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8/9/2019 Multivariate Take Home

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According to the slopes of the above plot, it is very clear that 3 principal components (PCs) would

be enough to do the analysis.

Addition to that one may consider the residual matrices to determine the number of PCs to keep. It

also suggests that 3 PCs would be ideal (please find the calculated 3 residual matrices in the

attached excel sheet there are 3 separate calculations to see what happened when only 1 or 2 factorsconsidered).


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SPSS Output:

Total Variance Explained

Component Rotation Sums of Squared Loadings

Total % of Variance Cumulative %

1 2.831 40.450 40.450

2 2.216 31.657 72.106

3 1.760 25.148 97.254

Extraction Method: Principal Component Analysis.

• Using the varimax rotation it can beconverted into interpretable data. Also when

3 components are selected 97.25% of totalvariance is explained.

By looking at the data rotated data it can be said that X1, X2 and X3 are highly correlated and X4 also

indicates somewhat strong relation to that group where X4 correlated to X5 and X6 even more.

X7 is not related to any of others, demonstrating completely isolated.

Above component plot in rotated space gives a very clear picture about the variables. X1, X2 and X3 are

in a side and X5 and X6 on the other side where X4 in the middle and little closer to the X5 and X6 than

X1, X2 and X3. X7 is away from the rest of the variables.

It these variables were seen as they belongs to 3 categories, say short, medium and long X1, X2 and X3

are belongs to the short category clearly and X5 and X6 clearly to the medium and X4 is somewhere

middle but much more closer to the medium category. Thus, X7 belong to the long category.


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