1.
Exploratory Data Analysis
1.3.
EDA Techniques
1.3.3.
Graphical Techniques: Alphabetic
1.3.3.19.
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Linear Residual Standard Deviation Plot
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Purpose:
Detect changes in linear residual standard deviation
between groups
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Linear residual standard deviation (RESSD) plots are used to
grahically assess whether or not linear fits are
consistent across groups. That is, if your data has groups,
you may want to know if a single fit can be used across all
the groups or whether the separate fits are required for each
group.
The residual standard deviation is a goodness of fit
measure. That is, the smaller the residual standard
deviation, the more of the data that the fit explains.
Linear RESSD plots are typically used in conjunction
with linear intercept and
linear slope plots.
The linear intercept and slope plots convey whether or
not the fits are consistent across groups while the
linear RESSD plot conveys whether the adequacy of the
fit is consistent across groups.
In some cases, you might not have groups. Instead you
have different data sets and you want to know if the
same fit can be adequately applied to each of the data
sets. In this case, simply think of each distinct data
set as a group and apply the linear RESSD plot as for
groups.
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Sample Plot
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This linear RESSD plot shows that the residual standard
deviations from a linear fit is about 0.0025 for all the
groups.
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Definition:
Group residual standard deviation versus group id
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Linear RESSD plots are formed by:
- Vertical axis: Group residual standard deviations from
linear fits
- Horizontal axis: Group identifier
A reference line is plotted at the residual standard
deviation from a linear fit using all the data. This reference
line will typically be much greater than any of the individual
residual standard deviations since it is in a sense a sum of
all the group residual standard deviations (this is not
strictly true since the groups will in fact be generating
slightly different fits).
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Questions
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The linear RESSD plot can be used to answer the
following questions.
- Is the residual standard deviation from a linear fit
constant across groups?
- If the residual standard deviations vary, is there
a discernable pattern across the groups?
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Importance:
Checking group homogeneity
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For grouped data, it may be important to know whether the
different groups are homogeneous (i.e., similar) or
heterogeneous (i.e., different). Linear RESSD plots help
answer this question in the context of linear fitting.
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Related Techniques
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Linear Intercept Plot
Linear Slope Plot
Linear Correlation Plot
Linear Fitting
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Case Study
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The linear residual standard deviation plot is demonstrated in
the Alaska pipline
data case study.
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Software
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Most general purpose statistical software programs do not
support a linear residual standard deviation plot. However, if
the statistical program can generate linear fits over a group,
it should be feasible to write a macro to generate this plot.
Dataplot
supports a linear residual standard deviation plot.
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