Expose the scale effect

Why this lab See how variable units decide which component PCA finds.

PCA finds variance, and variance carries units squared. Inflate one variable, then standardize. The component will visibly swing toward the variable with the largest numerical scale—even when the underlying relationship never changed. Standardizing replaces the covariance matrix with the correlation matrix, the same analysis on \( z \)-scores, so every variable starts with equal unit variance rather than equal loadings or guaranteed equal contribution.