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Cell["\<\
On the Numerical Accuracy of Mathematica 5.0 for Doing Linear and Nonlinear \
Regression\
\>", "Title"],
Cell["Marc Nerlove", "Author"],
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"This article presents the results of performing the linear and nonlinear \
regressions used as benchmarks by the National Institute of Standards and \
Technology (NIST) with ",
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" 5.0. The performance is nearly flawless."
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\n\tBy diligent discovery;",
"\[Ellipsis] ",
"\[CloseCurlyDoubleQuote]\n\t\t",
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"Introduction"
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"There is a small but growing literature on the numerical accuracy of \
various computer programming packages. A major contributor to the assessment \
of the accuracy of econometric software, as well as statistical add-ons to \
third-level programming languages widely used by econometricians, such as \
GAUSS, MATLAB, Maple, and ",
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", has been Bruce D. McCullough ([",
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", 27] assessed the reliability of the statistical procedures in Excel 97 \
for estimation of both linear and nonlinear regression, random number \
generation, and the calculation of cumulative distributions and concluded \
that \[OpenCurlyDoubleQuote]Excel\[CloseCurlyQuote]s performance in all three \
areas is found to be inadequate. Persons desiring to conduct analyses of \
statistical data are advised not to use Excel.\[CloseCurlyDoubleQuote] \
McCullough made a complete assessment of all of ",
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" 4.0\[CloseCurlyQuote]s then extant statistical functions [",
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"]. In 2000, I made a similar assessment for ordinary least squares (OLS) \
linear regression analysis using Excel 2000 and the Numerical Algorithms \
Group\[CloseCurlyQuote]s (NAG\[CloseCurlyQuote]s) Statistical Add-Ins for \
Excel software (",
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"). I found that the \[OpenCurlyDoubleQuote]NAG-enhanced\
\[CloseCurlyDoubleQuote] version of Excel did not do significantly better \
than the non-enhanced version. In the same paper, I also compared the \
performance of ",
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" 4.1."
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"The basis for McCullough\[CloseCurlyQuote]s assessments as well as mine \
were comparisons with the benchmark results for the Statistical Reference \
Datasets (StRD) that are available from the NIST (",
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Cell["\<\
My comparison of Excel 2000 with the benchmark linear regression analyses \
produced results that did not differ significantly from those McCullough \
obtained for Excel 97. Notwithstanding the excellent reputation of NAG\
\[CloseCurlyQuote]s software, the performance of the Excel add-on is not \
superior to Excel. For cases in which Excel performs well, the NAG add-on \
also does well, but when Excel performs unsatisfactorily, the NAG add-on does \
poorly as well. However, often the results differ from the certified results \
in a different direction from those obtained directly in Excel. In the case \
of linear regression, on the other hand, Excel on its own does not do much \
worse than many other packages analyzed by McCullough and others. My \
comparisons at the time suggested that McCullough\[CloseCurlyQuote]s \
judgment, at least with respect to linear regression, may have been unduly \
critical; however, I do agree that the statistical functions in Excel should \
not be used with or without NAG enhancement.\
\>", "Text"],
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", 211] undertook a careful analysis of the statistical functions in GAUSS \
for Windows Version 3.2.27, also using comparisons with the StRD. He found \
\[OpenCurlyDoubleQuote]",
"\[Ellipsis] ",
"that the algorithms used by GAUSS sometimes fail rather badly to provide \
accurate results. We blame both the algorithms used and the language itself.\
\[CloseCurlyDoubleQuote] I have not yet undertaken a similar reassessment of \
the more recent and allegedly significantly improved versions of GAUSS."
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fourth-level programming languages or statistical packages. With respect to \
univariate statistics, analysis of variance, and linear regression, \
McCullough reported that \[OpenCurlyDoubleQuote]All [SAS] results are quite \
accurate,\[CloseCurlyDoubleQuote] in terms of six digits of accuracy or \
better, although SAS failed to deliver any solution in one of the worst \
cases. Even though SAS failed to achieve convergence in a number of cases, \
the results for nonlinear regression were similar. The performance of all \
three packages with respect to random number generation and the calculation \
of probabilities for statistical distributions was notably poorer than for \
OLS linear regression. "
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" is not restricted as to precision; however, precision may be specified. \
The default is to use machine arithmetic, which is typically 16 digits of \
precision in internal calculations (a typical value of ",
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" is ",
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precision in the final result. Note that accuracy and precision are not the \
same as defined in ",
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". A higher level of precision may be attained by setting ",
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"is used, increasing the level of precision in this way may not be \
possible. This is because within the code the computation has been carried \
out in floating-point notation. No matter how many degrees of arbitrary \
precision are requested, the result is still contaminated with the errors \
from floating-point arithmetic. Arbitrary precision only works well when the \
computation has been carried out uncontaminated with floating-point error. In \
",
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rational form, which yields exact results, but this still will not avoid the \
problem of inverting an ill-conditioned matrix."
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"At default precision, ",
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" is quite accurate although McCullough obtained no solution in one StRD \
case of OLS linear regression and one in an StRD case of nonlinear \
regression. When ",
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" is raised to 20 digits, McCullough reports that astonishing, almost \
perfect, accuracy, as compared with the NIST benchmark results, is obtained \
in all cases considered. Actually, ",
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"\[CloseCurlyQuote]s default level of precision gives exact matches to the \
benchmark results in most cases, but the results ",
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" displays are rounded to six places and thus may not look quite the same. \
To display the results to more places, use ",
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". The increase in computational time using a higher level of precision \
than default in direct, and therefore symbolically pure, computation of the \
OLS estimates appears to be negligible no matter how high the level of \
precision is specified. Although it is certainly true that increased accuracy \
may not matter for the conclusions to be drawn from a statistical analysis, \
it may also happen that rounding errors in the course of an otherwise \
straightforward calculation may result in wildly different results or that no \
solution is found. If the cost of obtaining accurate results even in \
problematic cases is not great, it is certainly prudent to obtain what \
increased accuracy may be possible. If a preprogrammed package is used, as it \
is in this article, it may not be possible to control for rounding error \
because of the original coding."
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"In this article, I discuss the details of my own comparisons of ",
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employs summary measures, which must of necessity leave out a lot of relevant \
detail in the case of many parameters, but I present a full range of results. \
A separate section deals with the more computationally difficult benchmark \
cases for nonlinear regression."
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Cell[TextData[{
"In the next section, I describe the NIST StRD benchmarks, particularly the \
11 designed for benchmarking OLS linear regression (i.e., linear in the \
parameters to be estimated, so polynomial regression is not excluded) and the \
27 nonlinear benchmark datasets. I also discuss the way in which the NIST \
certified results have been obtained for the linear regression StRD set. In \
Section 3, I discuss the general problems of nonlinear regression analysis \
and the difficulty obtaining appropriate significance tests short of \
computing the parameter estimates by maximum likelihood (ML). In Section 4, I \
summarize the results of using Version 5.0 of ",
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Essentially the same results may be obtained directly by writing out the \
standard textbook formulae in ",
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"although these formulae are not the best way of carrying out the requisite \
numerical calculations. Details of the numerical results are presented in \
Appendices A and B, in which tabular comparisons are made of the NIST StRD \
benchmark results with those obtained using ",
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". The NIST StRD Datasets and Certified Results for Linear and Nonlinear \
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The NIST describes the statistical benchmark program on their website as \
follows.\
\>", "Text"],
Cell["\<\
\[OpenCurlyDoubleQuote]Currently datasets and certified values are provided \
for assessing the accuracy of software for univariate statistics, linear \
regression, nonlinear regression, and analysis of variance. The collection \
includes both generated and \[OpenCurlyQuote]real-world\[CloseCurlyQuote] \
data of varying levels of difficulty. Generated datasets are designed to \
challenge specific computations. These include the classic Wampler datasets \
for testing linear regression algorithms and the Simon & Lesage datasets for \
testing analysis of variance algorithms. Real-world data include challenging \
datasets such as the Longley data for linear regression, and more benign \
datasets such as the Daniel & Wood data for nonlinear regression. Certified \
values are \[OpenCurlyQuote]best-available\[CloseCurlyQuote] solutions. The \
certification procedure is described in the web pages for each statistical \
method. \
\>", "Quote"],
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average, and higher). Strictly speaking the level of difficulty of a dataset \
depends on the algorithm. These levels are merely provided as rough guidance \
for the user. Producing correct results on all datasets of higher difficulty \
does not imply that your software will pass all datasets of average or even \
lower difficulty. Similarly, producing correct results for all datasets in \
this collection does not imply that your software will do the same for your \
particular dataset. It will, however, provide some degree of assurance, in \
the sense that your package provides correct results for datasets known to \
yield incorrect results for some software\[CloseCurlyDoubleQuote] (",
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The following edited comments from the NIST website describe these datasets \
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\>", "Text"],
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\[OpenCurlyDoubleQuote]Both generated and \[OpenCurlyQuote]real-world\
\[CloseCurlyQuote] data are included. Generated datasets challenge specific \
computations and include the Wampler data developed at NIST (formerly NBS) in \
the early 1970s. Real-world data include the challenging Longley data, as \
well as more benign datasets from our statistical consulting work at NIST. \
\>", "Quote"],
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\[OpenCurlyDoubleQuote]\[Ellipsis] Two datasets are included for fitting a \
line through the origin. We have encountered codes that produce negative \
R-squared and incorrect F-statistics for these datasets. Therefore, we assign \
them an \[OpenCurlyQuote]average\[CloseCurlyQuote] level of difficulty. \
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datasets are multicollinear. They include the Longley data and several NIST \
datasets developed by Wampler. \
\>", "Quote"],
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\[OpenCurlyDoubleQuote]\[Ellipsis] Certified values are provided for the \
parameter estimates, their standard deviations, the residual standard \
deviation, R-squared, and the standard ANOVA table for linear regression. \
Certified values are quoted to 16 significant digits and are accurate up to \
the last digit, due to possible truncation errors. \
\>", "Quote"],
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level of difficulty, one possible remedy is to center the data and rerun the \
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variable, reduces the degree of multicollinearity. The code may produce \
correct results for the centered data. You can judge this by comparing \
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Cell["\<\
The following edited comments from the NIST website describe these datasets \
in more detail.\
\>", "Text"],
Cell[TextData[{
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"\[Ellipsis] ",
"Hiebert [",
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"] notes that \[OpenCurlyQuote]testing to find a \
\[OpenCurlyDoubleQuote]best\[CloseCurlyDoubleQuote] code is an all but \
impossible task and very dependent on the definition of \
\[OpenCurlyDoubleQuote]best.\[CloseCurlyDoubleQuote]\[CloseCurlyQuote] \
Whatever other criteria are used, the test procedure should certainly attempt \
to measure the ability of the code to find solutions. But nonlinear least \
squares regression problems are intrinsically hard, and ",
StyleBox["it is generally possible to find a dataset that will defeat even \
the most robust codes",
FontSlant->"Italic"],
". ",
StyleBox["So most evaluations of nonlinear least squares software should \
also include a measure of the reliability of the code, that is, whether the \
code correctly recognizes when it has (or has not) found a solution",
FontSlant->"Italic"],
". The datasets provided here are particularly well suited for such testing \
of robustness and reliability. [Emphasis added.]"
}], "Quote"],
Cell["\<\
\[OpenCurlyDoubleQuote]\[Ellipsis] both generated and \
\[OpenCurlyQuote]real-world\[CloseCurlyQuote] nonlinear least squares \
problems of varying levels of difficulty [are included]. The generated \
datasets are designed to challenge specific computations. Real-world data \
include challenging datasets such as the Thurber problem, and more benign \
datasets such as Misra1a. The certified values are \
\[OpenCurlyQuote]best-available\[CloseCurlyQuote] solutions, obtained using \
128-bit precision and confirmed by at least two different algorithms and \
software packages using analytic derivatives.\
\>", "Quote"],
Cell[TextData[{
"\[OpenCurlyDoubleQuote]\[Ellipsis] For some of these test problems, \
however, it is unreasonable to expect the correct solution from a nonlinear \
least squares procedure when finite difference derivatives are \
used\[Ellipsis]. These difficult problems are impossible to solve correctly \
when the matrix of predictor variables is only ",
StyleBox["approximate",
FontSlant->"Italic"],
" because the user did not supply analytic derivatives."
}], "Quote"],
Cell["\<\
\[OpenCurlyDoubleQuote]\[Ellipsis] the datasets have been ordered by level of \
difficulty (lower, average, and higher). This ordering is meant to provide \
rough guidance for the user. Producing correct results on all datasets of \
higher difficulty does not imply that your software will correctly solve all \
datasets of average or even lower difficulty. Similarly, producing correct \
results for all datasets in this collection does not imply that your software \
will do the same for your own particular dataset. It will, however, provide \
some degree of assurance, in the sense that your package provides correct \
results for datasets known to yield incorrect results for some software. \
\>", "Quote"],
Cell["\<\
\[OpenCurlyDoubleQuote]The robustness and reliability of nonlinear least \
squares software depends on the algorithm used and how it is implemented, as \
well as on the characteristics of the actual problem being solved. Nonlinear \
least squares solvers are particularly sensitive to the starting values \
provided for a given problem. For this reason, we provide three sets of \
starting values for each problem: the first is relatively far from the final \
solution; the second relatively close; and the third is the actual certified \
solution.\
\>", "Quote"],
Cell[TextData[{
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"\[Ellipsis] ",
"sometimes good starting values are not available. For testing purposes, \
therefore, it is of interest to see how a code will perform when the starting \
values are not close to the solution, even though such starting values might \
be ridiculously bad from a practical standpoint. In general, it can be \
expected that a particular code will fail more often from the starting values \
far from the solution than from the starting values that are relatively \
close. How serious it is that a code fails when using starting values far \
from the solution will depend on the types of problems for which the code \
will be employed.\[CloseCurlyDoubleQuote] (",
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"In my assessment of ",
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" 5.0, I use only the NIST starting values, which are different from the \
certified results, except in one instance. This is the MGH10 dataset, for \
which ",
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" gives no results for both the first and second starting values. When the \
certified results are used as the starting value, ",
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" crashes. The problem of choosing good starting values is central to \
nonlinear regression. As discussed later, I believe that such a choice should \
not be made automatically, but rather involve some prior investigation."
}], "Text"]
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Cell["\<\
The general statistical model assumed for the linear least-squares regression \
problems is\
\>", "Text"],
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" matrix of predictor (independent) variables. The specific functional form \
for each dataset is different from set to set and is specified in the \
certified results for that set, summarized in Appendix A. Unless the constant \
term in the regression is suppressed, ",
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nonzero intercept. If we want to make inferences about ",
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assumptions about the joint distribution of ",
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","
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" of goodness-of-fit is defined as"
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Cell[TextData[{
"when an intercept (frequently represented by including a column of ones in \
the matrix ",
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") is included and defined as"
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regression."
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Cell[TextData[{
"\[OpenCurlyDoubleQuote]For all datasets, multiple precision calculations \
(accurate to 500 digits) were made using the preprocessor and FORTRAN \
subroutine package of Bailey (1995). Data were read in exactly as multiple \
precision numbers and all calculations were made with this very high \
precision. The results were output in multiple precision, and only then \
rounded to fifteen significant digits. These multiple precision results are \
an idealization. They represent what would be achieved if calculations were \
made without roundoff or other errors. Any typical numerical algorithm (i.e., \
not implemented in multiple precision) will introduce computational \
inaccuracies, and will produce results which differ slightly from these \
certified values.\[CloseCurlyDoubleQuote] (See the certification methodology \
description for each dataset at ",
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}], "Quote"],
Cell[TextData[{
"Although not generally advisable, it is perfectly possible to simply write \
out these equations in ",
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" and solve a particular problem, since standard methods for solving for \
inverses of well-conditioned matrices may not give accurate answers for \
ill-conditioned matrices. This was what, in fact, went wrong with most of the \
extant computer packages for doing ordinary least-squares regression when \
Longley [",
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indeed, gets this problem right, albeit with a warning message in the program \
exhibited for the computation of ",
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"."
}], "Text"],
Cell[TextData[{
"Daniel Lichtblau comments on the difference between these two methods of \
doing OLS linear regression as follows: \[OpenCurlyDoubleQuote]What we [",
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"] actually work with [in the add-on package, ",
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"] are singular values. In effect, this is a method to compute a \
pseudo-inverse (which we do not actually do, unless necessitated by the \
various report option settings). In contrast, matrix inversion will be done \
using Gaussian elimination, with appropriate warnings if the matrix is found \
to be ill conditioned.\[CloseCurlyDoubleQuote]"
}], "Text"],
Cell["Here is my \[OpenCurlyDoubleQuote]direct\[CloseCurlyDoubleQuote] \
program.", "Text"],
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The reader, of course, will have to fill in the exact location of the \
Longley.txt file, which is copied as a .txt file in Appendix C.\
\>", "Text"],
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results are:"
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arithmetic in particular. So when doing linear least-squares regression it \
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",
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Following the NIST description, the statistical model assumed for nonlinear \
regression in the benchmark calculations is the so-called generic univariate \
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differ from one benchmark case to the next. They are reported in Appendix B, \
in which comparisons between the results obtained by ",
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described as follows."
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\[OpenCurlyDoubleQuote]The certified values for the nonlinear least-squares \
regression problems were obtained using 128-bit precision with the reported \
results confirmed by at least two different algorithms and software packages \
using analytic derivatives.\
\>", "Quote"],
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Cell["\<\
\[OpenCurlyDoubleQuote]The certified values for the standard deviations of \
the estimates of the model parameters are the square roots of the diagonal \
elements of the asymptotic covariance matrix,\
\>", "Quote"],
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\[OpenCurlyDoubleQuote]The certified value of the residual sum of squares is \
defined by\
\>", "Quote"],
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", it is thus possible to derive all of these estimates by maximum \
likelihood. In this case, the standard errors of the estimates are obtained \
asymptotically as the square roots of the diagonal elements of the inverse of \
the information matrix (the Hessian of the likelihood function evaluated at \
the maximizing point). (See the standard econometric presentations of \
nonlinear regression methods in Davidson and MacKinnon [",
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models from all other statistical models is that the only way in which \
randomness affects the dependent variable is through an ",
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" error term or disturbance.\[CloseCurlyDoubleQuote] However, this may be \
less of a restriction than you might at first think. For example, suppose a \
multiplicative disturbance ",
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"; then a simple logarithmic transformation suffices to return things to \
additivity: ",
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", and the disturbance, or at least lack of correlation, is an assumption \
common to both linear and nonlinear regression. A problem arises, however, if \
the appropriate transformation depends on parameters to be estimated. For \
example, a common generalization is a transformation of the dependent \
variable involving another parameter to be estimated:"
}], "Text"],
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the same estimates as maximum likelihood. Maximum likelihood is still an \
effective method, however, since the distribution of the ",
Cell[BoxData[
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"s, given the ",
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Cell[BoxData[
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Cell[BoxData[
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". A more serious limitation is the necessity of specifying the functional \
form of ",
Cell[BoxData[
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". Whereas, in the case of linear regression we hardly ever think about \
alternative functional forms, except perhaps to worry about interactions, the \
very fact that we are considering nonlinear regression underscores a concern \
about the appropriate functional form. In recent years, there has been an \
efflorescence of work on nonparametric methods explicitly designed to cope \
with this problem. (See, especially Haerdle [",
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standard texts, such as Gallant [",
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"], each with somewhat different emphasis. Most emphasis falls on \
computational issues and problems of parametric inference. A very good brief \
expository introduction is Gallant [",
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Cell[TextData[{
"Most algorithms for computing nonlinear regression parameters are based on \
Hartley\[CloseCurlyQuote]s [",
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"] modified Gauss\[Dash]Newton method (Hartley and Booker, [",
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functions in general and the problem of finding the minimum of an \
analytically specified sum of squares (see the previous SS). In general, we \
can evaluate only the function itself analytically and perhaps its gradient. \
Using only these two pieces is the basis for the method of steepest descent, \
sometimes also known as the Gauss\[Dash]Newton method. But, in the case of \
nonlinear least squares, we know a great deal more: we know the Hessian \
matrix. Hartley\[CloseCurlyQuote]s insight was to exploit this information \
explicitly, rather than build it up piecemeal during the iterative process of \
descent. His modified Gauss\[Dash]Newton method is called the inverse Hessian \
method. Levenberg\[CloseCurlyQuote]s insight was to recognize that simple \
steepest descent is much faster and more accurate when you are close to the \
minimum and to suggest separating the problem of getting into the \
neighborhood of the minimum from \[OpenCurlyDoubleQuote]zipping in.\
\[CloseCurlyDoubleQuote] Marquardt\[CloseCurlyQuote]s contribution was an \
elegant algorithm designed to vary smoothly between the two methods as the \
minimum point was approached. ",
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"\[CloseCurlyQuote]s ",
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nonlinear least squares and for solving systems of nonlinear equations (a \
harder problem). One surprising conclusion he drew [",
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CounterBox["Reference", "Hiebert1981"],
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ButtonStyle->"Hyperlink"],
", 15] was that, \[OpenCurlyDoubleQuote]On the basis of this testing and \
these specific implementations of the Levenberg\[Dash]Marquardt and the \
augmented Gauss\[Dash]Newton methods, one method does not appear to be \
superior to the other.\[CloseCurlyDoubleQuote] Perhaps, for this reason, the \
NIST uses a variety of methods, each considered appropriate for the problem \
at hand. However, the NIST is not more explicit about the methods used in \
specific cases than the statements quoted earlier."
}], "Text"],
Cell[TextData[{
"Standard-error calculations and inference for nonlinear least-squares \
estimates are all based on asymptotic results (Hartley and Booker, [",
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" does not say how its calculations are carried out in the description of \
the ",
StyleBox["NonlinearRegress", "MR"],
" function; however, the code is available in the ",
StyleBox["Statistics`NonlinearRegress`", "MR"],
"package, and it appears that the same formulae are used."
}], "Text"],
Cell[TextData[{
"Comparisons of the results from ",
StyleBox["NonlinearRegress", "MR"],
" with the NIST benchmarks for each of the 27 NIST StRD nonlinear \
regression examples with their published starting values are presented in \
summary form in Appendix B. The NIST actually ran all computations using not \
only these two starting values but also the final benchmark answers as \
starting values because some nonlinear regression algorithms have a problem \
if you start from the right answer. However, in a few cases, I also tried \
starting at the benchmark answers: in the case of MGH10, as noted earlier, \
and for those few starting values for which ",
StyleBox["Mathematica",
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" did not converge: Lanczos2; MGH17; MGH09; as well as MGH10. However, as \
noted by the NIST, MGH10 is a particularly difficult problem: \
\[OpenCurlyDoubleQuote]This problem was found to be difficult for some very \
good algorithms. There is a local minimum at (+inf, -14.07 ",
"\[Ellipsis] ",
", -inf, -inf) with final sum of squares \
0.00102734.\[CloseCurlyDoubleQuote] [",
ButtonBox[
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}], "Text"],
Cell[TextData[{
"The crucial problem of choosing good starting values is discussed \
extensively by Bates and Watts [",
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", 665\[Dash]666]. Bates and Watts suggest using a linearized form of the \
expectation function, while Seber and Wild suggest grid search or randomized \
starting values. Ratkowsky [",
ButtonBox[
CounterBox["Reference", "Ratkowsky1983"],
ButtonData:>"Ratkowsky1983",
ButtonStyle->"Hyperlink"],
"] gives a much more extensive discussion. When only one or two parameters \
are involved, a graphical approach works wonders. However, when three or more \
parameters are involved, special techniques are required and the difficulties \
are formidable. I have been unable to ascertain how the NIST chose their \
starting values, which are always one quite close to and another far away \
from the final answer, but ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" does offer an alternative. Before invoking ",
StyleBox["NonlinearRegress", "MR"],
", you could use ",
StyleBox["NMinimize", "MR"],
" with no starting values (or some known to cause problems) assumed to find \
the minimum of the appropriate sum of squares. This is a very elaborate and \
well-documented method in ",
StyleBox["Mathematica",
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" for finding global minima. Such more sophisticated methods may not be \
very efficient compared to the algorithm ",
StyleBox["Mathematica",
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" employs in ",
StyleBox["NonlinearRegress", "MR"],
", but may work in such difficult cases. In computing the results reported \
here, I avoid the problem of choosing starting values by simply using those \
reported by the NIST."
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Cell[TextData[{
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". Discussion of the Results Using ",
StyleBox["Mathematica",
FontSlant->"Italic"],
"\[NonBreakingSpace]5.0"
}], "Section"],
Cell[CellGroupData[{
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Cell[TextData[{
"There is really not much to say about the performance of ",
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" in doing linear regression. ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" is remarkably accurate with only one negligible but puzzling anomaly: In \
the cases of Wampler1 and Wampler2, both fifth degree polynomials with \
artificially constructed data, the true SEs are 0, as is the correct estimate \
of ",
Cell[BoxData[
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StyleBox["Mathematica",
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" delivers very small numbers of the order of ",
Cell[BoxData[
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" to ",
Cell[BoxData[
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". While this is not a practical problem of any significance, some \
explanation is needed in view of ",
StyleBox["Mathematica",
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"\[CloseCurlyQuote]s otherwise stellar performance. I would attribute it to \
",
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[",
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Cell[TextData[{
"Nonlinear regressions present a greater challenge. In all but five out of \
27 difficult nonlinear regression problems, ",
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FontSlant->"Italic"],
" converged to the benchmark values within the default number of \
iterations, ",
StyleBox["MaxIter=100", "MR"],
" for both of the two start values given by the NIST. But there were \
serious problems with five of the problems, including one case in which no \
convergence was obtained even starting from the final benchmark result. \
However, in all five cases, informative error messages were given by ",
StyleBox["Mathematica",
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" and no spurious results were presented. Here is a summary."
}], "Text"],
Cell[CellGroupData[{
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Cell[BoxData[
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Cell[TextData[{
"As noted earlier, this is an exceptionally difficult problem given the \
observations on ",
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" and ",
Cell[BoxData[
\(TraditionalForm\`x\)]],
". Start 1 produced an overflow in the computation. There were no problems, \
however, encountered in obtaining the benchmark results from start\
\[NonBreakingSpace]2."
}], "Text"]
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Cell["Lanczos2", "Subsubsection"],
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Cell[TextData[{
"Note that this is the same functional form as MGH17 without a constant \
term. In both examples the data has been generated by the NIST. No \
convergence was obtained for the default number of iterations from start 1 \
with an error message to that effect. Convergence was, however, obtained for \
",
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" from start 1 and from start 2 for ",
StyleBox["MaxIter=100", "MR"],
" to the correct benchmark results."
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Cell["MGH09", "Subsubsection"],
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Cell["\<\
No convergence was obtained from start 1 even by increasing the number of \
iterations to 500. The following error message suggests that the function is \
extremely flat, at least in one direction.\
\>", "Text"],
Cell["\<\
FindFit::\"lstol\":\"The line search decreased the step size to within \
tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find \
a sufficient decrease in the norm of the residual. You may need more than \
MachinePrecision digits of working precision to meet these tolerances.\"\
\>", "Message",
GeneratedCell->False,
CellAutoOverwrite->False],
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"Convergence to the benchmark results for ",
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" from start 2 was obtained without any problems."
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}, Open ]],
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\[Beta]\_3\)\)\) + \[Epsilon]\)], "DisplayFormula"],
Cell["\<\
No convergence was obtained from start 1 or from start 2 for 10,000 \
iterations. Starting from the benchmark results produced an abnormal program \
termination with a message that the fitting algorithm failed.\
\>", "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell["Bennett5", "Subsubsection"],
Cell[BoxData[
\(TextForm\`y = \(\[Beta]\_1\) \((x + \[Beta]\_2)\)\^\(-\(1\/\[Beta]\_3\)\
\) + \[Epsilon]\)], "DisplayFormula"],
Cell["\<\
For start 1, convergence was obtained only for 10,000 iterations. Although \
the benchmark coefficients and standard errors were obtained, the benchmark \
estimate of residual variance was not. For start 2, convergence to the \
benchmark results within 100 iterations was obtained.\
\>", "Text"],
Cell[TextData[{
"Note that ",
StyleBox["Mathematica",
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"\[CloseCurlyQuote]s ",
StyleBox["NonlinearRegress", "MR"],
" is extremely fast. The time to run a regression once the data is set up \
and the command given is imperceptible for the default number of 100 \
iterations. Even for 10,000 iterations, the running time is barely \
perceptible on a Dell Workstation, PWS 340, with an ",
Cell[BoxData[
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" Pentium chip."
}], "Text"],
Cell[TextData[{
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"\[CloseCurlyQuote]s ",
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" is an extremely fast and accurate algorithm when it works. When it does \
not, it delivers error messages rather than spurious results. Presently, \
there is no provision in the ",
StyleBox["NonlinearFit", "MR"],
" package for obtaining reasonably good start values. "
}], "Text"]
}, Open ]]
}, Open ]]
}, Closed]],
Cell[CellGroupData[{
Cell[TextData[{
CounterBox["Section"],
". Discussion of the Results Using ",
StyleBox["Mathematica",
FontSlant->"Italic"],
"\[NonBreakingSpace]5.1"
}], "Section"],
Cell["Darren Glosemeyer", "SecondAuthor"],
Cell[TextData[{
"Kernel Developer\nKernel Technology Group\n",
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FontSlant->"Italic"],
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Cell[TextData[{
"The following results were obtained in ",
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" 5.1 on an ",
Cell[BoxData[
\(TraditionalForm\`Intel\^\[RegisteredTrademark]\)]],
" Pentium 4 Windows XP computer. Version 5.1 does a little better on some \
examples than 5.0."
}], "Text"],
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\($Version\)], "Input"],
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Cell[TextData[{
"The following comments are for the examples for which problems were noted \
in 5.0. Results for the other examples in the NIST benchmarks still give \
correct results in 5.1. For most examples, just the parameter tables are \
shown; however, the ",
Cell[BoxData[
\(TraditionalForm\`s\^2\)]],
" values were also checked against the benchmark."
}], "Text"],
Cell[TextData[{
"For three examples, differences between ",
StyleBox["Mathematica",
FontSlant->"Italic"],
"\[CloseCurlyQuote]s results and the benchmark result are attributable to \
numerical error in machine-precision arithmetic, numerical error in the NIST \
data, or a combination of those two sources. In the other examples, ",
StyleBox["NonlinearRegress", "MR"],
" either gets a correct result with default settings or obtains a correct \
result with an additional option in 5.1."
}], "Text"],
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Cell[CellGroupData[{
Cell["Wampler1", "Subsection"],
Cell["\<\
The numerical error in this example is a result of numerical error in \
machine-precision computation and can be expected.\
\>", "Text"],
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177156}, {12, 271453}, {13, 402234}, {14, 579195}, {15,
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{\(x\^5\), "1.000000000000002`", "2.6029299171933973`*^-14",
"3.841824527793086`*^13", "0.`"}
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RowSpacings->1,
ColumnSpacings->3,
RowAlignments->Baseline,
ColumnAlignments->{Left}],
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Power[ x, 2],
Power[ x, 3],
Power[ x, 4],
Power[ x, 5]}, {"Estimate", "SE", "TStat", "PValue"}}]]]], "Output"]
}, Open ]],
Cell[TextData[{
"Significance arithmetic (variable-precision arithmetic) can be used to get \
results of a desired precision or accuracy. ",
StyleBox["Regress", "MR"],
" can be forced to use significance arithmetic by applying ",
StyleBox["SetPrecision", "MR"],
" to the data. Here is an example with precision 20 data with the result \
displayed at machine\[Hyphen]precision. Because there is no random error in \
the original data, division by 0 will result in error messages when \
attempting to compute the ",
StyleBox["t",
FontSlant->"Italic"],
" statistics and p-values."
}], "Text"],
Cell[CellGroupData[{
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\(\(Off[Power::"\", Less::"\"];\)\), "\n",
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SetPrecision[w1, 20], {1, x, x\^2, x\^3, x\^4, x\^5}, x,
RegressionReport \[Rule] {ParameterTable}]]\)}], "Input"],
Cell[BoxData[
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}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Wampler2", "Subsection"],
Cell["\<\
In this example, there are two sources of numerical error: rounding in the \
original data and machine-precision arithmetic. While the NIST data was \
generated from a polynomial expression, the data is only given to five digits \
of accuracy, resulting in some roundoff or truncation error in the data. \
\>", "Text"],
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3.68928}, {9, 4.68559}, {10, 6. }, {11, 7.71561}, {12,
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Cell[CellGroupData[{
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RowSpacings->1,
ColumnSpacings->3,
RowAlignments->Baseline,
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}, Open ]],
Cell["\<\
As in the case of Wampler1, more precise results can be obtained by using \
higher precision input for the regression.\
\>", "Text"],
Cell[CellGroupData[{
Cell[BoxData[{
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SetPrecision[w2, 17], {1, x, x\^2, x\^3, x\^4, x\^5}, x,
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RowSpacings->1,
ColumnSpacings->3,
RowAlignments->Baseline,
ColumnAlignments->{Left}],
Function[ BoxForm`e$,
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}, Open ]],
Cell["\<\
However, increasing the precision of the input cannot make up for the fact \
that there is some numerical error in the original data. As the precision is \
increased, the significance of the roundoff or truncation error in the data \
from the NIST will show up as small deviations from the benchmark results.\
\>", "Text"],
Cell[CellGroupData[{
Cell[BoxData[{
\(\(Off[Power::"\", Less::"\"];\)\), "\n",
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RowSpacings->1,
ColumnSpacings->3,
RowAlignments->Baseline,
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}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["MGH17", "Subsection"],
Cell["\<\
Each value in the first set of starting points is about two orders of \
magnitude from the optimal value. Overflows are quickly encountered using the \
default Levenberg\[Dash]Marquardt method. Despite the tough starting values, \
good results can be obtained using Newton\[CloseCurlyQuote]s method instead \
of the default Levenberg\[Dash]Marquardt method.\
\>", "Text"],
Cell[BoxData[
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{\(\[Beta]\_5\), "0.022122699652517345`",
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RowSpacings->1,
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}, Open ]],
Cell["\<\
As in 5.0, this example converges to the correct result from the second set \
of starting values with default options.\
\>", "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell["Lanczos1", "Subsection"],
Cell[TextData[{
"With both sets of starting points, this example converges to the expected \
parameter estimates with default options in 5.1. The SEs and ",
Cell[BoxData[
\(TraditionalForm\`s\^2\)]],
" values are on the same order as the benchmark values, which is reasonable \
given the magnitudes of the SEs and ",
Cell[BoxData[
\(TraditionalForm\`s\^2\)]],
" and the fact that the benchmark data is given to 13 digits. For the first \
starting points, the SEs agree with the benchmark in at least the first \
digit. For the second starting points, the SEs agree with the benchmark in at \
least the first two digits."
}], "Text"],
Cell[BoxData[
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Cell[BoxData[{
\(\(res =
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\(\(res =
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Cell[TextData[{
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Cell[BoxData[
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" values matching the benchmark to three digits can be obtained."
}], "Text"],
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Cell[CellGroupData[{
Cell["Lanczos2", "Subsection"],
Cell["\<\
With both sets of starting points, this example converges to the expected \
result with default options in 5.1.\
\>", "Text"],
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Cell["\<\
The research on which this article is based has been supported by the \
Maryland Agricultural Experiment Station. I am also indebted to two anonymous \
referees, as well as Daniel Lichtblau, Bruce McCullough, Charles Renfro, and, \
above all, Colin Rose for helpful comments. The author assumes responsibility \
for remaining errors.\
\>", "Text"]
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"(1) ",
ButtonBox["www.nag.co.uk/stats/ae_soft.asp",
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"(3) McCullough [",
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"] has also looked at several popular econometrics packages, such as \
E-Views, LIMDEP, SHAZAM, and TSP. The results are generally comparable to \
those obtained for SAS."
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Reliability of Econometric Software,\[CloseCurlyDoubleQuote] ",
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FontSlant->"Italic"],
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Statistical Procedures in Microsoft Excel 97,\[CloseCurlyDoubleQuote] ",
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Its Numerical Accuracy,\[CloseCurlyDoubleQuote]",
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ShowSelection->True,
CellMargins->{{54, 24}, {0, 15}},
CellGroupingRules->{"TitleGrouping", 0},
PageBreakBelow->False,
LineSpacing->{1.125, 0},
CounterIncrements->"Title",
CounterAssignments->{{"Subtitle", 0}, {"Section", 0}, {"Subsection", 0}, {
"Subsubsection", 0}, {"List", 0}, {"NumberedFigure", 0}, {
"NumberedTable", 0}, {"NumberedProgram", 0}, {"Equation", 0}, {
"Text", 0}, {"SmallText", 0}, {"Reference", 0}},
FontFamily->"Times",
FontSize->36,
FontSlant->"Italic"],
Cell[StyleData["Title", "Presentation"]],
Cell[StyleData["Title", "Printout"],
CellMargins->{{72, 72}, {14, 0}},
CellFrameMargins->False,
FontColor->GrayLevel[0],
Background->None]
}, Closed]],
Cell["Sub(sub)titles are optional, follows Title, precedes Author.",
"EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Subtitle"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{54, 24}, {5, 2}},
CellGroupingRules->{"TitleGrouping", 10},
PageBreakBelow->False,
LineSpacing->{1.25, 0},
CounterIncrements->"Subtitle",
FontFamily->"Times",
FontSize->24,
FontSlant->"Italic"],
Cell[StyleData["Subtitle", "Presentation"]],
Cell[StyleData["Subtitle", "Printout"],
CellMargins->{{72, 72}, {12, 2}},
FontSize->12,
FontSlant->"Plain"]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["Subsubtitle"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{54, 24}, {5, 2}},
CellGroupingRules->{"TitleGrouping", 10},
PageBreakBelow->False,
LineSpacing->{1, 0},
CounterIncrements->"Subtitle",
StyleMenuListing->None,
FontFamily->"Times",
FontSize->18,
FontSlant->"Italic"],
Cell[StyleData["Subsubtitle", "Presentation"]],
Cell[StyleData["Subsubtitle", "Printout"],
CellMargins->{{72, 72}, {6, 2}},
FontSize->10,
FontSlant->"Plain"]
}, Closed]],
Cell["\<\
SectionFirst should be used for the first section level heading in a \
notebook. SectionFirst sets the Subsection and Subsubsection counters to \
zero. Sets Section counter value to 1. If not preceded by Abstract space \
above should be adjusted to 18.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SectionFirst"],
CellFrame->False,
CellDingbat->"\[FilledSquare]",
CellMargins->{{67, 25}, {10, 30}},
Evaluatable->False,
CellGroupingRules->{"SectionGrouping", 40},
PageBreakBelow->False,
CounterIncrements->"Section",
CounterAssignments->{{"Section", 0}, {"Subsection", 0}, {
"Subsubsection", 0}},
AspectRatioFixed->True,
FontFamily->"Helvetica",
FontSize->16,
FontWeight->"Bold"],
Cell[StyleData["SectionFirst", "Presentation"],
FontSize->18],
Cell[StyleData["SectionFirst", "Printout"],
CellMargins->{{72, 72}, {2, 30}},
FontSize->12]
}, Closed]],
Cell["\<\
Section should be used for subsequent Section level headings. Sets counter \
values Subsection and Subsubsection to zero.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Section"],
CellFrame->False,
CellDingbat->"\[FilledSquare]",
CellMargins->{{67, 25}, {10, 30}},
Evaluatable->False,
CellGroupingRules->{"SectionGrouping", 40},
PageBreakBelow->False,
CounterIncrements->"Section",
CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}},
AspectRatioFixed->True,
FontFamily->"Helvetica",
FontSize->16,
FontWeight->"Bold"],
Cell[StyleData["Section", "Presentation"],
FontSize->18],
Cell[StyleData["Section", "Printout"],
CellMargins->{{72, 72}, {2, 30}},
FontSize->12]
}, Closed]],
Cell["\<\
Subsection is an optional style. Sets counter Subsubsection to zero.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Subsection"],
CellDingbat->"\[EmptySquare]",
CellMargins->{{67, 25}, {10, 26}},
CellGroupingRules->{"SectionGrouping", 50},
PageBreakBelow->False,
CounterIncrements->"Subsection",
CounterAssignments->{{"Subsubsection", 0}},
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold"],
Cell[StyleData["Subsection", "Presentation"]],
Cell[StyleData["Subsection", "Printout"],
CellDingbat->"\[EmptySquare]",
CellMargins->{{72, 72}, {2, 16}},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["Subsubsection"],
CellDingbat->"\[FilledSmallSquare]",
CellMargins->{{67, 25}, {6, 20}},
CellGroupingRules->{"SectionGrouping", 60},
PageBreakBelow->False,
CounterIncrements->"Subsubsection",
FontFamily->"Helvetica",
FontSize->12,
FontWeight->"Bold"],
Cell[StyleData["Subsubsection", "Presentation"]],
Cell[StyleData["Subsubsection", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {-4, 2}},
FontSize->9,
FontSlant->"Oblique"]
}, Closed]],
Cell["\<\
NoSpace heading variants used if a subsequent level heading directly follows \
its predecessor.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SubsectionNoSpace"],
CellDingbat->"\[EmptySquare]",
CellMargins->{{67, 25}, {10, 2}},
CellGroupingRules->{"SectionGrouping", 50},
PageBreakBelow->False,
CounterIncrements->"Subsection",
CounterAssignments->{{"Subsubsection", 0}},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold"],
Cell[StyleData["SubsectionNoSpace", "Presentation"]],
Cell[StyleData["SubsectionNoSpace", "Printout"],
CellDingbat->"\[EmptySquare]",
CellMargins->{{72, 72}, {2, 2}},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["SubsubsectionNoSpace"],
CellDingbat->"\[FilledSmallSquare]",
CellMargins->{{67, 25}, {6, 2}},
CellGroupingRules->{"SectionGrouping", 60},
PageBreakBelow->False,
CounterIncrements->"Subsubsection",
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->12,
FontWeight->"Bold"],
Cell[StyleData["SubsubsectionNoSpace", "Presentation"]],
Cell[StyleData["SubsubsectionNoSpace", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {-4, 2}},
FontSize->9,
FontSlant->"Oblique"]
}, Closed]],
Cell["\<\
NoDingbat heading variants used, for example, in the frontmatter.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SectionNoDingbat"],
CellFrame->False,
CellDingbat->None,
CellMargins->{{67, 25}, {10, 30}},
CellGroupingRules->{"SectionGrouping", 40},
PageBreakBelow->False,
CounterIncrements->"Section",
CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->16,
FontWeight->"Bold"],
Cell[StyleData["SectionNoDingbat", "Presentation"],
CellFrameMargins->{{0, 0}, {0, 4}}],
Cell[StyleData["SectionNoDingbat", "Printout"],
CellFrame->False,
CellMargins->{{72, 72}, {2, 30}},
CellFrameColor->GrayLevel[0],
FontSize->12]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["SubsectionNoDingbat"],
CellDingbat->None,
CellMargins->{{67, 25}, {10, 26}},
CellGroupingRules->{"SectionGrouping", 50},
PageBreakBelow->False,
CounterIncrements->"Subsection",
CounterAssignments->{{"Subsubsection", 0}},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold"],
Cell[StyleData["SubsectionNoDingbat", "Presentation"]],
Cell[StyleData["SubsectionNoDingbat", "Printout"],
CellMargins->{{72, 72}, {2, 16}},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["SubsectionNoSpaceNoDingbat"],
CellMargins->{{67, 25}, {2, 2}},
CellGroupingRules->{"SectionGrouping", 50},
PageBreakBelow->False,
CounterIncrements->"Subsection",
CounterAssignments->{{"Subsubsection", 0}},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold"],
Cell[StyleData["SubsectionNoSpaceNoDingbat", "Presentation"]],
Cell[StyleData["SubsectionNoSpaceNoDingbat", "Printout"],
CellMargins->{{72, 72}, {2, 2}},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["SubsubsectionNoDingbat"],
CellMargins->{{67, 25}, {6, 20}},
CellGroupingRules->{"SectionGrouping", 60},
PageBreakBelow->False,
CounterIncrements->"Subsubsection",
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->12,
FontWeight->"Bold"],
Cell[StyleData["SubsubsectionNoDingbat", "Presentation"]],
Cell[StyleData["SubsubsectionNoDingbat", "Printout"],
CellMargins->{{72, 72}, {-4, 2}},
FontSize->9,
FontSlant->"Oblique"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell["Styles for Body Text", "Section",
CellFrame->False,
CellDingbat->None,
ShowCellBracket->True,
CellMargins->{{0, 0}, {10, 40}},
CellFrameMargins->{{20, 4}, {8, 8}},
FontColor->GrayLevel[1],
Background->RGBColor[0.269902, 0.558434, 0.715618]],
Cell[CellGroupData[{
Cell[StyleData["Text"],
CellMargins->{{67, 24}, {4, 4}},
LineSpacing->{1, 4},
CounterIncrements->"Text",
FontFamily->"Times",
FontSize->12],
Cell[StyleData["Text", "Presentation"]],
Cell[StyleData["Text", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 12},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["SmallText"],
CellMargins->{{67, 24}, {4, 4}},
LineSpacing->{1, 4},
CounterIncrements->"SmallText",
FontFamily->"Times",
FontSize->10],
Cell[StyleData["SmallText", "Presentation"]],
Cell[StyleData["SmallText", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["Quote"],
CellMargins->{{83, 40}, {Inherited, Inherited}},
LineSpacing->{1, 3},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["Quote", "Presentation"]],
Cell[StyleData["Quote", "Printout"],
CellMargins->{{96, 96}, {2, 4}},
LineSpacing->{0, 12},
FontSize->10]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell["Styles for Input, Output, and Graphics", "Section",
CellFrame->False,
CellDingbat->None,
ShowCellBracket->True,
CellMargins->{{0, 0}, {10, 40}},
CellFrameMargins->{{20, 4}, {8, 8}},
FontColor->GrayLevel[1],
Background->RGBColor[0.269902, 0.558434, 0.715618]],
Cell["\<\
The cells in this section define styles used for active kernel sessions. Be \
careful when modifying, renaming, or removing these styles, because the front \
end associates special meanings with these style names.\
\>", "Text"],
Cell[TextData[{
"Input cell style to be used for ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" input statements that are followed by either Output or GraphicsOnly \
cell styles. Sets ",
"DefaultFormatType->DefaultInputFormatType."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Input"],
CellFrame->{{0.25, 0.25}, {0, 0.25}},
CellMargins->{{67, 24}, {-1, 10}},
Evaluatable->True,
CellGroupingRules->"InputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultInputFormatType,
AutoItalicWords->{},
ShowStringCharacters->True,
NumberMarks->True,
CounterIncrements->"Input",
FontSize->12,
FontWeight->"Bold",
Background->GrayLevel[0.949996]],
Cell[StyleData["Input", "Presentation"],
FontSize->14],
Cell[StyleData["Input", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
CellFrameMargins->False,
LineSpacing->{1.25, 0},
FontSize->9,
Background->None]
}, Closed]],
Cell[TextData[{
"InputOnly cell style to be used for ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" input statements that produce no output or graphic. See Program and \
ProgramNoLabel cell styles for presenting segments of code that do not \
evaluate."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["InputOnly"],
CellFrame->{{0.25, 0.25}, {0, 0.25}},
CellMargins->{{67, 24}, {10, 10}},
Evaluatable->True,
CellGroupingRules->"InputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultInputFormatType,
AutoItalicWords->{},
ShowStringCharacters->True,
NumberMarks->True,
CounterIncrements->"Input",
FontSize->12,
FontWeight->"Bold",
Background->GrayLevel[0.949996]],
Cell[StyleData["InputOnly", "Presentation"],
FontSize->14],
Cell[StyleData["InputOnly", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
LineSpacing->{1.25, 0},
FontSize->9,
Background->None]
}, Closed]],
Cell[TextData[{
"Output cell style is usually generated by the ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" kernel. To follow Input cell style. Sets \
DefaultFormatType->DefaultOutputFormatType."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Output"],
CellFrame->{{0.25, 0.25}, {0.25, 0}},
CellMargins->{{67, 24}, {10, 0}},
CellEditDuplicate->True,
CellGroupingRules->"OutputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
CounterIncrements->"Output",
StyleMenuListing->None,
FontSize->12,
Background->GrayLevel[0.949996]],
Cell[StyleData["Output", "Presentation"],
FontSize->14],
Cell[StyleData["Output", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {2, 4}},
CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.25, 0},
FontSize->9,
Background->None]
}, Closed]],
Cell["\<\
OutputPreserved cell style to be used to retain original output for Timing \
results and such. \
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["OutputPreserved"],
CellFrame->{{0.25, 0.25}, {0.25, 0}},
CellMargins->{{67, 24}, {10, 0}},
CellEditDuplicate->False,
CellGroupingRules->"OutputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->False,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
CounterIncrements->"Output",
FontSize->12,
Background->GrayLevel[0.949996]],
Cell[StyleData["OutputPreserved", "Presentation"],
FontSize->14],
Cell[StyleData["OutputPreserved", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {2, 4}},
CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.25, 0},
FontSize->9,
Background->None]
}, Closed]],
Cell[TextData[{
"OutputOnly cell style to be used for output generated by the ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" kernel without the Input. Sets \
DefaultFormatType->DefaultOutputFormatType."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["OutputOnly"],
CellFrame->True,
CellMargins->{{67, 24}, {15, 10}},
CellEditDuplicate->True,
CellGroupingRules->"OutputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
CounterIncrements->"Output",
StyleMenuListing->None,
FontSize->12,
Background->GrayLevel[0.949996]],
Cell[StyleData["OutputOnly", "Presentation"],
FontSize->14],
Cell[StyleData["OutputOnly", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {2, 4}},
CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.25, 0},
FontSize->9,
Background->None]
}, Closed]],
Cell["Variants for use embedded in NumberedList.", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["InputInList"],
CellFrame->{{0.25, 0.25}, {0, 0.25}},
CellMargins->{{103, 24}, {-1, 10}},
Evaluatable->True,
CellGroupingRules->"InputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultInputFormatType,
AutoItalicWords->{},
ShowStringCharacters->True,
NumberMarks->True,
CounterIncrements->"Input",
StyleMenuListing->None,
FontFamily->"Courier",
FontSize->12,
FontWeight->"Bold",
Background->GrayLevel[0.949996]],
Cell[StyleData["InputInList", "Presentation"],
FontSize->14],
Cell[StyleData["InputInList", "Printout"],
CellFrame->False,
CellMargins->{{109, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
CellFrameMargins->False,
LineSpacing->{1.25, 0},
FontFamily->"Courier",
FontSize->9,
Background->None]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["InputOnlyInList"],
CellFrame->{{0.25, 0.25}, {0, 0.25}},
CellMargins->{{103, 24}, {10, 10}},
Evaluatable->True,
CellGroupingRules->"InputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultInputFormatType,
AutoItalicWords->{},
ShowStringCharacters->True,
NumberMarks->True,
CounterIncrements->"Input",
StyleMenuListing->None,
FontFamily->"Courier",
FontSize->12,
FontWeight->"Bold",
Background->GrayLevel[0.949996]],
Cell[StyleData["InputOnlyInList", "Presentation"],
FontSize->14],
Cell[StyleData["InputOnlyInList", "Printout"],
CellFrame->False,
CellMargins->{{109, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
LineSpacing->{1.25, 0},
FontFamily->"Courier",
FontSize->9,
Background->None]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["OutputInList"],
CellFrame->{{0.25, 0.25}, {0.25, 0}},
CellMargins->{{103, 24}, {10, 0}},
CellEditDuplicate->True,
CellGroupingRules->"OutputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
CellLabelAutoDelete->True,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
CounterIncrements->"Output",
StyleMenuListing->None,
FontFamily->"Courier",
FontSize->12,
Background->GrayLevel[0.949996]],
Cell[StyleData["OutputInList", "Presentation"],
FontSize->14],
Cell[StyleData["OutputInList", "Printout"],
CellFrame->False,
CellMargins->{{109, 72}, {2, 4}},
CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.25, 0},
FontFamily->"Courier",
FontSize->9,
Background->None]
}, Closed]],
Cell[TextData[{
"Message cells are sometimes generated by the ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" kernel during evaluation. To follow Input cell style, precede Output \
cell style."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Message"],
CellFrame->{{0.25, 0.25}, {0, 0}},
CellDingbat->"\[WarningSign]",
CellMargins->{{67, 24}, {0, 0}},
CellGroupingRules->"OutputGrouping",
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
ShowCellLabel->False,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0.869993],
CellFrameLabelMargins->-9,
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->10,
FontColor->RGBColor[0, 0, 1],
Background->GrayLevel[0.949996]],
Cell[StyleData["Message", "Presentation"],
FontSize->12],
Cell[StyleData["Message", "Printout"],
CellFrame->True,
CellDingbat->None,
CellMargins->{{96, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
CellFrameMargins->4,
CellFrameColor->GrayLevel[0],
LineSpacing->{0, 10},
FontSize->8,
FontColor->GrayLevel[0],
Background->None]
}, Closed]],
Cell[TextData[{
"Print cells are usually generated by the ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" kernel from such commands as ?Plot."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Print"],
CellFrame->True,
CellMargins->{{67, 24}, {0, 0}},
CellGroupingRules->"OutputGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GroupPageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
ShowCellLabel->False,
CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
CellFrameColor->GrayLevel[0],
DefaultFormatType->DefaultOutputFormatType,
AutoItalicWords->{},
StyleMenuListing->None,
FontSize->10],
Cell[StyleData["Print", "Presentation"],
FontSize->12],
Cell[StyleData["Print", "Printout"],
CellFrame->True,
CellMargins->{{96, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
CellFrameMargins->4,
CellFrameColor->GrayLevel[0],
LineSpacing->{0, 11},
FontSize->9,
Background->None]
}, Closed]],
Cell["\<\
Graphics cell usually output by kernel. To be preceded by Input cell, \
followed by Output cell.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Graphics"],
CellFrame->{{0.25, 0.25}, {0, 0}},
CellMargins->{{67, 24}, {0, 0}},
CellGroupingRules->"GraphicsGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
ShowCellLabel->True,
CellLabelPositioning->Left,
CellLabelAutoDelete->True,
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
FormatType->InputForm,
ImageMargins->{{30, 0}, {0, 0}},
StyleMenuListing->None,
Background->GrayLevel[0.949996]],
Cell[StyleData["Graphics", "Presentation"]],
Cell[StyleData["Graphics", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {8, 10}},
LineSpacing->{0, 12},
ImageSize->{144, 144},
Background->None]
}, Closed]],
Cell["\<\
GraphicsOnly cell to follow Input cell, not followed by Output cell. Set \
Graphics cell to GraphicsOnly cell manually.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["GraphicsOnly"],
CellFrame->{{0.25, 0.25}, {0.25, 0}},
CellMargins->{{67, 24}, {10, 0}},
CellGroupingRules->"GraphicsGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
ShowCellLabel->True,
CellLabelPositioning->Left,
CellLabelAutoDelete->True,
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
FormatType->InputForm,
ImageMargins->{{30, 0}, {0, 0}},
Background->GrayLevel[0.949996]],
Cell[StyleData["GraphicsOnly", "Presentation"]],
Cell[StyleData["GraphicsOnly", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {8, 10}},
LineSpacing->{0, 12},
ImageSize->{144, 144},
FontSize->10,
Background->None]
}, Closed]],
Cell["\<\
PictureGroup cell style used to group graphic cells that comprise an \
animation.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["PictureGroup"],
CellFrame->{{0.25, 0.25}, {0.25, 0}},
CellMargins->{{67, 17}, {0, 0}},
CellGroupingRules->"GraphicsGrouping",
CellHorizontalScrolling->True,
PageBreakWithin->False,
GeneratedCell->True,
CellAutoOverwrite->True,
ShowCellLabel->True,
CellLabelAutoDelete->True,
CellFrameColor->GrayLevel[0.869993],
DefaultFormatType->DefaultOutputFormatType,
FormatType->InputForm,
ImageMargins->{{30, 0}, {0, 0}},
StyleMenuListing->None,
Background->GrayLevel[0.949996]],
Cell[StyleData["PictureGroup", "Presentation"]],
Cell[StyleData["PictureGroup", "Printout"],
CellFrame->False,
CellMargins->{{96, 72}, {8, 10}},
LineSpacing->{0, 12},
ImageSize->{144, 144},
FontSize->10,
Background->None]
}, Closed]],
Cell[TextData[{
"PlacedGraphics cell style to be used when importing a graphic from \
another application or when presenting a graphic not associated with ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" input. May be followed by NumberedFigureCaption."
}], "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["PlacedGraphics"],
CellFrame->False,
CellMargins->{{67, 24}, {10, 10}},
CellGroupingRules->"GraphicsGrouping",
CellHorizontalScrolling->True,
ShowCellLabel->False,
CellLabelAutoDelete->True,
TextAlignment->Center],
Cell[StyleData["PlacedGraphics", "Presentation"]],
Cell[StyleData["PlacedGraphics", "Printout"],
CellMargins->{{72, 72}, {8, 10}},
LineSpacing->{0, 12},
FontSize->10,
Background->None]
}, Closed]],
Cell["\<\
CellLabel style definition controls how labels appear when a cell has \
ShowCellLabels->True.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["CellLabel"],
CellMargins->{{5, Inherited}, {Inherited, Inherited}},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->8,
FontSlant->"Oblique",
FontColor->RGBColor[0.115343, 0.350561, 0.362966]],
Cell[StyleData["CellLabel", "Presentation"],
FontSize->10,
FontColor->RGBColor[0.115343, 0.350561, 0.362966]],
Cell[StyleData["CellLabel", "Printout"],
LineSpacing->{1, 0},
FontSize->6,
FontColor->GrayLevel[0]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell["Styles for Automatic Numbering and Lists", "Section",
CellFrame->False,
CellDingbat->None,
ShowCellBracket->True,
CellMargins->{{0, 0}, {10, 40}},
CellFrameMargins->{{20, 4}, {8, 8}},
FontColor->GrayLevel[1],
Background->RGBColor[0.269902, 0.558434, 0.715618]],
Cell["\<\
NumberedEquation is for DisplayFormula cells that number sequentially \
throughout a notebook. Sets as DefaultFormatType->TraditionalForm.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["NumberedEquation"],
CellMargins->{{67, 24}, {5, 10}},
PageBreakAbove->False,
CellFrameLabels->{{None, Cell[
TextData[ {"(",
CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}},
DefaultFormatType->TraditionalForm,
TextAlignment->Center,
SingleLetterItalics->True,
SpanMaxSize->Infinity,
CounterIncrements->"NumberedEquation",
FormatTypeAutoConvert->False,
FontFamily->"Times",
FontSize->12,
UnderoverscriptBoxOptions->{LimitsPositioning->True},
GridBoxOptions->{AllowScriptLevelChange->False}],
Cell[StyleData["NumberedEquation", "Presentation"],
FontSize->14],
Cell[StyleData["NumberedEquation", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
FontSize->10]
}, Closed]],
Cell["\<\
NumberedFigureCaption to be used directly after a PlacedGraphic cell. Use the \
TMJStyles.nb palette to begin the cell and paste in the word \"Figure\" and \
the NumberedFigure counter value. Allows for a descriptive caption.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["NumberedFigureCaption"],
CellDingbat->"\[FilledUpTriangle]",
CellMargins->{{67, 24}, {8, 10}},
PageBreakAbove->False,
CellLabelPositioning->Left,
TextAlignment->Left,
CounterIncrements->"NumberedFigure",
FormatTypeAutoConvert->False,
FontFamily->"Helvetica",
FontSize->10],
Cell[StyleData["NumberedFigureCaption", "Presentation"]],
Cell[StyleData["NumberedFigureCaption", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {18, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell["\<\
NumberedTableCaption to be used directly after a Table cell. Use the \
TMJStyles.nb palette to begin the cell and paste in the word \"Table\" and \
the NumberedTable counter value. Allows for a descriptive caption.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["NumberedTableCaption"],
CellDingbat->"\[FilledUpTriangle]",
CellMargins->{{67, 24}, {8, 10}},
PageBreakAbove->False,
CounterIncrements->"NumberedTable",
FontFamily->"Helvetica",
FontSize->10],
Cell[StyleData["NumberedTableCaption", "Presentation"]],
Cell[StyleData["NumberedTableCaption", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {18, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell["\<\
NumberedProgramCaption to be used directly after a Program cell. Use the \
TMJStyles.nb palette to begin the cell and paste in the word \"Listing\" and \
the NumberedProgram counter value. Allows for a descriptive caption.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["NumberedProgramCaption"],
CellDingbat->"\[FilledUpTriangle]",
CellMargins->{{67, 24}, {8, 10}},
PageBreakAbove->False,
CounterIncrements->"NumberedProgram",
FormatTypeAutoConvert->False,
FontFamily->"Helvetica",
FontSize->10],
Cell[StyleData["NumberedProgramCaption", "Presentation"]],
Cell[StyleData["NumberedProgramCaption", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {18, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell["\<\
Use of Caption style by itself should be discouraged. See cell styles for \
NumberedFigureCaption, NumberedTableCaption, NumberedProgramCaption and the \
TMJStyles.nb palette.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Caption"],
CellDingbat->"\[FilledUpTriangle]",
CellMargins->{{67, 24}, {Inherited, 5}},
PageBreakAbove->False,
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->10],
Cell[StyleData["Caption", "Presentation"]],
Cell[StyleData["Caption", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell["\<\
BulletedList is an optional style. Adds a CellDingbat of FilledSmallCircle. \
Text indents left a little more.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BulletedList"],
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{104, 24}, {Inherited, Inherited}},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["BulletedList", "Presentation"]],
Cell[StyleData["BulletedList", "Printout"],
CellMargins->{{109, 72}, {2, Inherited}},
LineSpacing->{0, 12},
FontSize->10]
}, Closed]],
Cell["\<\
BeginNumberedList to be used as the first item in a numbered list sequence. \
Use the TMJStyles.nb palette to begin the cell and paste in the List counter \
value.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BeginNumberedList"],
CellMargins->{{79, 24}, {Inherited, Inherited}},
ParagraphIndent->-24,
CounterIncrements->"List",
CounterAssignments->{{"List", 0}},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["BeginNumberedList", "Presentation"],
ParagraphIndent->-31],
Cell[StyleData["BeginNumberedList", "Printout"],
CellMargins->{{85, 72}, {2, Inherited}},
LineSpacing->{0, 12},
ParagraphIndent->-24,
FontSize->10]
}, Closed]],
Cell["\<\
NumberedList to be used for subsequent items in a numbered list sequence with \
a single-digit label. Use the TMJstyles.nb palette to begin the cell and \
paste in the List counter value.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["NumberedList"],
CellMargins->{{79, 24}, {Inherited, Inherited}},
ParagraphIndent->-24,
CounterIncrements->"List",
FontFamily->"Times",
FontSize->12],
Cell[StyleData["NumberedList", "Presentation"]],
Cell[StyleData["NumberedList", "Printout"],
CellMargins->{{85, 72}, {2, Inherited}},
LineSpacing->{0, 12},
ParagraphIndent->-24,
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["NolabelList"],
CellMargins->{{103, 10}, {Inherited, Inherited}},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["NolabelList", "Presentation"]],
Cell[StyleData["NolabelList", "Printout"],
CellMargins->{{109, 72}, {2, Inherited}},
LineSpacing->{0, 12},
ParagraphIndent->0,
FontSize->10]
}, Closed]],
Cell["\<\
BeginSubList to be used as the first item in a lettered list sequence used as \
a subitem to a NumberedList item. Use the TMJStyles.nb palette to begin the \
cell and paste in the SubList counter value. Sets SubList counter to 0.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BeginSubList"],
CellMargins->{{95, 10}, {Inherited, Inherited}},
ParagraphIndent->-24,
CounterIncrements->"SubList",
CounterAssignments->{{"SubList", 0}},
FontFamily->"Times",
FontSize->12,
CounterBoxOptions->{CounterFunction:>(Part[
CharacterRange[ "a", "z"], #]&)}],
Cell[StyleData["BeginSubList", "Presentation"]],
Cell[StyleData["BeginSubList", "Printout"],
CellMargins->{{85, 72}, {2, Inherited}},
LineSpacing->{0, 12},
ParagraphIndent->-24,
FontSize->10]
}, Closed]],
Cell["\<\
SubList to be used as subsequent items in a lettered list sequence used as a \
subitem to a NumberedList item. Use the TMJStyles.nb palette to begin the \
cell and paste in the SubList counter value. Increments SubList counter.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SubList"],
CellMargins->{{95, 10}, {Inherited, Inherited}},
ParagraphIndent->-24,
CounterIncrements->"SubList",
FontFamily->"Times",
FontSize->12,
CounterBoxOptions->{CounterFunction:>(Part[
CharacterRange[ "a", "z"], #]&)}],
Cell[StyleData["SubList", "Presentation"]],
Cell[StyleData["SubList", "Printout"],
CellMargins->{{85, 72}, {2, Inherited}},
LineSpacing->{0, 12},
ParagraphIndent->-24,
FontSize->10]
}, Closed]],
Cell["\<\
SubListBulleted to be used as subsequent items in a bulleted list sequence \
used as a subitem to a NumberedList item.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SubListBulleted"],
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{113, 10}, {Inherited, Inherited}},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["SubListBulleted", "Presentation"]],
Cell[StyleData["SubListBulleted", "Printout"],
CellMargins->{{119, 72}, {2, Inherited}},
TextJustification->1,
Hyphenation->True,
LineSpacing->{0, 12},
FontSize->10]
}, Closed]],
Cell["\<\
Reference style to be used in the bibliography portion of a notebook. One \
cell for each bibliography entry. Use the TMJStyles.nb palette to begin cell \
and paste in the Reference counter value. Use Inline style SB for bold font \
changes. Use Inline style SO for italic font changes.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Reference"],
CellMargins->{{79, 25}, {Inherited, Inherited}},
ParagraphIndent->-24,
CounterIncrements->"Reference",
FontFamily->"Helvetica",
FontSize->10],
Cell[StyleData["Reference", "Presentation"],
ParagraphIndent->-25],
Cell[StyleData["Reference", "Printout"],
CellMargins->{{85, 72}, {2, 4}},
LineSpacing->{0, 10},
ParagraphIndent->-24,
FontSize->8]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell["Journal Element Styles", "Section",
CellFrame->False,
CellDingbat->None,
ShowCellBracket->True,
CellMargins->{{0, 0}, {10, 40}},
CellFrameMargins->{{20, 4}, {8, 8}},
FontColor->GrayLevel[1],
Background->RGBColor[0.269902, 0.558434, 0.715618]],
Cell["\<\
OnlineHeader to be used at the beginning of a notebook. Precedes the Title \
cell.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["OnlineHeader"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{0, 25}, {0, 0}},
CellGroupingRules->{"TitleGrouping", 30},
PageBreakBelow->False,
CellFrameMargins->{{54, 4}, {2, 8}},
LineSpacing->{1, 1},
StyleMenuListing->None,
FontFamily->"Times",
FontSize->12,
FontWeight->"Plain",
FontSlant->"Italic",
FontColor->GrayLevel[1],
Background->RGBColor[0.725383, 0.0545968, 0.0770581]],
Cell[StyleData["OnlineHeader", "Presentation"],
FontSize->14],
Cell[StyleData["OnlineHeader", "Printout"],
PageWidth->PaperWidth,
CellFrame->False,
CellMargins->{{72, 72}, {0, 0}},
FontSize->10,
FontColor->GrayLevel[0],
Background->None]
}, Closed]],
Cell["\<\
Cell Style PreTitle to be used for such things that precede a title as in \
EDITOR'S PICK. Should be entered all caps with a space between each letter, \
two spaces between words. FontTracking is set to Wide.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["PreTitle"],
ShowCellBracket->False,
CellMargins->{{54, 25}, {Inherited, 0}},
CellGroupingRules->{"TitleGrouping", 0},
PageBreakBelow->False,
CellFrameMargins->{{55, 4}, {8, 20}},
LineSpacing->{1.125, 0},
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold"],
Cell[StyleData["PreTitle", "Presentation"]],
Cell[StyleData["PreTitle", "Printout"],
CellMargins->{{72, 72}, {14, 0}},
CellFrameMargins->False,
FontSize->12,
FontColor->GrayLevel[0],
Background->None]
}, Closed]],
Cell["\<\
Author to be used after the Title cell with author name(s). Author name(s) \
may be preceded by \"Edited by \" for certain columns. Text in author cell to \
be used as the left page header. Usually followed by an Address cell.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Author"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{54, 24}, {4, 0}},
CellGroupingRules->"NormalGrouping",
PageBreakBelow->False,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold",
FontSlant->"Plain"],
Cell[StyleData["Author", "Presentation"],
FontSize->16],
Cell[StyleData["Author", "Printout"],
CellMargins->{{72, 72}, {4, 4}},
LineSpacing->{0, 14},
FontSize->12]
}, Closed]],
Cell["\<\
Abstract to be used after the Author cell. Contains a short summary of the \
article.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Abstract"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{54, 86}, {4, 25}},
LineSpacing->{1, 3},
FontFamily->"Times",
FontSize->14,
FontWeight->"Bold",
FontSlant->"Plain"],
Cell[StyleData["Abstract", "Presentation"],
FontSize->16],
Cell[StyleData["Abstract", "Printout"],
CellMargins->{{72, 72}, {Inherited, 2}},
LineSpacing->{0, 12},
FontSize->10,
FontWeight->"Bold",
FontSlant->"Plain"]
}, Closed]],
Cell["\<\
BeginQuestion is used in the In and Out column directly after a section cell. \
Followed by either Question or Input, InputOnly, etc. Last paragraph of the \
question should be in EndQuestion cell style.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BeginQuestion"],
CellFrame->{{0, 0}, {0, 2}},
CellDingbat->"Q:",
CellMargins->{{89, 34}, {8, 8}},
CellFrameMargins->{{0, 0}, {2, 4}},
LineSpacing->{1, 2},
FontFamily->"Times",
FontSize->14,
FontWeight->"Bold",
FontColor->RGBColor[0.115511, 0.321752, 0.580118]],
Cell[StyleData["BeginQuestion", "Presentation"]],
Cell[StyleData["BeginQuestion", "Printout"],
PageWidth->PaperWidth,
CellFrame->{{0, 0}, {0, 2}},
CellMargins->{{72, 72}, {4, 16}},
LineSpacing->{0, 12},
FontSize->10,
FontWeight->"Plain",
FontColor->GrayLevel[0]]
}, Closed]],
Cell["\<\
Question used for text cells within the Question portion of a QuestionAnswer.\
\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["Question"],
CellMargins->{{89, 34}, {8, 8}},
LineSpacing->{1, 2},
FontFamily->"Times",
FontSize->14,
FontWeight->"Bold",
FontColor->RGBColor[0.115511, 0.321752, 0.580118]],
Cell[StyleData["Question", "Presentation"]],
Cell[StyleData["Question", "Printout"],
PageWidth->PaperWidth,
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 12},
FontSize->10,
FontWeight->"Plain",
FontColor->GrayLevel[0]]
}, Closed]],
Cell["\<\
EndQuestion used in the In and Out column as the last paragraph of the \
question.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["EndQuestion"],
CellFrame->{{0, 0}, {2, 0}},
CellMargins->{{89, 35}, {8, 8}},
LineSpacing->{1, 2},
FontFamily->"Times",
FontSize->14,
FontWeight->"Bold",
FontColor->RGBColor[0.115511, 0.321752, 0.580118]],
Cell[StyleData["EndQuestion", "Presentation"]],
Cell[StyleData["EndQuestion", "Printout"],
CellFrame->{{0, 0}, {2, 0}},
CellMargins->{{72, 72}, {18, 4}},
LineSpacing->{0, 12},
FontSize->10,
FontWeight->"Plain",
FontColor->GrayLevel[0]]
}, Closed]],
Cell["\<\
BeginEndQuestion is used in the In and Out column directly after a section \
cell. Used if the question is a single text paragraph.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BeginEndQuestion"],
CellFrame->{{0, 0}, {2, 2}},
CellDingbat->"Q:",
CellMargins->{{89, 35}, {8, 8}},
LineSpacing->{1, 2},
FontFamily->"Times",
FontSize->14,
FontWeight->"Bold",
FontColor->RGBColor[0.115511, 0.321752, 0.580118]],
Cell[StyleData["BeginEndQuestion", "Presentation"]],
Cell[StyleData["BeginEndQuestion", "Printout"],
CellMargins->{{72, 72}, {18, 14}},
LineSpacing->{0, 12},
FontSize->10,
FontWeight->"Plain",
FontColor->GrayLevel[0]]
}, Closed]],
Cell["\<\
BeginAnswer is used in the In and Out column directly after an EndQuestion or \
BeginEndQuestion cell style to begin the answer portion. Followed by Text or \
Input/Output etc.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["BeginAnswer"],
CellDingbat->"A:",
CellMargins->{{89, 35}, {Inherited, Inherited}},
LineSpacing->{1, 4},
CounterIncrements->"Text",
FontFamily->"Times",
FontSize->12],
Cell[StyleData["BeginAnswer", "Presentation"]],
Cell[StyleData["BeginAnswer", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 12},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["Answer"],
CellMargins->{{89, 35}, {Inherited, Inherited}},
LineSpacing->{1, 4},
FontFamily->"Times",
FontSize->12],
Cell[StyleData["Answer", "Presentation"]],
Cell[StyleData["Answer", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 12},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["EditorialComment"],
CellFrame->False,
CellDingbat->"\[FilledCircle]",
CellMargins->{{36, 25}, {Inherited, Inherited}},
LineSpacing->{1, 3},
CounterIncrements->"Text",
FontColor->RGBColor[1, 0, 0],
Background->GrayLevel[1]],
Cell[StyleData["EditorialComment", "Presentation"]],
Cell[StyleData["EditorialComment", "Printout"],
CellMargins->{{24, 80}, {Inherited, 0}},
LineSpacing->{1, 3},
FontSize->10,
FontColor->GrayLevel[0]]
}, Closed]],
Cell["\<\
SecondAuthor to be used after a Section cell. Author name(s) credit a \
particular portion of a notebook. Used for columns Tech Support and Tricks of \
the Trade. Usually followed by a Text cell with author affiliation/email, \
etc.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SecondAuthor"],
ShowCellBracket->False,
ShowSelection->True,
CellMargins->{{67, 24}, {Inherited, Inherited}},
CellGroupingRules->"NormalGrouping",
PageBreakBelow->False,
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->14,
FontWeight->"Bold",
FontSlant->"Plain"],
Cell[StyleData["SecondAuthor", "Presentation"],
FontSize->16],
Cell[StyleData["SecondAuthor", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 14},
FontSize->12]
}, Closed]],
Cell["\<\
SectionAboutAuthor to be used as the section head for the About the Author \
portion of a notebook.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["SectionAboutAuthor"],
CellMargins->{{54, 25}, {10, 60}},
CellGroupingRules->{"SectionGrouping", 40},
PageBreakBelow->False,
CellFrameMargins->4,
FontFamily->"Helvetica",
FontSize->12,
FontWeight->"Bold"],
Cell[StyleData["SectionAboutAuthor", "Presentation"]],
Cell[StyleData["SectionAboutAuthor", "Printout"],
CellFrame->False,
CellMargins->{{72, 72}, {0, 30}},
FontSize->12]
}, Closed]],
Cell["\<\
TextAboutAuthor is to be used for the text in the About the Author portion of \
a notebook. The last paragraph should be affiliation and contact information \
with author name set in bold.\
\>", "EditorialComment"],
Cell[CellGroupData[{
Cell[StyleData["TextAboutAuthor"],
CellMargins->{{54, 24}, {2, 5}},
LineSpacing->{1, 3},
CounterIncrements->"Text",
FontSize->12],
Cell[StyleData["TextAboutAuthor", "Presentation"],
FontSize->14],
Cell[StyleData["TextAboutAuthor", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
LineSpacing->{0, 11},
FontSize->9]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["Subsubsubsection"],
CellDingbat->None,
CellMargins->{{67, 25}, {6, 20}},
CellGroupingRules->{"SectionGrouping", 70},
PageBreakBelow->False,
CounterIncrements->"Subsubsubsection",
StyleMenuListing->None,
FontFamily->"Helvetica",
FontSize->12,
FontWeight->"Bold"],
Cell[StyleData["Subsubsubsection", "Presentation"]],
Cell[StyleData["Subsubsubsection", "Printout"],
CellDingbat->None,
CellMargins->{{72, 72}, {-4, 2}},
FontSize->9,
FontWeight->"Bold",
FontSlant->"Plain"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell["Display Formulas and Programming", "Section",
CellFrame->False,
CellDingbat->None,
ShowCellBracket->True,
CellMargins->{{0, 0}, {10, 40}},
CellFrameMargins->{{20, 4}, {8, 8}},
FontColor->GrayLevel[1],
Background->RGBColor[0.269902, 0.558434, 0.715618]],
Cell[CellGroupData[{
Cell[StyleData["DisplayFormula"],
CellMargins->{{67, 24}, {4, 4}},
CellHorizontalScrolling->True,
PageBreakAbove->False,
DefaultFormatType->TraditionalForm,
TextAlignment->Center,
ScriptLevel->0,
SingleLetterItalics->True,
SpanMaxSize->Infinity,
FormatTypeAutoConvert->False,
FontFamily->"Times",
FontSize->12,
UnderoverscriptBoxOptions->{LimitsPositioning->True},
GridBoxOptions->{AllowScriptLevelChange->False}],
Cell[StyleData["DisplayFormula", "Presentation"]],
Cell[StyleData["DisplayFormula", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
PrivateEvaluationOptions->{"OutputFormPageWidth"->342},
LineSpacing->{1.25, 0},
FontSize->10]
}, Closed]],
Cell[CellGroupData[{
Cell[StyleData["ChemicalFormula"],
CellMargins->{{67, 24}, {4, 4}},
PageBreakAbove->False,
DefaultFormatType->DefaultInputFormatType,
AutoSpacing->False,
ScriptLevel->1,
ScriptBaselineShifts->{0.6, Automatic},
SingleLetterItalics->False,
ZeroWidthTimes->False,
FontFamily->"Times",
FontSize->12],
Cell[StyleData["ChemicalFormula", "Presentation"],
FontSize->14],
Cell[StyleData["ChemicalFormula", "Printout"],
CellMargins->{{72, 72}, {2, 4}},
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Cell["\<\
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FontWeight->"Light",
FontSlant->"Oblique",
FontTracking->"Condensed"],
Cell["\<\
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Cell[StyleData["SCB"],
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FontTracking->"Condensed"],
Cell["\<\
SCBO used to change selection to sans serif font (FontWeight->\"Bold\", \
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Cell[StyleData["SCBO"],
FontFamily->"Helvetica",
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FontSlant->"Oblique",
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Cell["\<\
SXR used to change selection to sans serif font (FontWeight->\"ExtraBold\", \
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Cell[StyleData["SXR"],
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FontWeight->"ExtraBold",
FontTracking->"Condensed"],
Cell["\<\
SXO used to change selection to sans serif font (FontWeight->\"ExtraBold\", \
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Cell[StyleData["SXO"],
FontFamily->"Helvetica",
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FontTracking->"Condensed"]
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Cached data follows. If you edit this Notebook file directly, not
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you save this file from within Mathematica.
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*)
(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)