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# Canonical Correlation, MMRA Assignment

Multivariate Data Analysis
Psychology 6140

• Johnson & Wichern, Ch. 10, 11
• Tabachnick & Fidell, Ch. 6

## Problem

Shin (1971) collected data on intelligence using six creativity measures and six achievement measures for 116 subjects in the eleventh grade in suburban Pittsburgh. The Otis Quick Scoring Mental Ability Test, Guilford's Divergent Productivity Battery, and Kropp and Stoker's Lisbon Earthquake Achievement Test were used to gather one IQ score, six creativity measures, and six achievement measures for each subject. In addition to the IQ variable (1), the variables included in the creativity test were ideational fluency (2), spontaneous flexibility (3), associational fluency (4), expressional fluency (5), originality (6), and elaboration (7). The achievement measures were knowledged (8), comprehensive (9), application (10), analysis (11), synthesis (12), and evaluation 13). The correlation matrix for the study is presented in the table below.

Inspection of the table indicates that four out of the six creativity measures (tests 4, 5, 6, and 7) are highly correlated with synthesis and evaluation (tests 12 and 13), as is IQ (test 1). What else do you notice?

1. Use canonical correlation analysis to investigate the relationship between (the six achievement variables and IQ) and the six creativity variables.
2. By partialing out the IQ variable from both sets of variables, (use the PARITAL stmt in PROC CANCORR) use partial canonical correlation analysis to analyze the data and compare your results with part a.
3. Would a multivariate regression analysis of the data be meaningful? If so, why? If not, why not?

The data has been entered (in the form needed to create a _type_='CORR' dataset) in the file creative.dat on Pavlov in the directory k:\home\sasuser\psy6140\data.

Matrix of Interecorrelations among IQ, Creativity, and Achievement Variables

```CORR  IQ       1.0   .    .    .    .    .    .    .    .    .    .    .    .
CORR  IFLUENCY .16  1.0   .    .    .    .    .    .    .    .    .    .    .
CORR  FLEXIB   .32  .71  1.0   .    .    .    .    .    .    .    .    .    .
CORR  AFLUENCY .24  .12  .12  1.0   .    .    .    .    .    .    .    .    .
CORR  EFLUENCY .43  .34  .45  .43  1.0   .    .    .    .    .    .    .    .
CORR  ORIGINAL .30  .27  .33  .24  .33  1.0   .    .    .    .    .    .    .
CORR  ELABORAT .43  .21  .11  .42  .46  .32  1.0   .    .    .    .    .    .
CORR  KNOWLEDG .67  .13  .27  .21  .39  .27  .38  1.0   .    .    .    .    .
CORR  COMPREHE .67  .18  .24  .15  .36  .33  .26  .62  1.0   .    .    .    .
CORR  APPLICAT .57  .08  .14  .09  .25  .13  .23  .44  .66  1.0   .    .    .
CORR  ANALYSIS .59  .10  .16  .09  .25  .12  .28  .58  .66  .64  1.0   .    .
CORR  SYNTHESI .45  .13  .23  .42  .50  .41  .47  .46  .47  .37  .53  1.0   .
CORR  EVALUATI .24  .08  .15  .36  .28  .21  .26  .30  .24  .19  .29  .58  1.0
N              116  116  116  116  116  116  116  116  116  116  116  116  116
```