MATH5806 Applied Regression Analysis
The Complete Exam Bible · T2 2026MATH5806 Overview
- UNSW School of Mathematics and Statistics
- Term 2, 2026
Within UNSW School of Mathematics and Statistics, MATH5806 Applied Regression Analysis builds regression from likelihood theory upward — maximum likelihood and least-squares estimation, the exponential family, deviance, and Score/Wald/likelihood-ratio inference for the linear Gaussian model — then widens that same machinery out to general linear models (multiple regression, ANOVA, ANCOVA), generalised linear models (logistic, Poisson, log-linear), resampling (cross-validation, bootstrap), shrinkage (ridge, Lasso), nonlinear and spline regression, and generalized additive models, with every method implemented in R.
A derive-it-then-code-it course, not a push-the-button statistics service course: the lecturer's stated philosophy is to "go into great details in the theory only for the Linear Model in order to leave time to play with modern and more sophisticated nonlinear models", and the assessment note says flatly that the tasks "will have a mathematical and a computational component".
- MATH5806 grading 55% final exam (in-person, 2 hours, exam period) | 20% mid-term test (in-person, Week 7, 1 hour, date/time TBC) | 15% individual assignment (available from Week 7, due Week 9) | 10% quiz (in-person, Week 4, 25 minutes). [Moodle table = the published course material. The Week 1 lecture slide gives a slightly older variant: quiz 30 minutes, assignment "Take home. 2 weeks".
- MATH5806 task mode In-person, 2 hours, sat during the UNSW exam period, aligned to CLOs 1-6; like every other task it will have a mathematical and a computational component. Check the current MATH5806 course site and official timetable for any remaining sitting conditions.
- MATH5806 mark trap The bridge between the algebra and the R output, not either side alone. CLO4 is literally Relate the output of statistical software to the theoretical formulas presented in the lectures, the lecturer states every assessment will have a mathematical and a computational component, and the tutorials pair a hand derivation with an R implementation of the same object: Week 1 derives the Poisson MLE then asks for log-likelihoods and standardised residual plots in R; Week 2 asks students to derive the Score, Wald and likelihood-ratio statistics and then report observed values, p-values and conclusions from real survey counts. Secondary sink: timing.
- MATH5806 rule check Treat the MATH5806 hurdle status as unconfirmed. Check the current official course outline for any component-level pass rule before relying on the overall mark.
How MATH5806 is assessed
| Component | Weight | Format |
|---|---|---|
| Quiz | 10% | In-person · 25 minutes in the current assessment table |
| Mid-term Test | 20% | In-person · 1 hour |
| Assignment | 15% | Individual |
| Final Exam | 55% | In-person · 2 hours |
The current course-page table controls and gives the Quiz length as 25 minutes; an older lecture slide says 30 minutes, so the live course-page value is used. Confirm any later operational update in the course site.
What MATH5806 covers
Build the course in three arcs: Regression Purpose and Assessment Map establishes the frame, Linear Gaussian Models deepens it, and Tutorial Computation and Final-Exam Synthesis tests the complete method.
Regression Purpose and Assessment Map
prediction versus inference · response and predictors · model scope · choose a regression goal and define the population-level relationship before fitting02Simple Linear Regression Estimation
least squares · slope and intercept · fitted values and residuals · derive the fitted line and separate observed response, fitted mean and residual03Inference for Regression Coefficients
sampling distributions · standard errors · tests and confidence intervals · connect a coefficient estimate to its uncertainty and a precisely stated hypothesis04Linear Gaussian Models
matrix model · Gaussian errors · estimator covariance · move between scalar and matrix representations while preserving dimensions and assumptions05Residual Diagnostics and Assumption Checks
residual patterns · variance structure · influence and model revision · use a diagnostic pattern to identify which assumption or observation needs investigation06Tutorial Computation and Final-Exam Synthesis
derivation · software verification · interpretation under pressure · combine hand calculation, R output and an assumption-aware conclusion without treating output as self-explanatoryThe Week 2 tutorial asks students to derive the Score and Wald statistics for a binomial parameter by hand and to implement Newton-Raphson in R on the same sheet.
55% of the mark sits in a single 2-hour in-person final, and 85% of the mark is in-person overall (10% quiz + 20% mid-term + 55% exam).
Assessment in MATH5806 is distributed as follows: 55% final exam (in-person, 2 hours, exam period) | 20% mid-term test (in-person, Week 7, 1 hour, date/time TBC) | 15% individual assignment (available from Week 7, due Week 9) | 10% quiz (in-person, Week 4, 25 minutes).
[Moodle table = the published course material. The Week 1 lecture slide gives a slightly older variant: quiz 30 minutes, assignment "Take home. 2 weeks".
The operational assessment conditions matter here. In-person, 2 hours, sat during the UNSW exam period, aligned to CLOs 1-6; like every other task it will have a mathematical and a computational component.
Check the current MATH5806 course site and official timetable for any remaining sitting conditions.
What makes MATH5806 demanding is concrete: The bridge between the algebra and the R output, not either side alone.
CLO4 is literally Relate the output of statistical software to the theoretical formulas presented in the lectures, the lecturer states every assessment will have a mathematical and a computational component, and the tutorials pair a hand derivation with an R implementation of the same object: Week 1 derives the Poisson MLE then asks for log-likelihoods and standardised residual plots in R; Week 2 asks students to derive the Score, Wald and likelihood-ratio statistics and then report observed values, p-values and conclusions from real survey counts.
Secondary sink: timing.
Treat the MATH5806 hurdle status as unconfirmed.
Check the current official course outline for any component-level pass rule before relying on the overall mark.
For enrolment planning, No formal prerequisite is stated in the verified course material, but the course publishes an explicit "Knowledge assumed" slide: linear algebra (vector spaces, linear independence, matrix multiplication, diagonalisation, projections), multivariate calculus (partial derivatives, critical points, integrals), prior exposure to R, and probability/statistics up to "asymptotic normality of maximum likelihood estimators".
Build the course in three arcs: Regression Purpose and Assessment Map establishes the frame, Linear Gaussian Models deepens it, and Tutorial Computation and Final-Exam Synthesis tests the complete method.
Worked example: Applied Regression Analysis integrated response
- 1Write the narrow claim that sampling distributions is being used to support.
- 1Attach the specific observation, source or condition required by residual patterns.
- 1Use derivation to state a counter-case, failed assumption or observation that would change the claim.
- 1Revise the conclusion so the evidence and this boundary are both visible: Practice values and questions here are independently authored and are not university assessment items.
Key terms
- maximum likelihood estimator (MLE)
- The maximum likelihood estimator is the parameter value that maximises the likelihood, or equivalently the log-likelihood, of the observed sample under the specified model.
- exponential family of distributions / natural parameter
- An exponential-family density has form h(y) exp{ηT(y)−A(η)}; η is the natural parameter linking the sufficient statistic T(y) to the log normalising function.
- deviance
- Deviance is twice the difference between the saturated model's log-likelihood and the fitted model's log-likelihood, measuring lack of fit relative to a perfect fit.
- Score, Wald and likelihood-ratio statistics
- Score, Wald and likelihood-ratio tests assess parameter restrictions using respectively the likelihood slope at the null, the estimate's distance from the null, and the maximised likelihood difference between nested models.
- Gauss-Markov assumptions
- The Gauss–Markov conditions require a linear-in-parameters model with full-rank regressors and errors having zero conditional mean, constant variance and no cross-observation covariance; then OLS is BLUE.
- hat matrix, leverage h_ii and Cook's distance
- The hat matrix H = X(X'X)⁻¹X' maps observed responses to fitted values, h_ii measures observation leverage, and Cook's distance measures how strongly deleting an observation changes the fitted model.
- standardized vs studentized residuals
- A standardised residual divides by a common estimated error scale adjusted for leverage, while a studentised deleted residual uses an error variance estimated with that observation omitted.
- variance inflation factor (VIF) and multicollinearity
- Multicollinearity is strong linear dependence among predictors; VIF_j = 1/(1−R_j²) quantifies how much it inflates the sampling variance of coefficient j relative to orthogonal predictors.
MATH5806 FAQ
Is MATH5806 hard?
The bridge between the algebra and the R output, not either side alone.
CLO4 is literally Relate the output of statistical software to the theoretical formulas presented in the lectures, the lecturer states every assessment will have a mathematical and a computational component, and the tutorials pair a hand derivation with an R implementation of the same object: Week 1 derives the Poisson MLE then asks for log-likelihoods and standardised residual plots in R; Week 2 asks students to derive the Score, Wald and likelihood-ratio statistics and then report observed values, p-values and conclusions from real survey counts.
Secondary sink: timing.
How is MATH5806 assessed?
55% final exam (in-person, 2 hours, exam period) | 20% mid-term test (in-person, Week 7, 1 hour, date/time TBC) | 15% individual assignment (available from Week 7, due Week 9) | 10% quiz (in-person, Week 4, 25 minutes). [Moodle table = the published course material. The Week 1 lecture slide gives a slightly older variant: quiz 30 minutes, assignment "Take home. 2 weeks".
What is the MATH5806 exam or final-task format?
In-person, 2 hours, sat during the UNSW exam period, aligned to CLOs 1-6; like every other task it will have a mathematical and a computational component. Check the current MATH5806 course site and official timetable for any remaining sitting conditions.
Does MATH5806 have a hurdle or component-level pass rule?
Treat the MATH5806 hurdle status as unconfirmed. Check the current official course outline for any component-level pass rule before relying on the overall mark.
What prerequisites or restrictions apply to MATH5806?
No formal prerequisite is stated in the verified course material, but the course publishes an explicit "Knowledge assumed" slide: linear algebra (vector spaces, linear independence, matrix multiplication, diagonalisation, projections), multivariate calculus (partial derivatives, critical points, integrals), prior exposure to R, and probability/statistics up to "asymptotic normality of maximum likelihood estimators".
Is MATH5806 offered in Term 2, 2026?
This resource is aligned to Term 2, 2026. Confirm your class and assessment timetable in the current institutional system.
Is this MATH5806 resource an official university guide?
No. It is an independent MATH5806 study resource; current institutional instructions remain authoritative for assessment operation.
How to study for the exam
Retrieve the course map, practise the recurring method—state the response, predictors and purpose, express the model and assumptions, derive or compute the estimator, diagnose departures and interpret coefficients conditionally—on changed scenarios, and verify every operational assessment detail in the live institutional system.
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