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


Purpose: Detect changes in linear slopes between groups 
Linear slope 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.
Linear slope plots are typically used in conjunction with linear intercept 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 slope plot as for groups. 

Sample Plot 
This linear slope plot shows that the slopes are about 0.174 (plus or minus 0.002) for all groups. There does not appear to be a pattern in the variation of the slopes. This implies that a single fit may be adequate. 

Definition: Group Slopes Versus Group ID 
Linear slope plots are formed by:


Questions 
The linear slope 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 slope plots help answer this question in the context of linear fitting.  
Related Techniques 
Linear Intercept Plot Linear Correlation Plot Linear Residual Standard Deviation Plot Linear Fitting 

Case Study  The linear slope plot is demonstrated in the Alaska pipeline data case study.  
Software  Most general purpose statistical software programs do not support a linear slope 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. 