1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.3. Graphical Techniques: Alphabetic


Purpose: Detect Changes in Linear Residual Standard Deviation Between Groups 
Linear residual standard deviation (RESSD) plots are used to
graphically assess whether or not linear fits are
consistent across groups. That is, if your data have groups,
you may want to know if a single fit can be used across all
the groups or whether separate fits are required for each
group.
The residual standard deviation is a goodnessoffit measure. That is, the smaller the residual standard deviation, the closer is the fit to the data. 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. 

Sample Plot 
This linear RESSD plot of the HSU12.DAT data set shows that the residual standard deviations from a linear fit are about 0.0025 for all the groups. 

Definition: Group Residual Standard Deviation Versus Group ID 
Linear RESSD plots are formed by:


Questions 
The linear RESSD plot can be used to answer the
following questions.


Importance: Checking Group Homogeneity 
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.  
Related Techniques 
Linear Intercept Plot Linear Slope Plot Linear Correlation Plot Linear Fitting 

Case Study  The linear residual standard deviation plot is demonstrated in the Alaska pipeline data case study.  
Software  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. 