Understand the idea
A two-component picture may show much less variation than the full reduced representation. Label the variance visible in it. Optional reference colouring belongs after fitting and does not prove classes are recovered.
Python skill: Selects the first two component coordinates for every row.
Meet the syntax
scores[:, :2]
ratios[:2].sum()scores[:, :2]- Selects the first two component coordinates for every row.
ratios[:2].sum()- Reports how much input variance those two plotted axes display, independently of the retained dimension.
Follow the code
Use the numbered comments to connect each Python block to the workflow above.
answer=float(pca.explained_variance_ratio_[:2].sum())
This practice: Read and run the Python. Next: Change · Two dimensions are a view.
Given data · PCA48
48 observations. Deterministic teaching observations; values illustrate the concept rather than a real population claim. The dataframe df is supplied afresh for each Run.
Reference labels are omitted from this preview and must remain outside fitting.
| a | b | c | d | e |
|---|---|---|---|---|
| 103.047 | 50.8622 | 22.7157 | 44.6184 | 0.906993 |
| 89.6002 | 44.3015 | 20.2703 | 40.1253 | -0.680116 |
| 107.505 | 53.9521 | 21.1565 | 41.7009 | 0.818161 |
| 109.406 | 54.2501 | 22.5252 | 44.9095 | 1.39291 |
| 80.4896 | 40.0557 | 14.1714 | 29.4087 | -3.27953 |
| 86.9782 | 44.1387 | 18.7213 | 37.5997 | -1.70077 |
| 101.278 | 50.4611 | 18.1185 | 36.0784 | -0.343557 |
| 96.8376 | 48.7875 | 17.4445 | 33.8533 | -0.987809 |
Column meanings and units
Column names describe the supplied features and target. Keep the stated units and row identities when making comparisons.
Synthetic data are deliberately small and reproducible. Their patterns illustrate an idea; they are not evidence about a real population.
| Column | Stored type |
|---|---|
| a | float64 |
| b | float64 |
| c | float64 |
| d | float64 |
| e | float64 |
Supplied setup · available if you need to inspect it
This code runs before your editor on every Run. These are the objects your exercise uses.
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
X=df.copy()
scaler=StandardScaler()
scaled=scaler.fit_transform(X)
pca=PCA().fit(scaled)
scores=pca.transform(scaled)
Your task · Follow
Report the variation visible in the first two axes.
Hint 1 — Think
The visible two-dimensional view may retain less variation than the full chosen representation.
Hint 2 — Tools
Summing the first two explained-variance ratios.
Hint 3 — Approach
Add the ratios for the plotted axes and report the resulting fraction.
Explained solution
answer=float(pca.explained_variance_ratio_[:2].sum())
The fraction states how much fitted input variation the picture can show and qualifies what it omits.
Helpful prior knowledge: Select a retained representation · Component weights and scores These links are guidance, not locks.
Sources and API context
Examples run with this Playground’s scikit-learn 1.4.2 / Pyodide 0.26.4 runtime.