Fitted regression: calculation, assumptions and frozen transfer
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.
Show design, rank and intermediate calculations; use written justification for model assumptions.
Keep exact identities separate from rounded intervals and diagnostics. Suggested time is an unvalidated estimate; public solutions are not an unseen assessment.
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0 of 3 tasks have recorded responses. No overall mastery score is assigned.
Six rows (x,z,y) are (−1,1,5),(−1,−1,3),(0,1,4),(0,−1,2),(1,1,9),(1,−1,7). Fit an intercept and both predictors; calculate residuals, variance estimate and estimated coefficient covariance under a stated model. Interpret the residual pattern.
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.
For the previous six-row fit, target row u=(1,0,0). Derive 95% mean and new-response intervals using t(.975,3), without confusing their targets. Explain whether either interval protects against the residual curvature and whether an exact fit after adding x² proves zero noise.
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.
Using the six-row first-lesson dataset, freeze original m(x,z)=5−x+2z and revised q(x,z)=4−x+2z+1.5x². Before revealing a new response at (2,0), record both predictions. The synthetic check response is 3.2. Compare squared losses, state the extrapolation issue, and decide what may be claimed after seeing it.
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 (x,z,y) are (−1,1,5),(−1,−1,3),(0,1,4),(0,−1,2),(1,1,9),(1,−1,7). Fit an intercept and both predictors; calculate residuals, variance estimate and estimated coefficient covariance under a stated model. Interpret the residual pattern.
For the previous six-row fit, target row u=(1,0,0). Derive 95% mean and new-response intervals using t(.975,3), without confusing their targets. Explain whether either interval protects against the residual curvature and whether an exact fit after adding x² proves zero noise.
Using the six-row first-lesson dataset, freeze original m(x,z)=5−x+2z and revised q(x,z)=4−x+2z+1.5x². Before revealing a new response at (2,0), record both predictions. The synthetic check response is 3.2. Compare squared losses, state the extrapolation issue, and decide what may be claimed after seeing it.
