Fitted regression: coefficients, uncertainty and validation
Fit actual multivariable data, derive conditional uncertainty and retain an honest diagnostic and validation record. Synthetic examples and public rubrics do not establish a completed empirical investigation.
Open any lesson. Completion records participation; automatic practice checks and human judgment of written arguments are separate. This unit retains its own versioned requirements.
Readiness and preparation
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Fitted regression: calculation, assumptions and frozen transfer
The mixed assessment has separate response history and review criteria; it does not change lesson participation records.
Lesson sequence
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Fit coefficients and audit residuals
Lesson details and objectives
Construct a numeric design and check a rank-aware least-squares fit against its defining equations.
- Build the design including its intercept and prove coefficient uniqueness from full rank.
- Compute coefficients, fitted values, residuals, SSE and residual degrees of freedom.
- Distinguish deterministic fit identities from model-dependent uncertainty.
6 practice tasks.
Choose the uncertainty target
Lesson details and objectives
Derive conditional mean and new-response intervals, including rank and zero-spread boundaries.
- Connect covariance and residual variance to Gaussian projections.
- Distinguish conditional mean uncertainty from new-response noise.
- Interpret leverage and intervals without treating model fit as model verification.
6 practice tasks.
Diagnose, freeze and evaluate a revision
Lesson details and objectives
Use residual and held-out evidence without turning fit agreement into a model-validation claim.
- Interpret residual structure under explicit model assumptions.
- Evaluate a frozen fitted transform on separately supplied responses.
- Retain revision evidence and reject unsupported causal or coverage claims.
6 practice tasks.