13.6 - Interpret Each Component

To interpret each component, we must compute the correlations between each variable and the corresponding canonical variate.

  1. The correlations between the sales variables and the canonical variables for Sales Performance are found at the top of the fourth page of the SAS output in the following table:

    Correlations Between the Sales Variables and Their Canonical Variables

      sales1 sales2 sales3
    growth 0.9799 0.0006 -0.1996
    profit 0.9464 0.3229 0.0075
    new 0.9519 -0.1863 0.2434

    Looking at the first canonical variable for sales, we see that all correlations are uniformly large. Therefore, you can think of this canonical variate as an overall measure of Sales Performance. For the second canonical variable for Sales Performance, none of the correlations are particularly large, and so, this canonical variable yields little information about the data. Again, we had decided earlier not to look at the third canonical variate pairs.

    A similar interpretation can take place with the Test Scores.

  2. b. The correlations between the test scores and the canonical variables for Test Scores are also found in the SAS output:

    Correlations Between the Test Scores and Their Canonical Variables

      scores1 scores2 scores3
    create 0.6383 -0.2157 0.6514
    mech 0.7212 0.2376 -0.677
    abs 0.6472 -0.5013 -0.5742
    math 0.9441 0.1975 -0.0942

    Because all correlations are large for the first canonical variable, this can be thought of as an overall measure of test performance as well, however, it is most strongly correlated with mathematics test scores. Most of the correlations with the second canonical variable are small. There is some suggestion that this variable may be negatively correlated with abstract reasoning.

    c. Putting (a) and (b) together, we see that the best predictor of sales performance is mathematics test scores as this indicator stands out the most.