
Dataplot Analysis of Four Typical Problems

Introduction

A computer language is a toola means of generating
solutions to problems. Before delving into the details of
the DATAPLOT language, let us first consider the types of
problems that the scientist/engineer/researcher typically
encounters. This will provide motivation for how the computer
language (as a tool) was developed. All computer languages
have their own areas of strength. The choice of problems
below serve as a frame of reference for both reader and
developer alike as to the type of problems that DATAPLOT
considers "important" and for which it has been designed
to be strong in.

List of Problems

The following are four typical problems.
 A graphics problem
An analyst has a data set consisting of (x,y) pairs.
Plot the data. Blow up" any interesting subregions of
the plot.
 A NonLinear Fitting
Problem
An analyst has a data set consisting of (x,y) pairs.
Read the data into the computer. Plot them. Perform a
nonlinear fit for the model y = exp(alpha+x)/(a+b+x).
Generate a superimposed plot of raw data and predicted
values from the fit. Generate a plot of residuals
versus x. Generate a normal probability plot of the
residuals.
 A Data Analysis Problem
An analyst has data consisting of a response variable and
3 independent variables (factors). Determine if the
factors affect the response. Determine if there is
interaction between the factors. Perofrm an analysis of
variance. Carry out a graphical analysis of variance.
 A Mathematics Problem
An analyst wishes to examine the function
x*exp(x) + sin(x**2) over the interval 0 to 3. Plot
the function over the interval. Determine any roots in
the interval. Determine its definite integral over
the interval.

Some Noteworthy Points

Several points are noteworthy:
 Graphics as a Core Activity.
Note the graphics component that exists in all of the
above problems. Graphics is a key activity in
both data analysis and mathematics.
 Time.
These problems should all take less than 10 minutes
to solve.
 Number of Lines of Code.
These problems should all be solvable with 1ess than
10 lines of code.
 Interactive Analysis.
These problems should be solvable interactively so that
in case some interesting tangent arises in the course
of the solution, the analyst can immediately pursue
it.
 Graphics Quality.
Ideally, the graphics should be all continuous and of
manuscriptquality if so desired.
 Variety of Graphics Devices.
On the other hand, if the analyst is working at a discrete
terminal or in batch, neither the logic of the analysis
nor the entered plot cammands should be any
different.
 Subset Analyses.
The analyst should not need to worry about whether the
graphics, fitting, or data analysis is being performed
over the full data set or over any complicated subsets
of the data. Performing analyses over subsets should
not result in irrelevant (as far as the scientist is
concerned) preliminary data extraction and manipulation.
It should be as easy to carry out any (and all) graphics
and analysis operations over a subset as it is to carry
it out over the full set.
 Sample Size.
The analyst should not need to worry about whether the
data set consists of 7 data points or 700 data points.
The number of data points is a nuisance parameter that the
analyst should not need to concern himself with.
 Data Format.
The analyst should not need to worry about how the data
is formatted upon input. This also is an unimportant
nuisance item.
 Predicted Values and Residuals.
The analyst should not need to worry about predicted
values and residuals from the fit. They should be
automatically available for further analysis and
plotting.
 Scope of Capabilities.
The analyst should be able to fluidly glide from graphics
to fitting to data analysis to mathematics activities
with no interruption and within the context of the
language.
 Ease of Use.
The ultimate objective of the analyst is not in learning
a computer language. It is in gaining insight into the
problem at hand; thus the computer language shouid be
natural, easy to learn, and easy to use. The language
that the analyst uses should preserve the continuity of
thought that is so important in scientific research.
 EnglishSyntax.
Ideally, the language should correspond as close as
possible to the Englishlanguage and mathematical
representation of the solution. This will allow the
analyst to "think science" as opposed to "think
computing" and will eliminate an unnecessary mapping
from conceptual solution to computerlanguage
solution.

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Date created: 06/05/2001
Last updated: 09/28/2016
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