Track 16 · Advanced Foundations · Lesson 5 of 8
Principal component analysis
Run and interpret a principal component analysis: decide whether to standardise, read variance explained and a scree plot, interpret loadings (allowing for arbitrary signs) and scores, and state what PCA cannot do.
A property analyst has six correlated measurements for each home sale — area, bedrooms, bathrooms, age, distance to the centre and price. Many of them say the same thing (“big house”). PCA finds a few uncorrelated summaries that keep most of the information, which helps to see structure, plot the data and avoid redundant predictors.
Principal component analysis (PCA) replaces correlated numeric variables by new variables, the principal components, which are uncorrelated weighted sums of the originals. The first component (PC1) is the direction along which the data vary the most; PC2 is the direction of greatest remaining variation at right angles to PC1; and so on. If the first two or three components capture most of the variation, they summarise the data well.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Decide whether to standardise before PCA and explain why units matter
- Compute and read variance explained, cumulative proportions and scree plots
- Interpret components from their loadings, ignoring the arbitrary overall sign
- Compute a component score from standardised values
- Explain why PCA is not feature selection and not a causal model