1.3.3.16.

Linear Correlation Plot

Purpose:
Detect changes in correlation between groups Linear correlation plots are used to assess whether or not correlations are consistent across groups. That is, if your data is in groups, you may want to know if a single correlation can be used across all the groups or whether separate correlations are required for each group.

Linear correlation plots are often used in conjunction with linear slope, linear intercept, and linear residual standard deviation plots. A linear correlation plot could be generated intially to see if linear fitting would be a fruitful direction. If the correlations are high, this implies it is worthwhile to continue with the linear slope, intercept, and residual standard deviation plots. If the correlations are weak, a different model needs to be pursued.

In some cases, you might not have groups. Instead you may have different data sets and you want to know if the same correlation 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
linear correlation plot showing that correlations are high for all groups

This linear correlation plot of the HSU12.DAT data set shows that the correlations are high for all groups. This implies that linear fits could provide a good model for each of these groups.

Definition:
Group Correlations Versus Group ID Linear correlation plots are formed by:

• Vertical axis: Group correlations
  
• Horizontal axis: Group identifier
  

A reference line is plotted at the correlation between the full data sets.

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

1. Are there linear relationships across groups?
2. Are the strength of the linear relationships relatively constant across the groups?

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 correlation plots help answer this question in the context of linear fitting.

Related Techniques Linear Intercept Plot
Linear Slope Plot
Linear Residual Standard Deviation Plot
Linear Fitting

Case Study The linear correlation plot is demonstrated in the Alaska pipeline data case study.

Software Most general purpose statistical software programs do not support a linear correlation plot. However, if the statistical program can generate correlations over a group, it should be feasible to write a macro to generate this plot.