Ficha 9 Análise em Componentes Principais

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MULTIVARIATE STATISTICS: 
PRINCIPAL COMPONENT ANALYSIS 
 
GRAÇA TRINDADE 
ISCTE – IUL, 2012-2013 1 
 
 
CASE STUDY 10: 
 
In a market survey about the purchasing behavior of consumers in a particular country, 384 
consumers were asked about the importance of the following 10 variables related to the main 
reasons for buying in a particular shopping center (using a scale of 1 = not important up to 5 = 
extremely important). 
Descriptive Statistics Communalities 
 Mean 
Std. 
Deviation 
Analysis 
n 
Prices 3,56 ,912 384 
Diversification of 
products 
3,11 ,865 384 
Convenient location 
of distributor 
2,59 ,979 384 
Quality of products 4,06 ,836 384 
Image of products 3,04 ,924 384 
Image of 
Distributors 
2,62 ,962 384 
Product Features 2,99 1,032 384 
Special Promotions 2,38 ,973 384 
Image of the 
shopping center 
2,71 ,981 384 
Publicity 2,38 ,932 384 
 
 Initial Extraction 
Prices 1,000 ,867 
Diversification of 
products 
1,000 ,546 
Convenient location 
of distributor 1,000 ,583 
Quality of products 1,000 ,623 
Image of products 1,000 ,584 
Image of 
Distributors 
1,000 ,390 
Product Features 1,000 ,664 
Special Promotions 1,000 ,594 
Image of the 
shopping center 
1,000 ,607 
Publicity 1,000 ,612 
 
 
KMO and Bartlett’s Test 
Kaiser-Meyer-Olkin Measure of Sampling Adequacy ,67 
Bartlett’s Test of Sphericity Approx. Chi-Square 495,1 
 df 45 
 Sig. ,000 
 
Total Variance Explained 
Component Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings 
 Total 
% of 
Variance Cumulative % Total 
% of 
Variance Cumulative % Total 
% of 
Variance Cumulative % 
1 2,5 24,8 24,8 2,755 39,355 39,355 1,970 28,138 28,138 
2 1,4 14,4 39,2 1,029 14,699 54,054 1,63 23,295 51,433 
3 1, 1 11,1 50,3 1,021 14,587 68,641 1,205 17,207 68,641 
4 1,0 10,4 60,7 
5 (a) (b) ( c) 
6 ,8 7,8 77,7 
7 ,7 6,7 84,4 
8 ,6 6,0 90,4 
9 ,5 5,3 95,8 
10 ,5 4,7 100,0 
Extraction Method: Principal Component Analysis. 
 
 
MULTIVARIATE STATISTICS: 
PRINCIPAL COMPONENT ANALYSIS 
 
GRAÇA TRINDADE 
ISCTE – IUL, 2012-2013 2 
 
 
Rotated Component Matrix 
 
Component 
1 2 3 4 
Publicity ,762 ,140 ,045 (d) 
Special Promotions ,730 ,088 -,075 ,218 
Image of the 
shopping center 
,597 ,431 ,047 -,251 
Product Features -,001 ,769 -,052 ,265 
Image of products ,258 ,696 ,120 -,138 
Image of Distributors ,371 ,481 ,141 -,034 
Diversification of 
products 
,031 ,061 ,736 -,011 
Quality of products -,209 ,264 ,714 ,017 
Convenient location 
of distributor 
,352 -,256 ,611 ,140 
Prices ,002 ,050 ,078 ,926 
 
a) Decide about the adequacy of the data to the performed analysis. 
b) Compute and interpret the values of (a), (b), (c) and (d) missing in respective tables. 
c) What proportion of the variance of the variable Prices is explained by the four 
retained components? 
d) What was the used criterion for selecting the number of components to be retained in 
the final solution? Do you consider it as appropriate? What other criteria could have 
been used? 
e) Give an interpretation for the four extracted components. 
f) How do you explain that the variable Publicity, which has the smallest sample mean, 
has the greatest weight in Principal Component 1?