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PCA on a Small Dataset
Four observations of two features (already centred):
| x_1 | x_2 |
|---|---|
| 3 | 1 |
| 1 | 3 |
| -1 | -3 |
| -3 | -1 |
- Compute the sample covariance matrix (divide by n - 1).
- Find both eigenvalues and the first principal component direction. What fraction of variance does PC1 explain?
- Project the four points onto PC1. Then explain what would have changed if x_2 had been recorded in units 100× smaller (e.g. cents instead of dollars) and you had not standardised.
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