Canonical Correlation Exercise

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Canonical Correlation Exercise

(1) Discuss the importance of the variable in the dependent set. Spell out the linear composite variate selected.

Canonical Correlations
1 .992
2 .859
3 .327

Test that remaining correlations are zero:
Wilk's Chi-SQ DF Sig.
1 .004 251.994 12.000 .000
2 .234 65.351 6.000 .000
3 .893 5.104 2.000 .078

The third function should be removed because of its lack of statistical difference.

With the canonical relationship deemed statistically significant and the magnitude of the canonical root and the redundancy index acceptable, the researcher proceeds to making substantive interpretations of the results. Although the second function could be considered practically nonsignificant, owing to the low redundancy value, it is included in the interpretation phase for illustrative reasons. These interpretations involve examining the canonical functions to determine the relative importance of each of the original variables in deriving the canonical relationships. The three methods for interpretation are (1) canonical weights (standardized coefficients), (2) canonical loadings (structure correlations), and (3) canonical cross-loadings. However, because canonical weights are typically unstable, particularly in instances of multicollinearity, owing to their calculation solely to optimize the canonical correlation, the canonical loading and cross-loadings are considered more appropriate.

Raw Canonical Coefficients for Set-1
1 2
salegrth -.050 .150
saleprft -.034 -.236
newacct -.065 .265

Canonical Loadings for Set-1
1 2
salegrth -.976 .051
saleprft -.963 -.269
newacct -.944 .236

Cross Loadings for Set-1
1 2 3
salegrth -.969 .044 -.069
saleprft -.955 -.231 .008
newacct -.937 .202 .076

| |canonical loading squared1 |Average loading squared1 |Canonical R^2 |Redundancy Index | |Canonical Function1 | | | | | |Dependent set | | |salegrth |-0.976 |0.952576 | |0.984064 | | |saleprft |-0.963 |0.927369 | | | | |newacct |-0.944 |0.891136 | | | | |Sum | |2.771081 |0.923693667 |0.984064 |0.908973684 | |Independent set | | | | | |createst |-0.627 |0.393129 | | | | |mechtest |-0.725 |0.525625 | | | | |absttest |-0.617 |0.380689 | | | | |mathtest |-0.955 |0.912025 | | | | | | |2.211468 |0.737156 |0.984064 |0.725408682 |

|Canonical Function2 |canonical loading squared2 |Average loading squared2 |Canonical R^2 |Redundancy index |...
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