.9332.9273.682.4%292.7101.941
.114.1%123.9234.9208.4100.0%118.79.09.07.6%132.369.759.14
4.7%310.7108.4103.633.3%370.4293.7310.383.8%207.6121.910
3.649.9%348.0468.7349.9100.0%189741897.046.583-
14.77%232.994.493.440.1%270.6315.1227.183.9%304.443.332.
610.7%114.4248.4240.9100.0%109.411.111.110.2%145.698.478
.153.7%322.072.485.326.5%349.3316.3322.992.4%172.377.178.
045.3%253.6424.3333.4100.0%189751897.056.667-
13.75%202.966.763.331.2%277.7326.3250.090.0%315.733.725.
78.1%111.0224.7210.3100.0%135.936.933.924.9%143.991.677.
353.7%267.465.369.325.9%345.6249.9243.470.4%218.6116.610
6.748.8%273.1575.0452.1100.0%189761897.066.750-
12.76%180.663.162.634.7%262.1276.6213.381.4%342.123.320.
35.9%89.3181.0172.3100.0%123.720.320.316.4%142.983.073.9
51.7%231.980.781.735.2%245.4232.7269.7100.0%227.9126.011
5.150.5%329.0540.4480.4100.0%189771897.076.833-
11.30%208.448.445.121.7%295.1318.4257.787.3%314.146.346.
314.7%122.4192.3176.1100.0%135.67.37.35.4%156.371.463.74
0.8%219.448.350.322.9%300.7228.4271.990.4%212.4113.098.6
46.4%300.9499.6380.3100.0%189781897.086.917-
9.94%244.694.990.036.8%250.3176.9145.057.9%381.320.925.9
6.8%106.4243.3216.9100.0%129.08.17.15.5%155.665.758.137.4

%216.062.661.628.5%360.7223.0275.376.3%203.395.981.740.2
%323.7410.9358.6100.0%189791897.097.000-
7.05%245.4117.699.340.5%285.1315.1230.981.0%364.4215.416
1.944.4%69.9370.7334.1100.0%116.68.38.37.1%151.4104.381.6
53.9%220.062.067.930.8%317.7263.4292.692.1%211.6157.1131
.061.9%326.4477.1368.0100.0%1897101897.107.083-
6.80%266.7170.9160.060.0%339.7337.7275.781.2%427.9163.71
42.033.2%105.4288.1273.9100.0%149.326.028.018.8%152.3100
.986.756.9%223.074.778.935.4%284.3228.4258.791.0%365.042
6.1382.3100.0%285.6526.3425.0100.0%1897111897.117.167-
7.11%208.756.451.624.7%269.0265.9218.181.1%312.644.739.0
12.5%70.0174.1166.6100.0%127.316.316.312.8%141.465.356.7
40.1%303.190.688.629.2%295.9173.7193.065.2%181.3118.9119
.666.0%261.6384.4366.4100.0%1897121897.127.250-
5.98%304.741.040.113.2%298.9260.1190.363.7%284.932.027.0
9.5%44.6182.7177.9100.0%139.721.921.915.6%125.364.956.04
4.7%153.153.954.935.8%173.7142.4171.498.7%175.067.466.03
7.7%274.7401.3363.1100.0%189811898.017.333-
7.41%266.030.128.110.6%343.1230.0189.655.2%289.324.021.6
7.5%87.0214.3208.7100.0%124.42.92.92.3%119.373.658.749.2
%180.354.656.631.4%267.1224.3244.491.5%208.044.336.317.4
%314.7403.7370.7100.0%189821898.027.417-
7.10%208.143.939.018.7%277.3183.6146.352.8%281.923.317.4
6.2%66.6187.4178.7100.0%111.63.63.63.2%125.656.346.437.0
%169.348.947.928.3%199.7163.1169.384.8%174.754.147.727.3
%266.0333.9289.7100.0%189831898.037.500-
6.56%314.096.393.329.7%357.9298.6222.762.2%313.439.328.7
9.2%55.7243.0214.4100.0%127.99.49.47.4%144.773.967.346.5
%236.7123.1125.753.1%223.4213.9219.698.3%193.483.977.440
.0%289.0354.7333.9100.0%189841898.047.583-
6.49%263.9130.6118.144.8%274.3330.7163.359.5%293.945.735
.412.1%52.6301.0249.6100.0%128.39.99.97.7%126.989.970.055
.2%174.079.086.449.7%258.6264.9263.7100.0%200.0105.4101.
450.7%287.7574.3439.0100.0%189851898.057.667-
7.05%306.790.383.627.2%261.3330.3207.679.4%295.471.059.3
20.1%59.1297.9262.0100.0%135.029.429.421.8%129.190.472.1

55.9%151.063.469.946.3%268.3285.9271.9100.0%196.198.693.
747.8%284.1521.6404.6100.0%189861898.067.750-
8.27%249.0103.983.733.6%238.1262.4181.376.1%276.466.752.
419.0%52.1196.3187.6100.0%126.713.613.610.7%138.179.764.
646.7%189.970.371.937.8%249.4273.3279.6100.0%169.776.368
.340.2%271.3463.3342.1100.0%189871898.077.833-
9.64%350.1154.7142.940.8%291.9217.0190.765.3%301.943.335
.311.7%57.0203.1203.7100.0%129.610.310.37.9%151.765.154.9
36.2%218.374.780.336.8%249.3233.0254.1100.0%224.3148.712
8.957.5%304.7484.1373.7100.0%189881898.087.917-
8.63%256.494.984.933.1%306.6284.4244.979.9%244.475.344.0
18.0%30.0278.4263.0100.0%103.03.43.43.3%174.9109.492.052.
6%211.772.374.035.0%262.1267.0244.693.3%195.0154.3137.97
0.7%283.9394.4331.7100.0%189891898.098.000-
7.06%262.7122.4115.443.9%302.6251.0216.771.6%278.484.465
.923.7%30.9288.6271.3100.0%121.612.611.69.5%141.7115.789.
062.8%175.950.752.429.8%277.0316.7300.9100.0%183.7152.41
47.480.2%245.6502.0367.6100.0%1898101898.108.083-
6.24%424.7193.9159.437.5%392.6374.9309.378.8%417.756.055
.113.2%57.1358.7333.7100.0%164.329.929.918.2%192.9147.91
13.759.0%279.198.782.329.5%340.9284.3256.075.1%225.0187.
0151.467.3%346.4571.9399.0100.0%1898111898.118.167-
4.98%366.2208.7122.033.3%357.9284.2231.164.6%321.956.853
.116.5%69.5253.6234.9100.0%153.426.826.817.5%138.288.970.
150.7%211.678.771.533.8%235.4185.9191.481.3%179.8197.117
4.497.0%278.0405.5298.6100.0%1898121898.128.250-
3.71%362.936.621.65.9%250.9210.7146.658.4%474.4147.7126.
426.6%42.0262.0227.3100.0%137.316.612.49.1%133.367.453.0
39.8%255.997.994.036.7%251.6261.1188.975.1%203.976.670.9
34.8%207.1364.3297.9100.0%189911899.018.333-
3.19%397.126.325.46.4%312.7313.1197.963.3%286.032.620.07.
0%41.4249.1211.6100.0%171.918.317.410.1%162.4140.994.958
.4%385.6110.1110.128.6%370.1220.6175.947.5%176.626.420.4
11.6%269.9357.7263.097.5%189921899.028.417-
3.48%205.722.420.49.9%214.9256.4172.480.3%268.163.129.71
1.1%55.1229.4173.1100.0%207.762.460.429.1%121.4100.963.1

52.0%272.986.686.631.7%304.1195.1163.453.7%180.972.160.0
33.2%211.6353.7230.4100.0%189931899.038.500-
1.76%257.956.145.117.5%273.6326.1217.379.4%331.331.321.6
6.5%136.3309.6227.4100.0%204.427.625.612.5%169.3154.1107
.763.6%400.4168.0168.042.0%292.9257.0194.466.4%202.475.7
64.431.8%258.0443.4297.6100.0%189941899.048.583-
0.49%273.688.184.130.8%317.4397.9238.175.0%252.073.746.6
18.5%174.4376.6184.9100.0%200.934.029.714.8%170.3194.411
9.670.2%379.0189.0189.049.9%273.4353.7187.068.4%210.4124
.4104.149.5%216.0495.1330.4100.0%189951899.058.667-
0.08%325.0154.7100.330.9%306.9399.1266.386.8%287.451.636
.712.8%151.0376.3161.9100.0%198.722.121.410.8%155.7173.7
102.766.0%387.4256.4237.461.3%193.9856.3159.382.2%220.01
22.1110.450.2%186.0501.3279.6100.0%189961899.068.7501.18
%281.474.169.624.7%231.7313.0200.686.6%295.656.740.713.8
%175.6300.1163.393.0%206.464.963.930.9%165.0247.9110.767
.1%341.6177.6177.652.0%257.7536.0192.774.8%209.6145.4132
.463.2%205.0426.6275.0100.0%189971899.078.8332.06%272.3
261.343.315.9%201.7265.3176.187.3%269.990.457.021.1%210.
7260.4162.377.0%183.023.119.310.5%172.0133.087.150.7%323
.4257.7157.748.8%264.9484.4210.479.4%204.7116.3106.752.1
%237.4464.6286.7100.0%189981899.088.9172.50%248.0123.66
2.025.0%198.3256.3174.488.0%259.6129.457.722.2%171.6348.
3177.0100.0%147.920.319.112.9%143.7137.093.965.3%365.418
9.4172.347.1%264.1449.6196.774.5%288.3160.4153.753.3%241
.7571.6347.3100.0%189991899.099.0002.84%224.758.654.024.
0%141.4206.6118.984.0%201.6161.660.329.9%187.9401.0172.9
92.0%169.139.036.921.8%143.7162.195.466.4%348.7224.4221.
663.5%235.7575.1179.476.1%226.9316.0273.6100.0%266.7465.
4254.495.4%1899101899.109.0832.35%246.3116.4101.641.2%2
14.9316.4189.688.2%303.1157.3116.638.5%207.0330.3187.990.
8%207.971.167.132.3%168.0207.6122.973.1%332.9212.7212.76
3.9%240.7531.9175.973.1%255.4230.4215.684.4%216.0407.425
6.4100.0%1899111899.119.1671.87%213.332.431.414.7%167.4
256.3152.090.8%230.997.348.921.2%208.9249.6163.778.4%169
.719.919.011.2%150.9143.987.758.1%303.7167.6167.655.2%26

0.6468.1197.175.7%187.0101.190.748.5%226.7374.1281.0100.0
%1899121899.129.2501.71%225.720.619.68.7%151.7195.9137.
690.7%177.640.330.417.1%182.3219.9165.190.6%190.435.334.
318.0%117.799.166.456.4%279.9163.1140.150.1%210.6432.616
4.678.2%173.783.077.944.8%214.0363.0303.6100.0%19001190
0.019.3331.71%249.016.316.36.5%191.9251.4168.787.9%175.3
37.422.713.0%184.9249.1164.188.8%178.330.130.116.9%131.0
149.485.465.2%267.6115.9115.943.3%269.0294.6164.661.2%14
8.143.042.428.6%252.7390.3275.3100.0%190021900.029.4171.
61%154.721.421.413.9%125.4208.6111.689.0%126.174.736.929
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0%279.7115.7115.041.1%217.9234.0133.461.2%125.781.368.35
4.3%145.0327.6247.7100.0%190031900.039.5001.02%185.049.
644.624.1%152.6232.7129.684.9%146.968.947.732.5%191.0329
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0.3116.036.3%229.0294.7151.666.2%158.4122.7105.966.8%192
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9%138.1244.7129.093.4%108.770.452.047.8%148.6239.4136.19
1.6%162.357.153.332.8%127.3205.393.073.1%372.3188.9186.7
50.2%181.4455.7136.475.2%187.0129.1100.753.9%139.3483.62
60.3100.0%190051900.059.667-
0.16%184.939.736.619.8%106.9193.0103.997.2%108.4107.149.
045.2%119.4268.0106.188.9%175.362.158.333.3%108.7187.383
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092.449.2%184.3441.1317.7100.0%190061900.069.750-
0.16%198.020.418.49.3%124.6180.4112.690.4%102.645.932.63
1.8%161.7250.6117.672.7%206.492.486.341.8%89.0171.975.08
4.3%246.782.982.933.6%234.4308.9161.168.7%257.7103.689.4
34.7%231.0398.1262.9100.0%190071900.079.833-
2.48%173.723.322.312.8%115.3180.796.383.5%77.035.325.633.
2%162.0223.4122.375.5%252.1198.0160.063.5%101.7122.976.3
75.0%235.3116.3116.349.4%248.7325.9681.0100.0%236.4120.7
110.746.8%239.7449.6282.4100.0%190081900.089.917-
2.92%168.916.415.49.1%102.9134.791.989.3%51.437.023.746.1
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7.6%251.1229.1177.170.5%220.0348.0155.470.6%293.9131.310

8.036.8%345.4499.6349.7100.0%190091900.0910.000-
3.64%152.930.129.119.1%163.3208.1162.399.4%92.481.054.65
9.0%139.1273.4103.474.3%281.1215.7208.474.1%123.0206.688
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059.345.3%134.9308.9116.786.5%1900101900.1010.083-
4.46%174.325.025.014.3%162.9202.7139.985.9%99.7569.052.9
53.0%173.4289.0137.479.2%346.4298.0256.974.1%141.4192.19
4.767.0%213.7388.0166.177.7%261.0466.1216.482.9%42.451.4
38.490.6%110.9176.692.083.0%1900111900.1110.167-
2.64%241.916.916.97.0%123.9187.1123.9100.0%72.968.046.66
3.9%170.4215.6135.179.3%202.4135.3133.766.1%143.6166.393
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6.395.9%71.382.668.395.8%1900121900.1210.250-
0.53%234.924.723.410.0%96.9150.196.9100.0%47.663.153.710
0.0%135.0206.9143.0100.0%199.986.383.341.7%123.9123.684.
468.2%199.9120.3120.360.2%224.7343.0164.973.4%112.4116.0
97.086.3%75.789.463.984.3%190111901.0110.3331.40%359.43
4.633.99.4%169.4165.7110.965.4%57.036.930.453.4%146.7234.
4149.0100.0%165.771.469.441.9%126.3164.190.771.8%204.410
6.398.348.1%299.1425.1226.675.7%60.024.624.641.0%82.4115.
190.9100.0%190121901.0210.4172.05%274.039.037.313.6%131
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03.423.115.915.3%117.9158.186.173.1%183.993.693.650.9%22
6.3251.7152.967.6%32.37.96.018.6%50.183.962.9100.0%19013
1901.0310.5002.77%234.6125.184.936.2%137.9178.0124.990.6
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140.4213.4108.076.9%264.3135.1134.050.7%248.3385.0178.37
1.8%46.050.037.080.4%57.0156.094.4100.0%190141901.0410.5
832.89%300.9251.4198.165.9%200.0223.4179.389.6%132.4114.
390.668.4%114.7291.0124.4100.0%212.4104.490.942.8%161.92
99.3125.477.5%346.7330.6226.765.4%237.1556.7186.778.7%64
.389.148.475.3%70.4175.178.7100.0%190151901.0510.6674.37
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81.5%136.3322.0128.494.2%202.6118.990.444.6%215.7378.418
0.383.6%295.9282.1186.162.9%171.4545.4133.778.0%159.0327
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94.9402.7185.963.0%203.7223.9169.483.2%134.0112.498.973.8
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83.1%249.6296.7156.462.7%240.0527.6169.670.7%259.0331.62
26.687.5%141.6185.9147.7100.0%190171901.0710.8334.18%26
0.6382.3207.979.8%198.3228.0182.391.9%125.4137.190.972.4
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8.9%343.3386.9215.162.7%213.9510.9150.170.2%433.0557.336
7.684.9%159.6208.0145.391.0%190181901.0810.9174.68%508.
3635.6415.081.6%247.9300.1180.772.9%122.7100.088.672.2%1
31.4261.0136.6100.0%222.1139.1134.460.5%197.6191.7141.07
1.4%249.7159.6156.662.7%288.7506.7199.769.2%341.0412.630
1.088.3%153.0168.7142.393.0%190191901.0911.0004.07%353.
7521.3298.184.3%316.0455.4259.382.1%86.7100.775.787.3%12
7.7273.9148.6100.0%281.1194.1186.666.4%209.6284.9175.383.
6%259.0178.0178.068.7%264.3584.7192.973.0%379.4554.1312.
782.4%185.3214.7186.4100.0%1901101901.1011.0834.44%219.
6214.1151.168.8%297.1385.6231.377.8%68.198.762.091.0%117
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87.1%149.6198.7145.397.1%1901111901.1111.1674.10%280.72
02.4188.967.3%218.9195.9122.155.8%53.451.746.987.7%107.9
184.9125.6100.0%301.7213.4205.168.0%219.4225.7150.168.4%
291.9370.6177.760.9%261.0525.7205.678.8%198.9307.3158.77
9.8%122.6160.6117.996.2%1901121901.1211.2502.62%147.474
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118.4100.0%130.657.752.340.0%165.9184.7129.478.0%234.916
0.4119.350.8%213.9420.3165.077.2%121.495.063.752.5%113.4
126.776.367.3%190211902.0111.3335.21%233.0177.7106.445.7
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49.7%261.3419.7192.073.5%180.677.368.938.1%169.6176.7113
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174.9136.468.6%60.744.741.668.5%111.6193.9124.7100.0%226
.1170.9166.973.8%157.6194.7131.683.5%236.3114.1113.347.9
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65.8%190231902.0311.5003.68%312.3296.9230.073.7%214.024

5.1159.674.6%102.0101.997.395.4%91.0243.9128.9100.0%349.
7289.1272.377.9%169.7260.0144.985.4%339.7346.3199.358.7%
236.1630.3175.674.3%338.1188.6179.453.1%222.1227.7153.76
9.2%190241902.0411.5835.76%308.1555.0265.186.0%202.1253
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7262.1243.473.2%188.0284.9159.084.6%385.4557.1298.477.4%
176.7946.4141.680.1%325.9283.1236.072.4%196.6291.4160.68
1.7%190251902.0511.6676.18%302.1508.0247.782.0%186.7264
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91.0263.677.7%188.0317.7173.692.3%350.1481.7303.986.8%18
3.3800.3159.186.8%458.4627.7392.485.6%238.7394.0204.385.6
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44.381.9%110.4202.996.187.1%114.7240.9104.791.3%296.9227
.4214.372.2%180.7245.3149.782.8%309.7323.1262.784.8%189.
3542.9157.783.3%430.9449.0357.983.1%219.9328.4184.483.9%
190271902.0711.8334.64%273.1278.0222.981.6%152.7176.312
0.979.1%212.4730.0190.389.6%149.1211.4158.3100.0%278.722
7.0218.178.3%169.7154.9123.772.9%333.3375.4296.488.9%213
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05.784.5%283.4358.3264.793.4%151.9329.6133.688.0%264.420
8.0199.075.3%190.1210.4156.482.3%396.0534.7358.690.5%187
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%190291902.0912.0005.67%333.3909.0286.686.0%199.9252.01
76.788.4%147.1178.4138.093.8%135.6329.0110.181.2%364.433
6.4308.384.6%168.6297.7142.784.7%374.0515.6343.791.9%190
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145.186.5%190.0204.6177.993.6%129.9255.7122.994.6%274.92
29.7219.079.7%190.4210.6163.385.7%307.3400.3279.390.9%21
0.1781.0197.193.8%378.6583.4301.179.5%226.0268.4198.087.6
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206.092.6%117.0135.1108.492.7%131.3180.0115.688.0%191.61
56.7146.176.3%168.9218.0147.787.5%278.7321.6258.792.8%20
3.1671.4186.391.7%277.6243.3176.963.7%209.7239.1185.688.5
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8.086.0%98.195.381.783.3%102.7170.088.686.2%164.1118.611
4.369.6%117.6143.089.075.7%335.6375.3305.691.1%186.0464.
7172.792.9%247.9144.1115.946.7%150.6154.3125.783.5%1903
11903.0112.3338.64%226.6251.1132.058.3%243.0265.3207.085
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55.6%169.6241.7142.984.2%231.3191.7163.070.5%190.4466.91
67.087.7%292.989.985.329.1%196.1184.3155.979.5%19032190
3.0212.4178.39%168.4211.0108.664.5%200.6246.1188.493.9%8
1.187.075.993.5%124.3214.4108.187.0%253.4217.0205.781.2%
145.9238.3122.183.7%228.4188.4180.779.1%176.0401.7151.38
6.0%282.4121.4114.740.6%169.0185.7154.491.4%190331903.0
312.5007.78%207.9385.7173.783.6%174.9234.9165.494.6%166.
7187.3155.693.3%108.3247.9100.392.6%416.3383.0363.187.2%
155.1275.9129.183.2%302.7349.9267.488.3%166.6654.9154.49
2.7%240.9163.1147.461.2%188.4229.9180.195.6%190341903.0
412.5838.21%400.1679.3364.091.0%241.6301.0228.694.6%168.
7199.0156.993.0%82.1234.776.993.6%409.7386.7362.088.4%13
0.9253.4110.784.6%414.0713.6392.094.7%145.6849.7138.495.1
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2.7178.196.5%89.4245.479.488.8%416.3381.0360.386.5%116.7
271.390.477.5%399.0493.0376.394.3%140.7876.6132.994.4%71
2.4957.9685.996.3%212.7287.0202.995.4%190361903.0612.750
7.79%259.4408.6244.794.3%193.6252.3185.395.7%251.1290.62
46.198.0%114.3192.1102.689.8%320.0229.0217.367.9%144.421
9.6107.374.3%295.9245.7218.773.9%166.3848.1147.788.8%368
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.62%382.0432.1358.193.8%172.7217.6166.996.6%234.6247.121
6.792.4%125.4248.9116.692.9%475.9427.0415.387.3%130.9180
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1539.0308.184.2%142.6168.0125.988.3%190381903.0812.9176.
62%343.0389.4296.386.4%200.0273.3188.494.2%205.9252.619
6.095.2%137.1243.1127.793.1%404.3357.6349.986.5%195.1247
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3235.6193.372.9%159.7198.1140.387.8%190391903.0913.0006.
09%196.9191.6140.771.5%271.0342.9255.994.4%125.1153.012

3.398.5%115.4264.1113.498.3%204.4201.7178.187.1%189.9319
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6264.6178.769.7%120.9188.7115.695.6%1903101903.1013.083
4.34%197.4173.3126.764.2%189.0208.4159.184.2%109.6122.41
08.699.1%138.9206.4132.195.2%236.9207.6197.083.2%188.331
2.0158.184.0%283.7391.4242.385.4%224.1568.6212.794.9%250
.7311.7211.384.3%81.7150.779.096.7%1903111903.1113.1671.
31%179.479.775.942.3%142.1142.6124.387.4%113.3105.985.67
5.5%125.4176.9111.789.1%80.941.439.448.8%186.1245.7143.7
77.2%210.1196.9183.187.2%218.3500.1209.495.9%193.9223.01
40.072.2%98.3101.174.375.6%1903121903.1213.2500.40%123.
450.748.639.4%86.179.469.680.8%104.9113.795.691.1%161.01
96.0142.488.5%98.452.752.753.6%190.6188.0164.986.5%210.7
192.4186.088.3%157.4359.7150.195.4%146.917.110.06.8%87.1
123.357.465.9%190411904.0113.333-
0.53%103.355.445.444.0%111.4122.999.189.0%68.171.964.194.
1%160.0197.6143.489.6%104.754.753.751.3%262.0272.7232.48
8.7%133.386.385.364.0%224.1326.3186.983.4%119.637.624.12
0.2%82.183.057.069.4%190421904.0213.4171.65%72.331.720.3
28.1%84.4112.170.383.2%63.766.957.089.5%157.4230.1138.68
8.0%138.085.985.962.2%187.9220.1162.786.6%128.9102.1100.
978.3%177.3302.9167.394.4%120.043.729.924.9%65.996.049.7
75.5%190431904.0313.5002.30%215.4109.9100.346.6%196.119
7.0159.681.4%128.1132.3116.991.2%183.6308.3170.092.6%134
.385.482.461.4%208.1258.1182.987.9%177.9151.6148.983.7%2
20.6452.9208.994.7%141.466.750.035.4%87.0185.074.385.4%1
90441904.0413.5832.71%129.9203.173.356.4%205.6240.1178.4
86.8%121.0137.1114.094.2%154.9266.6135.187.3%115.082.379
.368.9%171.4252.9140.381.8%161.1143.1140.187.0%198.6464.
9189.795.5%185.6128.6116.662.8%120.3208.194.178.3%19045
1904.0513.6671.83%151.088.682.754.8%172.9196.1140.381.2%
153.9207.0150.197.6%175.3273.9153.487.5%143.4114.9108.97
5.9%172.9237.6150.687.1%309.4278.4274.788.8%184.4546.617
2.193.3%193.0226.0136.170.5%109.3199.199.390.8%19046190
4.0613.7500.77%139.192.386.061.8%142.6148.7117.382.3%99.
1110.996.997.7%176.9228.6159.490.1%119.686.986.972.6%228

.7245.6203.188.8%217.4193.4187.186.1%198.0487.6186.194.0
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833-
0.35%169.7123.7106.762.9%193.4207.1168.387.0%191.0192.01
86.097.4%175.3202.3161.191.9%98.764.162.363.1%199.3170.7
157.178.9%150.0126.3124.382.9%188.0373.6175.793.5%171.11
98.1141.782.8%103.098.361.659.8%190481904.0813.9170.44%
176.3156.3125.471.2%193.6190.3160.983.1%124.1135.0123.19
9.2%160.0240.3148.392.7%288.7247.6244.684.7%201.6198.915
5.677.2%157.1163.4136.486.8%167.1306.3156.793.8%228.1228
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8.3138.1115.083.2%248.9265.9224.490.2%187.7207.9185.798.9
%181.7249.0169.393.2%289.4253.1253.087.4%257.3293.9231.1
89.8%212.4216.0202.695.4%201.9416.0196.397.2%148.0147.11
24.183.9%72.4129.053.173.4%1904101904.1014.0833.63%147.
7178.9118.079.9%195.4215.0170.487.2%140.6185.6138.698.6%
179.4259.0165.992.4%144.6105.6102.670.9%221.3277.7185.68
3.9%284.3302.7273.796.3%190.4432.4182.795.9%212.3344.117
7.383.5%93.3125.768.773.7%1904111904.1114.1675.05%147.6
167.186.358.5%183.7212.4168.791.8%129.6142.1128.699.2%17
9.3219.6169.194.3%231.3189.9189.982.1%193.9217.7166.485.9
%268.7299.3253.994.5%157.0292.9152.196.9%117.7116.386.67
3.5%98.4118.471.072.1%1904121904.1214.2505.44%147.1115.
999.667.7%168.0186.6144.385.9%63.464.662.498.4%187.0222.
3180.496.5%93.452.449.452.9%122.7141.6108.388.2%122.7110
.4110.389.9%156.9355.9154.498.5%120.168.160.750.5%84.199.
459.170.3%190511905.0114.3335.31%165.4146.195.157.5%182
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343.943.947.5%139.0168.3120.386.5%131.3112.1105.180.1%18
8.7415.4180.995.8%104.156.745.743.9%87.7107.464.973.9%19
0521905.0214.4174.71%136.9115.686.663.3%152.1133.1108.37
1.2%61.770.659.496.3%169.3266.3156.392.3%120.487.186.972.
1%180.4187.9153.184.9%113.799.990.779.8%132.0360.1125.19
4.8%102.748.747.145.9%86.1105.766.176.8%190531905.0314.5
006.60%110.0105.484.977.1%221.6262.6199.990.2%144.7181.4
142.698.5%202.1352.9186.192.1%347.9307.4307.788.5%194.02

29.6172.789.0%214.7198.0190.088.5%184.6445.7175.395.0%15
2.7105.687.157.1%104.1123.783.680.2%190541905.0414.5838.
53%122.7121.793.976.5%175.3231.7156.689.3%195.1212.3192.
398.5%194.4361.0185.695.4%319.6293.9293.992.0%165.0209.7
144.987.8%364.1351.3334.691.9%126.6509.7120.194.9%197.72
00.3152.677.2%124.1166.9109.788.4%190551905.0514.6678.99
%190.9257.4177.493.0%217.4275.9208.695.9%138.6176.0134.6
97.1%191.4346.7182.995.5%264.9244.0240.190.7%155.4222.31
32.084.9%345.3324.9317.792.0%153.6561.9149.397.2%234.919
7.9183.478.1%112.0178.391.481.6%190561905.0614.7508.67%
237.9246.7202.084.9%251.1348.4236.094.0%125.6131.6122.09
7.2%202.1326.1188.693.3%412.7374.9372.790.3%154.1192.913
7.088.9%328.6320.7302.091.9%146.9490.0144.498.3%299.1394
.7262.387.7%121.9154.0105.486.5%190571905.0714.8338.49%
243.4269.9209.986.2%310.3374.0291.093.8%208.6209.9187.99
0.1%258.0356.3232.190.0%360.3335.9335.993.2%153.4137.611
5.975.5%254.7254.7227.789.4%189.7440.6181.095.4%348.7411
.9304.687.3%124.9143.7104.383.5%190581905.0814.9179.43%
261.1348.1210.380.5%262.9299.6221.684.3%280.7366.3268.09
5.5%275.4368.9249.790.7%268.9242.3237.388.3%158.6168.413
9.087.7%321.3312.3307.095.6%169.7406.6164.997.1%348.6458
.3325.693.4%119.7158.0103.686.5%190591905.0915.0009.90%
183.7236.4180.798.4%243.7291.9221.190.7%240.1254.0196.68
1.9%262.1407.9224.985.8%293.9272.7268.791.4%191.4278.116
2.484.9%379.3481.7352.693.0%186.4502.7178.995.9%423.4509
.1409.696.7%87.1136.374.385.2%1905101905.1015.0839.80%1
34.9213.9112.183.2%201.7257.1187.392.8%318.1374.1266.383.
7%266.1304.1213.380.1%321.3295.1294.191.6%190.1229.1159.
483.8%466.4560.4441.394.6%218.6527.7215.498.6%409.0513.7
375.491.8%108.4127.790.483.4%1905111905.1115.16710.26%1
56.4224.7123.178.7%188.6239.0169.689.9%209.7238.9161.176.
8%221.7246.0155.970.3%247.9226.1226.191.2%196.4200.7171.
187.1%391.3397.9374.195.6%198.0422.6193.797.8%271.6282.1
237.087.3%89.4110.068.376.4%1905121905.1215.25011.24%13
3.6189.0121.991.2%149.1193.6132.688.9%176.1175.3123.470.1
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88.9%275.0274.4256.193.1%172.3386.0164.995.7%140.065.461
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0.9122.787.3%186.1231.3166.189.3%126.6123.999.378.4%212.
1238.4157.974.4%123.073.773.759.9%204.3178.9169.783.1%17
8.6172.6153.185.8%177.3385.6172.797.4%118.373.373.362.0%
91.9124.766.672.5%190621906.0215.41712.54%105.6139.396.1
91.1%120.9166.4119.498.8%111.999.477.068.8%173.3236.3138
.980.1%185.7152.7152.782.2%164.3150.9131.079.7%191.3187.
0172.089.9%154.6376.7148.996.3%77.467.741.053.0%63.676.9
48.175.7%190631906.0315.50011.87%91.1140.090.999.7%149.
7189.1136.190.9%146.7151.0114.978.3%218.0314.0174.079.8%
277.1251.7248.989.8%248.6276.1225.390.6%187.1196.9167.18
9.3%194.3450.7185.795.6%94.748.434.336.2%83.796.362.774.9
%190641906.0415.5838.95%109.3175.4103.394.5%206.4286.41
92.093.0%216.0222.4179.182.9%217.0374.0181.183.5%443.640
2.0399.990.1%237.3271.7208.788.0%366.9369.0338.092.1%148
.7428.3145.097.5%93.9127.173.978.7%84.1119.966.679.1%190
651906.0515.6679.42%152.9467.4144.194.3%159.7308.1151.79
5.0%240.7233.0196.381.5%218.7348.7193.388.4%507.0477.447
7.494.2%209.6251.3183.187.4%479.1479.1446.693.2%151.9460
.7142.994.1%147.7191.0124.184.0%85.1118.178.391.9%190661
906.0615.75010.65%198.3532.1186.794.2%204.7291.6191.793.
6%333.1389.4290.787.3%205.4353.9178.186.7%455.6444.3420.
392.3%170.7192.9145.185.0%310.0302.4283.091.3%155.1419.0
150.396.9%158.4179.0127.080.2%91.7138.678.385.4%1906719
06.0715.83311.01%480.1820.9460.796.0%254.4364.9244.996.2
%279.9416.3252.390.1%257.7316.7220.085.4%492.0461.4460.4
93.6%169.1180.3144.185.2%233.1261.6248.9100.0%216.9435.6
211.797.6%165.7137.7119.071.8%96.4125.672.775.4%1906819
06.0815.91711.35%329.0772.6313.195.2%271.9366.4264.097.1
%282.7467.3249.088.1%232.0375.7202.987.4%668.3650.6645.6
96.6%158.3173.3133.484.3%373.6365.6349.993.7%193.9305.71
90.998.5%151.4337.1137.991.0%91.7125.072.378.8%19069190
6.0916.00010.45%758.02085.6743.998.1%323.1420.0316.397.9
%208.3601.7158.476.1%290.3528.0220.776.0%547.4550.3516.4
94.3%220.7303.1200.490.8%408.6422.4370.090.6%184.3477.91

77.096.0%174.7261.4159.091.0%91.0112.076.383.8%19061019
06.1016.08310.61%769.11558.3754.798.1%446.4549.0430.396.
4%210.9368.0193.691.8%256.4326.3235.491.8%507.0537.1478.
694.4%193.4235.6173.489.7%440.01719.3394.089.5%229.1514.
3221.696.7%175.3224.4143.181.7%98.4119.479.781.0%190611
1906.1116.16711.32%664.11221.1638.096.1%323.0379.7309.69
5.8%224.9546.4209.493.1%198.3257.0188.695.1%425.9399.639
3.092.3%163.3196.3138.684.9%380.1441.3338.689.1%197.6433
.7193.197.8%174.6190.9147.684.5%115.1130.693.481.1%19061
21906.1216.25012.16%306.4606.0248.781.2%230.7257.6197.38
5.5%127.6111.4119.193.4%204.0237.1191.794.0%296.1261.626
1.688.3%151.4152.4120.479.5%281.3244.6239.785.2%176.9374
.9173.698.1%162.1130.3112.769.5%99.9104.070.470.5%190711
907.0116.33314.15%126.9183.4108.185.2%256.7274.9248.096.
6%124.7799.4111.489.3%199.9236.3189.694.9%321.7284.1284.
188.3%137.0140.1111.481.3%200.3166.9156.077.9%244.3441.0
236.997.0%189.7166.1141.774.7%92.786.962.967.8%19072190
7.0216.41714.01%330.0328.0312.094.5%239.0256.0237.099.2%
123.0162.0116.094.3%189.0249.0177.093.7%230.0210.0196.08
5.2%174.0182.0146.083.9%238.0206.0186.078.2%204.0413.020
1.098.5%172.0176.0137.079.7%77.099.059.076.6%190731907.0
316.50013.60%453.9489.6423.693.3%320.7395.1303.194.5%28
2.3457.3249.688.4%218.3385.9206.994.8%355.6324.4321.690.4
%188.9236.1162.686.1%335.4347.4293.387.4%231.1498.7226.9
98.1%194.4176.1150.377.3%109.4129.172.666.3%190741907.0
416.58315.08%488.1679.6470.496.4%239.3370.1234.197.9%28
8.0458.4273.695.0%204.3351.7199.097.4%384.4364.7357.993.1
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97.7%348.9469.1310.088.9%156.6188.6120.076.6%190751907.
0516.66715.76%508.3748.1496.997.8%260.6389.6252.997.0%2
63.6361.1254.796.6%202.1346.0196.697.2%358.1352.4342.195.
5%174.0207.9148.185.1%415.3378.7372.489.7%213.7425.4211.
799.1%346.4575.3311.489.9%162.1213.6133.482.3%190761907
.0616.75014.65%429.7494.3420.797.9%256.0519.9248.497.0%2
10.0350.7210.0100.0%183.9296.9181.198.5%270.0246.3239.38
8.6%172.3177.4149.386.7%363.4327.3322.188.6%238.6415.623

4.198.1%291.9512.9254.387.1%177.9237.7156.387.9%1907719
07.0716.83314.69%418.7551.3399.195.3%244.7337.9235.396.1
%274.6403.7271.799.0%203.1260.7198.397.6%324.1299.3293.3
90.5%160.1159.6136.084.9%393.9385.4353.189.7%276.0433.92
68.797.4%317.3517.4282.088.9%193.7273.6165.985.6%190781
907.0816.91713.46%383.4473.7382.199.7%296.7365.3294.999.
4%207.1565.3206.099.4%213.3333.9208.697.8%301.7278.7276.
791.7%140.7161.9120.785.8%374.4360.6345.192.2%202.1269.3
194.096.0%335.9849.1308.391.8%210.1266.0176.484.0%19079
1907.0917.0009.96%401.1455.1392.697.9%313.7410.9304.397.
0%168.1390.3164.197.6%215.4380.4208.096.6%369.3351.9351.
995.3%166.7208.3140.684.3%406.9444.7371.991.4%311.9504.1
307.998.7%388.4721.7357.992.1%192.6252.4147.376.5%19071
01907.1017.0836.67%307.7372.3297.696.7%224.3323.3221.098
.5%131.3196.1131.3100.0%173.6216.6169.697.7%304.7265.326
1.385.7%149.1154.1119.179.9%333.4321.7303.491.0%235.7428
.0229.697.4%274.9333.3235.985.8%178.6218.0156.187.4%1907
111907.1117.1672.96%218.0194.7183.784.3%181.6207.9170.39
3.8%155.0154.1154.099.4%173.7197.0168.797.1%189.0112.010
6.056.1%166.1127.6117.670.8%229.0178.1176.176.9%251.4373
.0244.697.3%233.6118.1100.142.9%126.6118.387.168.8%19071
21907.1217.250-
3.12%143.1101.9100.970.5%156.0129.6120.076.9%37.437.636.
497.3%125.4127.6123.498.4%88.745.145.150.9%136.786.786.7
63.4%120.962.462.451.7%242.9310.0232.395.6%198.176.969.1
34.9%118.6111.688.974.9%190811908.0117.333-
5.88%230.795.994.941.1%272.4202.4181.666.6%64.635.329.04
4.9%164.7189.9152.492.5%118.958.358.349.0%151.0112.6111.
673.9%167.978.376.345.4%299.3362.0285.195.3%214.638.337.
017.2%143.0112.190.363.1%190821908.0217.417-
7.43%240.0128.9127.953.3%204.0133.0133.065.2%100.778.463
.362.8%134.9169.0121.690.1%150.484.684.656.2%152.186.386.
356.7%184.0100.196.052.2%243.9320.3222.991.4%186.636.432
.117.2%134.3116.691.468.1%190831908.0317.500-
9.02%290.9166.1165.456.9%210.6157.4146.469.5%98.370.651.
752.6%162.7192.3155.695.6%144.654.454.437.6%179.6103.010

3.057.4%192.7102.497.650.6%250.4336.6229.491.6%222.066.1
60.927.4%184.1143.0117.063.5%190841908.0417.583-
10.76%276.3174.6174.363.1%225.4198.7172.776.6%73.078.057
.678.9%153.6220.3147.395.9%145.465.665.645.1%173.4123.91
15.966.8%249.6156.6152.661.1%265.1350.1242.791.5%291.110
5.1100.734.6%182.4178.4133.373.1%190851908.0517.667-
11.61%197.9151.7151.776.7%190.0230.9163.085.8%98.0106.17
7.779.3%155.0227.7147.995.4%149.163.363.342.4%208.0140.1
133.964.4%257.1156.9153.959.8%259.4385.7242.793.6%430.32
42.3158.036.7%198.0184.3134.968.1%190861908.0617.750-
10.04%253.7173.0171.067.4%212.3259.4179.684.6%99.1100.98
4.084.7%121.3150.6121.4100.0%146.764.464.443.9%194.6123.
7122.062.7%232.3145.7144.062.0%272.6380.9248.691.2%626.0
252.9238.138.0%184.1217.1127.169.0%190871908.0717.833-
5.65%251.1183.4183.473.0%218.6195.1174.980.0%63.061.149.
979.1%131.3144.0120.391.6%216.7119.6119.655.2%193.7112.7
112.758.2%176.985.785.448.3%258.1328.4233.490.4%372.3138
.1127.034.1%179.1186.1126.370.5%190881908.0817.917-
4.06%154.3117.7117.776.3%194.6206.7185.795.4%106.7159.49
3.787.8%156.7190.7147.193.9%173.7101.1101.158.2%204.1119
.7119.758.6%168.1115.4109.465.1%215.9255.7188.387.2%318.
3157.6136.142.8%161.9147.1111.969.1%190891908.0918.000-
3.29%172.7138.9138.980.4%222.6249.7191.986.2%193.9252.11
85.695.7%176.3258.9169.195.9%168.1101.9101.960.6%244.417
6.4172.770.7%192.9134.6134.669.8%299.7407.1280.493.6%248
.4151.0115.746.6%140.3123.985.360.8%1908101908.1018.083-
0.91%208.0150.0150.072.1%208.9240.0193.992.8%235.1185.11
87.779.8%165.0186.1152.792.6%196.3119.3119.360.8%234.616
8.3164.069.9%256.9194.7191.974.7%300.6415.6280.793.4%335
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-
0.38%189.4131.6131.669.5%155.0167.3140.090.3%130.3128.01
14.988.2%131.3149.7127.397.0%155.772.772.746.7%234.9164.
4164.470.0%212.9169.3135.163.5%277.6376.0259.993.6%252.1
75.970.928.1%155.4128.7104.767.4%1908121908.1218.2501.02
%167.9100.7100.760.0%146.1126.9122.183.6%86.976.172.683.

6%117.1120.3113.196.6%153.671.771.746.7%159.798.697.661.
1%147.073.770.748.1%238.1323.6225.094.5%289.155.154.118.
7%186.7110.697.452.2%190911909.0118.3330.96%166.6118.41
18.471.1%182.3184.1169.793.1%84.164.657.668.4%130.6151.9
121.793.2%147.067.467.445.9%197.1125.1125.163.5%170.675.
675.644.3%274.3353.3256.093.3%243.139.931.913.1%169.9103
.487.051.2%190921909.0218.4171.24%129.996.696.674.4%144.
1214.1140.097.1%89.479.462.770.1%95.9105.689.793.6%140.1
69.169.149.3%197.6137.3137.369.5%178.689.089.049.8%192.6
298.1183.695.3%262.788.379.630.3%141.0106.490.163.9%1909
31909.0318.5002.67%178.4140.7140.778.9%180.9279.1164.691
.0%146.3196.3134.792.1%140.9161.6133.494.7%182.490.390.3
49.5%265.4191.7189.971.5%193.6117.6117.660.7%261.7405.72
54.197.1%350.0138.7134.438.4%172.9150.1130.075.2%190941
909.0418.5832.89%207.1169.3169.381.7%199.3316.0195.197.9
%138.9148.3134.797.0%142.9225.7141.398.9%188.6110.3110.3
58.5%227.0178.1165.172.8%254.7186.9186.973.4%263.6413.62
54.096.4%305.6100.088.729.0%174.6147.1115.065.9%1909519
09.0518.6672.30%262.7210.1210.180.0%265.6401.0249.694.0%
138.6137.3132.495.6%160.3236.1159.399.4%181.0115.1115.16
3.6%251.6202.4193.476.9%301.9222.3222.373.6%288.0434.328
0.197.3%425.3146.7138.032.4%165.7155.0123.474.5%1909619
09.0618.7503.82%261.7203.3203.377.7%278.0385.3272.397.9%
211.0225.3195.992.8%148.1201.6147.199.3%206.9144.1143.16
9.2%190.1147.1134.770.8%292.0239.7225.177.1%322.1421.130
8.095.6%348.3248.7183.052.5%187.7208.0149.479.6%1909719
09.0718.8335.16%548.0538.0538.098.2%248.9370.6244.798.3%
253.4269.3239.794.6%156.0176.6153.098.1%346.6266.3266.37
6.8%193.6134.4131.467.9%350.7281.4254.072.4%274.3380.025
7.493.9%349.0279.0191.654.9%167.9172.3122.372.9%1909819
09.0818.9176.32%575.4575.4575.4100.0%284.0359.3284.0100.
0%297.6326.1296.699.7%218.9251.4220.9100.0%400.0338.333
8.384.6%236.1192.7179.776.1%341.4315.3288.084.4%254.7348
.1239.193.9%346.1342.9233.767.5%107.3130.768.663.9%19099
1909.0919.0008.26%574.1574.1574.1100.0%283.0373.4283.010
0.0%357.7455.4354.799.2%207.6245.6205.699.0%372.4331.031

9.085.7%256.4246.0217.384.7%969.6317.3315.632.5%277.7399
.7269.697.1%346.9370.9340.198.1%105.1105.9100.195.2%1909
101909.1019.0838.88%685.3677.6661.696.5%274.1376.9266.39
7.1%363.3404.3363.3100.0%303.9329.1303.9100.0%335.3288.9
283.984.7%194.9227.6167.686.0%441.1423.1392.489.0%279.14
02.1270.496.9%357.7375.9345.396.5%154.9153.3140.991.0%19
09111909.1119.1679.55%649.4648.6638.698.3%209.9311.3206.
698.4%281.3312.9281.3100.0%240.6281.7246.6100.0%513.344
0.7440.785.9%160.3169.9135.984.8%327.4306.4288.188.0%226
.3303.0222.098.1%322.7332.0313.497.1%109.4127.4106.497.3
%1909121909.1219.2508.29%497.6507.6493.199.1%216.3280.0
215.499.6%197.4200.9197.4100.0%267.4293.4267.4100.0%395.
0327.0327.082.8%179.7157.0157.087.4%283.6234.4234.482.7%
249.7291.9247.699.1%194.9188.7178.991.8%97.096.490.993.7
%191011910.0119.3338.52%420.7420.3415.798.8%194.1242.31
93.199.5%192.1195.7192.1100.0%336.3367.0336.3100.0%415.7
334.4334.480.4%177.0163.6155.788.0%350.9305.9305.987.2%2
83.0478.0282.199.7%195.0180.9165.184.7%123.0129.4119.196.
9%191021910.0219.4179.04%275.7275.7275.7100.0%192.1222.
0192.1100.0%147.0146.4147.0100.0%274.9320.3274.9100.0%5
13.1454.4454.488.6%136.9126.7121.688.8%305.6324.3301.198.
6%282.9486.0282.9100.0%154.9104.496.162.1%101.7113.496.0
94.4%191031910.0319.5009.33%583.3588.3583.3100.0%322.44
05.6322.4100.0%317.9374.9337.9100.0%351.0417.4351.0100.0
%603.6579.6579.696.0%148.3146.3146.398.7%604.4669.9599.0
99.1%378.0612.0378.0100.0%342.9452.1320.193.4%114.0138.0
112.798.9%191041910.0419.5838.47%837.6836.1836.199.8%46
4.4517.1464.4100.0%454.4459.7454.4100.0%339.7436.0339.71
00.0%436.4409.3409.393.8%128.0124.7124.797.4%634.0684.96
34.0100.0%468.7584.7468.7100.0%414.3539.3407.398.3%123.3
152.0123.3100.0%191051910.0519.6677.49%699.7696.1696.19
9.5%388.0421.3388.0100.0%356.0363.0356.0100.0%316.3374.3
316.3100.0%608.4582.1580.195.4%163.1155.7155.795.4%576.7
574.9575.799.8%623.0708.1623.0100.0%395.7500.1395.7100.0
%125.9163.7125.9100.0%191061910.0619.7507.33%600.7600.7
600.7100.0%358.6370.6358.6100.0%417.6420.3417.6100.0%35

1.0402.7351.0100.0%896.1898.6892.699.6%242.9268.6241.699.
5%492.3491.3491.399.8%682.3729.1682.3100.0%417.0489.641
7.0100.0%146.9165.3146.9100.0%191071910.0719.8335.59%57
3.3566.6562.398.1%418.6450.3418.6100.0%575.3587.3575.310
0.0%450.3480.3450.3100.0%1119.61123.61119.6100.0%241.62
90.7241.6100.0%559.3562.3559.3100.0%676.3757.3676.3100.0
%439.1536.4439.1100.0%154.7176.7154.7100.0%191081910.08
19.9175.51%652.6643.3637.697.7%467.0473.3467.0100.0%489.
6488.6489.6100.0%421.3435.6421.3100.0%1122.91125.91122.9
100.0%179.0211.7179.0100.0%548.4582.6546.799.7%657.7713.
6657.7100.0%445.1492.9445.1100.0%187.6213.9187.6100.0%1
91091910.0920.0004.67%531.3531.3531.3100.0%396.1396.139
6.1100.0%533.1551.1533.1100.0%461.7506.3461.7100.0%1031.
01031.01031.0100.0%200.6217.7200.6100.0%558.1583.0557.99
9.9%648.3808.7663.3100.0%439.4480.0439.4100.0%181.3206.0
181.3100.0%1910101910.1020.0833.30%638.6600.4600.494.0%
375.4375.4375.4100.0%462.3462.3462.3100.0%361.9394.7361.
9100.0%1114.41114.41114.4100.0%236.0273.6236.0100.0%616
.6659.1616.6100.0%624.3724.3624.3100.0%463.4517.0463.410
0.0%250.3290.6250.3100.0%1910111910.1120.1673.25%466.74
32.0432.092.6%302.7317.7312.7100.0%418.9418.9418.9100.0%
313.6314.3313.6100.0%967.0967.0967.0100.0%206.4242.0206.
4100.0%483.6498.5483.6100.0%545.2631.5545.2100.0%407.64
35.9407.6100.0%215.4236.9215.4100.0%1910121910.1220.250
3.11%263.0183.7183.769.9%248.5231.6214.686.4%199.8193.01
93.096.6%338.1335.0337.499.8%461.2358.3358.377.7%143.316
5.9141.698.8%368.9308.4308.483.6%486.9551.9486.9100.0%21
3.3175.0163.476.6%163.3183.3163.199.9%191111911.0120.333
2.54%4341.0181.6181.64.2%346.1290.4258.474.7%522.0165.61
64.131.4%431.8419.7419.797.2%1118.1261.7261.723.4%225.12
19.1190.084.4%594.9144.4143.424.1%525.1578.7525.1100.0%4
63.7143.1142.130.7%157.1171.4152.997.3%191121911.0220.41
71.90%4426.6209.0209.04.7%484.3316.9310.964.2%1040.4202.
6202.019.4%457.2433.7433.794.9%886.6220.4219.424.8%217.5
197.6174.980.4%577.6190.0190.032.9%471.1523.3471.1100.0%
999.0119.6119.612.0%167.9175.1166.999.4%191131911.0320.5

001.53%6272.4349.0349.05.6%760.0358.6313.641.3%1270.931
2.1311.124.5%625.7570.4570.491.2%1482.2461.0458.030.9%29
6.1288.1259.387.6%854.1379.6374.443.8%756.1866.7756.1100.
0%2008.4168.7165.18.2%240.5242.4226.394.1%191141911.042
0.5831.57%9754.2488.4488.45.0%578.4406.6390.667.5%1599.9
386.7386.724.2%893.3698.7698.778.2%1952.1553.6551.628.3%
331.2282.9244.473.8%724.6557.1505.169.7%849.9966.4849.91
00.0%1570.8255.7251.916.0%246.1242.3226.391.9%191151911
.0520.6671.50%11418.1727.9727.96.4%669.3483.4477.471.3%1
968.7596.7596.730.3%917.5690.9685.974.8%2602.7756.0753.0
28.9%301.9261.1221.973.5%827.5634.1576.969.7%650.7788.76
50.7100.0%1108.1465.3463.941.9%310.0309.1291.193.9%1911
61911.0620.7501.37%10577.7646.1646.16.1%488.2342.1330.16
7.6%1703.8374.6374.622.0%827.9638.9608.973.5%2754.5797.6
796.628.9%292.4278.3210.672.0%539.9427.0371.668.8%556.26
57.0554.399.7%1618.8541.4539.333.3%375.6329.9309.782.5%1
91171911.0720.8331.00%13676.1935.4935.46.8%715.7462.146
2.164.6%2035.2485.9485.923.9%1262.5940.3940.374.5%3593.1
1087.11084.130.2%416.2408.3313.175.2%910.0543.0431.747.4
%651.7656.4578.388.7%2253.7646.0642.028.5%572.3453.3440.
376.9%191181911.0820.9171.76%8391.9688.3688.38.2%420.92
74.4274.465.2%1227.8343.7343.728.0%885.9669.3669.375.6%2
566.6814.4814.431.7%282.1273.0218.777.5%563.0250.3247.44
3.9%423.2414.0367.386.8%1494.7386.0381.025.5%387.4304.12
89.174.6%191191911.0921.0001.59%8094.7569.1569.17.0%329
.9207.0204.161.9%1393.0493.3493.335.4%797.7632.1632.179.2
%2823.8907.7906.132.1%277.2271.3211.976.4%754.1333.4331.
443.9%382.9405.9332.386.8%1514.9390.1386.125.5%380.5313.
4303.479.8%1911101911.1021.0831.46%7127.4733.6733.610.3
%383.6232.3214.155.8%1567.9502.3502.332.0%991.4689.6689.
669.6%2649.4850.4848.032.0%281.9269.3208.473.9%979.2398.
7392.740.1%364.0362.1300.382.5%1867.8506.9506.127.1%435.
7343.0331.076.0%1911111911.1121.1670.91%1741.3455.3455.
326.1%265.0197.7182.768.9%1461.5361.4361.424.7%1076.156
8.3568.352.8%2314.9738.9738.931.9%256.0270.4208.781.5%99
2.1310.9308.931.1%448.4380.0340.475.9%962.6373.0372.738.7

%343.8287.6274.679.9%1911121911.1221.2500.52%1413.9264.
9264.918.7%281.9182.4165.958.8%1656.4245.1245.114.8%141
2.6643.7643.745.6%1989.1299.6298.615.0%221.4190.6153.769.
4%867.9150.9149.917.3%399.3278.0243.761.0%375.2146.3145.
338.7%289.8231.4231.479.9%191211912.0121.3331.27%1884.4
428.9428.922.8%311.1204.0196.663.2%1889.3186.3186.39.9%1
441.1593.1593.141.2%2027.9383.3383.318.9%249.0169.4137.0
55.0%915.6137.9137.915.1%345.0233.3190.455.2%570.8206.72
06.736.2%335.0271.7264.078.8%191221912.0221.4173.79%169
2.7672.3672.339.7%281.0182.6170.660.7%1846.4197.6197.610.
7%1434.5571.1571.139.8%1951.0304.1304.115.6%266.6189.01
51.356.8%898.6131.3131.314.6%388.7267.7210.954.2%948.727
4.0274.028.9%303.4229.9226.674.7%191231912.0321.5004.33
%1795.1412.9412.923.0%343.0195.9195.957.1%1814.7254.725
7.714.2%1467.0654.1654.144.6%2011.9463.7463.723.0%278.12
35.9194.369.9%1090.9262.9262.924.1%572.4405.1292.451.1%9
28.4268.1268.128.9%383.9291.7286.774.7%191241912.0421.58
31.82%2197.1810.3810.336.9%435.1295.6284.665.4%1529.459
1.6591.638.7%1174.7689.3689.358.7%1825.71074.91069.458.6
%280.4235.6178.163.5%1138.1511.6511.644.9%607.3547.6420.
769.3%1356.9439.3436.332.2%404.6302.1302.174.7%19125191
2.0521.6672.43%2179.9885.1885.140.6%479.1298.0278.058.0%
1417.9733.0733.051.7%1075.8664.7664.761.8%1861.4951.6950
.051.0%282.6262.9200.170.8%1214.1580.6580.647.8%669.1582
.0436.465.2%901.3538.4535.459.4%466.5345.3344.373.8%1912
61912.0621.7502.81%2058.0783.0783.038.0%396.7256.7224.75
6.6%1252.6561.1561.144.8%1048.7549.6549.652.4%1952.0795.
1795.140.7%252.6194.1148.358.7%1039.6486.1486.146.8%680.
0548.3472.169.4%894.0531.1531.159.4%402.0296.4296.473.7%
191271912.0721.8333.69%1622.4843.3843.352.0%333.7249.62
36.670.9%1159.8460.7460.739.7%903.6503.3503.355.7%1678.3
967.4967.457.6%303.6214.6179.659.2%878.1422.4422.448.1%6
21.9522.6469.075.4%808.5497.3497.361.5%378.4275.4275.472.
8%191281912.0821.9175.06%1516.6775.4774.651.1%385.9224.
9224.958.3%1412.3553.3553.339.2%1026.9522.1522.150.8%17
83.91062.01062.059.5%316.9228.4197.662.4%859.9395.6395.6

46.0%639.0547.9479.175.0%741.3622.1532.071.8%432.2306.42
96.968.7%191291912.0922.0004.23%1209.6608.1606.050.1%34
1.7235.1223.165.3%1379.1597.7597.743.3%878.4549.1549.162.
5%1589.9960.7959.760.4%299.3245.3209.670.0%754.3383.638
3.650.9%578.6663.0468.981.0%760.1596.4550.672.4%421.6301
.6291.669.2%1912101912.1022.0835.60%1340.3736.9736.955.0
%336.7213.3201.359.8%1678.6600.9600.935.8%1106.8496.749
6.744.9%1737.01249.61248.671.9%299.6233.3195.465.2%691.0
419.3419.360.7%638.7691.6535.383.8%781.6577.1566.172.4%4
40.4306.0304.669.2%
1
Assignment 2
The Success of Employment Applications in Ohio during the
Gentleman’s Recession
On April 18, 1906, a 7.9 earthquake hit San Francisco,
California. The death total from the
earthquake and associated fires and mud slides is estimated to
have been 3,000. As many as 300,000
people, out of a population of 400,000, were made homeless.
Property damage amounted to $400
million, $250 million of which was covered by insurance.
With such an enormous claim upon the insurance industry,
insurance companies and the entire
financial system were subjected to enormous stress. The
following year, the Panic of 1907 broke out.
Stock prices tumbled. Banks were closed. And, an industrial
recession got underway.
Fortunately, J.P. Morgan and others stepped in to support stock

prices; and, banks issued $100
million of scrip (or, emergency money). And, the recession was
short-lived. Indeed, for a time, this
recession was called “The Gentlemen’s Recession,” as it was
said to have mostly affected investors and
did not much affect those in the working class.
The chart above shows an index of the business cycle during
the period.1 It is relatively easy to
see the sharp fall in the index during the recession that followed
the Panic of 1907. It is also relatively
easy to see the sharp recovery from this recession.
During the period, the State of Ohio operated employment
offices in five cities. From their
reports, monthly time series can be constructed for job
applications, job listings and job placements, for
1 The index is constructed from four underlying time series: (1)
railroad freight ton-miles, (2) deflated bank
clearings outside New York City, (3) an index of factory
employment, and (4) an index of business physical activity
(similar to today’s index of industrial production); and, is equal
to the average seasonally-adjusted deviation of
these time series from their trends.
2
men and for women, for each of the five cities, from Sept. 1890
to Oct. 1912.2 These employment offices
focused on inexperienced and unskilled workers, and “difficult

to place” individuals.3
The above chart displays the ratio of job placements to seekers,
for the total of men and women
in all five cities, juxtaposed against the business cycle
indicators. Two things should stand out:
First, there is a strong upward trend in the ratio through 1910.
After that, there is a sharp
decline. This decline, it turns out, is due to an administrative
change involving the differentiation of
“registered” from “not registered” job applicants. Accordingly,
the data following 1910 are not directly
comparable to the data through 1910.
Second, through 1910, there appears to be a weak, positive
correlation between the ratio and
the business cycle index. In particular, the ratio dips during the
recession that followed the Panic of 1893
and it dipped again during the recession that followed the Panic
of 1907.
In this assignment, you are to:
• Use the data in the accompanying spreadsheet, for the period
Sept. 1890 to Dec. 1910 (not to
the end of the data), to estimate two multiple regressions in
which the dependent variable is
the ratio of job placements to job seekers (in the first
regression) for men and (in the second
regression) for women for your city (your city code is in
Grades), and the two independent
variables are time and the business cycle index.
• Use the regression output to comment on
• [1] Whether the ratios are affected by the business cycle;

2 After the latter date, only quarterly data are reported; and,
referrals are reported, not placements.
3 For-profit employment agencies served experienced and
skilled workers well. Both government employment
offices and not-for-profit employment agencies focused on
inexperienced and unskilled workers, and “difficult to
place” individuals, with government employment offices
tending to displace not-for-profit employment agencies.
3
• [2] Whether the ratios are particularly sensitive to the business
cycle (affected by more than
one-to-one); and,
• [3] Whether the ratios fell by at least as much as would be
predicted following the Panic of
1907. (To perform this step correctly, you will need to compare
actual values of the Y-variable to
the forecast values of the Y-variable given the estimated
regression and the X-variables of the
specific period of time being investigated.)
CITY CODES:
01 – Cincinnati
02 – Cleveland
03 – Columbus
04 – Dayton
05 – Toledo

Case 3
Write a scholarly essay based on the article “If You Like It,
Does It Matter If It’s Real?” by Felipe de Brigard. This article,
along with the case upon which it is based, is discussed in
chapter 8 of our text.
Essay: Analysis of a Scholarly Article
The following guideline is one you must follow precisely. It
serves both as your guide to writing your analysis and as my
guide to grading your analysis.
You will analyze one of the assigned essays.
The first thing you must do is read the article, ideally two to
three distinct times. In each reading, you should use a different
color pen to mark important aspects of the essay.
Because this is a philosophical analysis of a philosophic essay
you should avoid the following:
· Personal attacks on the author; do not question the author’s
motives
· Complaining about the author’s writing style or choice of
words
· Suggesting that the author is confused or unclear
·
Moreover, you should avoid any lengthy, direct quotations. I do
want you to quote the essay three distinct times, but these
quotes should never be longer than two sentences. Be sure you
cite the quote in the precise way I show you in class.
Format
Your analysis must contain the following four sections:
· Introduction
· Summary
· Critique

· Conclusion
· Format
You must provide a heading at the beginning of each section.
That is, write, underline and make bold the heading:
Introduction, for example.
The formatting criteria are listed on a separate page. Thus, your
essay will be worth up to 50 points, 10 points per section.
Introduction
Your Introduction should consist of 2 to 3 paragraphs:
1. In the first and second paragraphs identify the article and
describe the problem or topic the essay addresses.
2. In the third paragraph articulate what your own analysis will
address and what it is you intend to accomplish. This replaces
the standard thesis statement: you will inform your reader of
what you intend to do and provide a map of your analysis.
Summary
This is the main body of your essay. It must do the following:
1. You should begin by summarizing those aspects of the article
that are relevant to your own critique. You should not attempt
to summarize the entirety of the article; you are not simply
writing a general review of the essay.
2. Your summary must represent the author’s views in the best
possible way. You do not want to misrepresent the author’s
views, or to represent them in such a way that you can then
easily destroy them. Avoid the “straw man” fallacy. If you don’t
know this fallacy look it up.
3. The summary of the author’s article must not include any
critical comments.
4. The summary should not simply elaborate on the sequence of
the author’s ideas. That is, you should not write a summary that
simply does this: “The author begins by discussing . . . . Then
she goes on to discuss . . . .” Your challenge is to present your
summary in a way that draws the relevant parts of the author’s
essay together in a way that prepares for your critical discussion

of it. That is, your summary must be related to your thesis, or
what I called your “map.”
Critique
1. Your critique should be organized according to your
summary. This means that your critique, like your summary,
will reflect those parts of the article that you have selected,
parts that develop and illuminate your thesis, or “map.”
2. Your critique might focus on ideas you embrace, ideas you
reject, and/or ideas about which you are unsure. Remember:
critique does not mean being negative. You might actually find
that you agree with an author, and if that is the case, you want
to reflect that in your critique.
3. One of your greatest challenges is to tease out the
philosophic aspects of the article. This requires you to draw
from your other readings: keep in mind the work of the
philosophers you have studied. Note Well: this part of your
“Critique” is the most important part of your “Critique.” You
must “step back” and “tease out” the philosophic principles “in
play” in the essay.
Conclusion
In your conclusion, restate – although not verbatim – your
thesis. Bring together the main themes of your essay and point
to a broader application or assessment. The conclusion should
be two to three paragraphs.
You should work carefully through the following check-list
prior to submitting your essay:
· My essay is double spaced.
· My margins are set at 1 inch all the way around
· My essay is written in Times New Roman font
· My essay is written in 12 point font
· My essay has page numbers on each page
· My essay contains my name on the right hand corner of the
first page
· My essay has no cover page or folder

· My essay’s pages are stapled together
· My essay does not use the words “feel” or “believe”
· My essay contains pronoun agreement throughout
· My essay does not contain any direct quotations from class
lectures
· My essay contains at least 3 direct citations from the original
article
· My essay cites the 3 direct citations exactly as instructed in
class
· My essay’s introduction contains my thesis/map
· My essay’s introduction follows the above guidelines
precisely
· My essay’s summary follows the above guidelines precisely
· My essay’s critique follows the above guidelines precisely
· My essay’s conclusion follows the above guidelines precisely
· My essay’s format follows the above points precisely
Philosophical Psychology
Vol. 23, No. 1, February 2010, 43–57
If you like it, does it matter if it’s real?
Felipe De Brigard
Most people’s intuitive reaction after considering Nozick’s
experience machine
thought-experiment seems to be just like his: we feel very little

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