1.
Exploratory Data Analysis
1.3.
EDA Techniques
1.3.3.
Graphical Techniques: Alphabetic
1.3.3.17.
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Linear Intercept Plot
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Purpose:
Detect changes in linear intercepts between groups
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Linear intercept plots are used to graphically 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.
Linear intercept plots are typically used in conjunction
with linear slope and
linear residual standard
deviation plots.
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 intercept plot as for
groups.
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Sample Plot
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This linear intercept plot shows that there is a shift in
intercepts. Specifically, the first 3 intercepts are
significiantly lower than the other groups.
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Definition:
Group intercepts versus group id
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Linear intercept plots are formed by:
- Vertical axis: Group intercepts from linear fits
- Horizontal axis: Group identifier
A reference line is plotted at the intercept from a linear fit
using all the data.
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Questions
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The linear intercept plot can be used to answer the
following questions.
- Is the intercept from linear fits relatively constant
across groups?
- If the intercepts vary across groups, is there a
discernable pattern?
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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 intercept plots help
answer this question in the context of linear fitting.
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Related Techniques
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Linear Correlation Plot
Linear Slope Plot
Linear Residual Standard Deviation Plot
Linear Fitting
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Case Study
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The linear intercept 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 intercept 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 intercept plot.
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