Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 100 minutes, as an unvalidated planning estimate. This collection contains 3 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Use sample covariance with divisor n−1 unless explicitly changed.
Show intermediate centered data, score/reconstruction checks and the error metric.
Sign-equivalent axes are accepted; distinguish mathematical ties from rounded numerical warnings. Timing is an unvalidated planning estimate.
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0 of 3 tasks have recorded responses. No overall mastery score is assigned.
Six rows are (7,11),(4,12),(2,10),(3,7),(6,8),(2,12). Independently compute covariance PCA, both score columns and rank-one reconstruction loss. Use n−1 and demonstrate the direct error identity rather than only quoting eigenvalues.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Rows are (−2,−1),(−2,1),(2,−1),(2,1). Compare covariance PCA before and after doubling variable2, and correlation PCA for both versions. Prove every degeneracy assertion and explain what a renderer may display.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Fit covariance PCA to training rows (−3,0),(0,0),(3,0), then freeze its preprocessing and one-dimensional transform. Evaluate rows (5,2),(5,−2). Compare a colleague who fits a new mean/axis to those two rows; explain correlation-mode availability and give a defensible validation report.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
Six rows are (7,11),(4,12),(2,10),(3,7),(6,8),(2,12). Independently compute covariance PCA, both score columns and rank-one reconstruction loss. Use n−1 and demonstrate the direct error identity rather than only quoting eigenvalues.
Rows are (−2,−1),(−2,1),(2,−1),(2,1). Compare covariance PCA before and after doubling variable2, and correlation PCA for both versions. Prove every degeneracy assertion and explain what a renderer may display.
Fit covariance PCA to training rows (−3,0),(0,0),(3,0), then freeze its preprocessing and one-dimensional transform. Evaluate rows (5,2),(5,−2). Compare a colleague who fits a new mean/axis to those two rows; explain correlation-mode availability and give a defensible validation report.
