University of Melbourne · S1 2026 · FACULTY OF SCIENCE

MAST90139 Statistical Modelling for Data Science

Q: How is MAST90139 assessed?

The supplied source confirms three written assignments submitted to Gradescope (logistic, binomial dose-response, and an ordinal/multinomial study) plus a final examination. The exact weights, exam length and whether the exam is open- or closed-book are not stated in the supplied material — confirm them in the official subject guide / Handbook, as they shift between cohorts.

- one subject, every graph, every model, every mark

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The Complete Exam Bible · S1 2026

MAST90139 Overview

Statistical Modelling for Data Science

— one engine, every response type, every mark

University of Melbourne
S1 2026
8 chapters
Science

Statistical Modelling for Data Science teaches one engine — the generalised linear model (GLM) — and then watches it bend to every response type: binary, grouped-binomial, count, contingency-table and multicategory (nominal and ordinal) data, all fitted in R.

Assessed by Assignment 1 — logistic regression Weight: confirm · Assignment 2 — binomial dose-response Weight: confirm + 2 more
Key terms Generalised linear model (GLM), Link function, Deviance, Odds ratio
How to prepare Build everything on Chapter 2, the GLM framework — random component, linear predictor and link &mdash…
Most asked What is on the MAST90139 final exam?

MAST90139 · University of Melbourne

An independent, AskSia-authored study guide. AskSia is not affiliated with, endorsed by, or sponsored by University of Melbourne; the course code and name are used for identification only.

Assessment

How MAST90139 is assessed

Component	Weight	Format
Assignment 1 — logistic regression	Weight: confirm	Binary / grouped logistic, odds-ratio interpretation · submitted to Gradescope (due ~early April)
Assignment 2 — binomial dose-response	Weight: confirm	Beetle-mortality dose-response, link comparison · Gradescope (due ~early May)
Assignment 3 — ordinal / multinomial	Weight: confirm	3-category ordinal response with polr · Gradescope (due ~end May)
Final examination	Weight: confirm	Read-the-R-output across the whole GLM arc — weight, length and book-status are not in the supplied source; confirm the exact split and format in your subject guide

Contents · every chapter, one map

What MAST90139 covers

Eight model families → one exam-ready map. Each links to its free chapter guide — and they are all the same generalised linear model.

Linear Models

Matrix form · OLS = MLE · LINE assumptions · the GLM springboard

The normal linear model is where every generalised linear model starts — and the case they all generalise.

1.1 The normal linear model in matrix form (y = Xβ + ε)
The design matrix, fitted values and residuals
1.2 OLS estimation — and why OLS = MLE under normality
Sampling distribution of β̂ · the t and F tests
1.3 The four LINE assumptions
Residual diagnostics — and where LINE breaks

Generalised Linear Models

The three components · exponential family · link functions · IRLS · deviance

This is the spine of the whole course.

The three components: random, systematic, link
The exponential family of distributions
Canonical vs non-canonical link functions
The mean–variance relationship Var(Y) = φV(μ)
Estimation by iteratively re-weighted least squares (IRLS)
Deviance and the saturated model

Logistic Regression

Logit link · odds ratios e^β · Wald vs LR tests · ROC & AUC

Logistic regression is the flagship GLM of MAST90139 and the single most examined model.

The binary response and why a line fails
The logit link and the logistic (S-shaped) curve
Coefficients as log-odds; e<sup>β</sup> as an odds ratio (★ the #1 skill)
Wald tests and likelihood-ratio tests
Confidence intervals for β and for the odds ratio
Classification: threshold, confusion matrix, sensitivity / specificity

Binomial Models

Grouped logistic · deviance goodness-of-fit · overdispersion · dose-response & LD50

When binary outcomes are grouped — r successes out of n trials at each covariate setting — the response is binomial and you fit grouped logistic regression.

Grouped (binomial) logistic regression: r successes out of n
Residual deviance and Pearson X² as goodness-of-fit statistics
The χ² goodness-of-fit test on n−q df
Dose–response models and LD50
Overdispersion: detecting D &gg; df
Estimating the dispersion φ and refitting quasi-binomial

Poisson Regression

Log link · rate ratios · offsets for rates · overdispersion & deviance GoF

When the response is a count — emails per hour, claims per policy, cases per region — the linear model breaks: counts are non-negative integers whose variance grows with their mean.

The Poisson distribution: mean = variance
The Poisson regression model and the log link
Reading e<sup>β</sup> as a rate ratio (★ the examined skill)
Offsets: modelling rates instead of counts (★)
Deviance and Pearson X² goodness-of-fit
Comparing nested models by ΔD vs χ²

Log-Linear Models

Contingency tables as Poisson counts · independence vs saturated · cross-product ratio

Log-linear models analyse a contingency table by treating each cell count as a Poisson response with a log link — so this is Poisson regression where the predictors are the table's classifying factors.

Contingency-table cells as Poisson counts
Independence ⇔ no interaction term (the central identity)
The saturated model and the hierarchy of terms
The cross-product (odds) ratio for a 2×2 table (★)
Interaction = association; uniform association
Log-linear &equiv; logistic for a two-way table

Multicategory Models

Baseline-category logit (nominal) · proportional odds (ordinal) · cumulative ORs

When the response has more than two categories, you extend logistic regression in one of two ways depending on whether the categories are ordered.

The multinomial response: more than two categories
Nominal: the baseline-category logit (multinom)
Ordinal: the cumulative-logit / proportional-odds model (polr)
The proportional-odds assumption and the single slope
Cumulative odds ratios
The polr() sign-convention trap (★ the known trap)

Model Checking

ΔD / likelihood-ratio test · AIC & BIC · residual diagnostics · leverage & influence

The final chapter answers two questions about any fitted GLM: did it fit? and is it the right model? Fit is judged by the deviance and the likelihood-ratio test: for nested models the drop in deviance ΔD = D₀ − D₁ is χ² on the difference in parameters, and for grouped data the residual deviance itself is a goodness-of-fit test.

Deviance and the likelihood-ratio test for nested models
Residual deviance as a goodness-of-fit test (grouped data)
AIC and BIC for ranking non-nested rivals
Deviance vs Pearson residuals — reading a good fit
Leverage and influence: hat values, half-normal plots, Cook's distance
Extension: random and mixed effects (GLMMs)

The exam is a read-the-R-output gauntlet: given a glm() / multinom() / polr() printout you must name the model and link, do the deviance / ΔD-vs-χ² arithmetic by hand, and translate a coefficient into an odds / rate / cumulative-odds statement.

This guide teaches each family to that standard, so you can read any printout and say exactly what it means.

Worked example · free

Reading a glm() printout — logistic coefficient to odds ratio, mark by mark

Q [6 marks]. A logistic regression of an outcome Y (1 = event) on a continuous predictor x returns the fitted model logit(π) = −2.0 + 0.80·x. (a) Interpret the slope 0.80 as an odds ratio. (b) Compute the fitted probability at x = 2.5. (c) The null deviance is 180 on 99 df and the residual deviance is 150 on 98 df — test whether x matters.

+2(a) Slope → odds ratio: in logistic regression the coefficient is on the log-odds scale, so e^β is the odds ratio: e^0.80 ≈ 2.23. Each one-unit rise in x multiplies the odds of the event by about 2.2.
+1(b) Linear predictor at x = 2.5: η = −2.0 + 0.80×2.5 = 0.
+1(b) Inverse-logit: π = 1 / (1 + e^−η) = 1 / (1 + e⁰) = 0.5 — the curve crosses 0.5 exactly where η = 0.
+1(c) Likelihood-ratio test: ΔD = D_null − D_resid = 180 − 150 = 30, on 99 − 98 = 1 df.
+1(c) Compare to χ²: 30 ≫ χ²_{1, 0.05} = 3.84, so reject H₀ — x is a highly significant predictor.

e^0.80 ≈ 2.23 (the odds roughly double per unit of x); the fitted probability at x = 2.5 is 0.5 (where η = 0); and the drop in deviance ΔD = 30 on 1 df vastly exceeds 3.84, so x is a strongly significant predictor.

Sia tip — The exam almost always wants the coefficient turned into a sentence: “the odds multiply by e^β” (logit), “the rate multiplies by e^β” (log/Poisson). State the multiplier, the direction, and what it acts on (odds vs rate). A coefficient with no interpretation rarely earns full marks.

Glossary

Key terms

Generalised linear model (GLM): A model with three parts: a random component (a response from an exponential-family distribution), a linear predictor η = Xβ, and a link function g that connects them, g(μ) = η. Linear, logistic, Poisson and log-linear regression are all special cases.
Link function: The function g that maps the mean μ onto the linear-predictor scale, g(μ) = η = Xβ. The logit link gives logistic regression (binary data), the log link gives Poisson regression (counts); each “canonical” link pairs with a distribution.
Deviance: The GLM analogue of the residual sum of squares: twice the log-likelihood gap between the saturated model and your fitted model. Smaller deviance means better fit; the drop in deviance between nested models is the likelihood-ratio test statistic.
Odds ratio: e raised to a logistic coefficient, e^β — the factor by which the odds of the event multiply for a one-unit rise in the predictor. Greater than 1 raises the odds, less than 1 lowers them; it is the headline output of any logistic fit.
Overdispersion: When count or grouped-binomial data vary more than the Poisson or binomial model allows (residual deviance far exceeds its degrees of freedom). It is fixed by estimating a dispersion parameter φ and refitting a quasi-likelihood model, then testing with an F test rather than χ².

FAQ

MAST90139 FAQ

Is MAST90139 hard?

It is procedural once the GLM framework clicks, but it is dense. The trick is realising that logistic, Poisson, log-linear and ordinal regression are the same three-part model with a different distribution and link — learn that engine cold and the rest is pattern-matching. The difficulty is reading R output fast and interpreting coefficients correctly under exam time.

How is MAST90139 assessed?

The supplied source confirms three written assignments submitted to Gradescope (logistic, binomial dose-response, and an ordinal/multinomial study) plus a final examination. The exact weights, exam length and whether the exam is open- or closed-book are not stated in the supplied material — confirm them in the official subject guide / Handbook, as they shift between cohorts.

What is on the MAST90139 final exam?

A read-the-R-output gauntlet across the whole GLM arc: given a glm(), multinom() or polr() printout, name the model and link, do the deviance / ΔD-vs-χ² arithmetic by hand, and translate a coefficient into an odds ratio (logit), a rate ratio (log) or a cumulative odds ratio (proportional odds).

What maths and software do I need for MAST90139?

You need matrix algebra, likelihood and the normal/exponential-family distributions, plus comfort reading regression output.

All fitting is done in R (the faraway package, with glm, polr and multinom); you are not asked to invert matrices by hand, but you are asked to read and interpret what R prints.

Is using AskSia for MAST90139 cheating?

No. AskSia is a study reference written in our own words — we host none of your lecturer's files, and Sia teaches you the method to read a printout and earn the marks; it does not complete or sit your assessments.

Chapter questions

Questions students ask in each MAST90139 chapter

Why does MAST90139 start with the linear model if the course is about GLMs?: Because every GLM is the linear model with two changes: a non-normal random component and a link function on the mean. Reviewing the linear model fixes the matrix vocabulary (design matrix, hat matrix, residuals) and the LINE assumptions, so that when those assumptions fail for binary or count data you can see exactly which piece the GLM replaces and why. Chapter 01 · Linear Models
What exactly makes something a GLM?: Three ingredients: a response from an exponential-family distribution (the random component), a linear predictor η = Xβ (the systematic component), and a link function g with g(μ) = η. Fix the distribution and the link and you have named a specific model. Almost every model in MAST90139 is one choice of those two ingredients. Chapter 02 · Generalised Linear Models
Why can't I just fit a straight line to a 0/1 response?: Two reasons. Fitted values from a line run below 0 and above 1, which are impossible probabilities; and the variance of a 0/1 (Bernoulli) response is π(1−π), which changes with the mean rather than staying constant. Logistic regression fixes both by modelling the log-odds linearly, so fitted probabilities stay in (0,1) and the right variance is built in. Chapter 03 · Logistic Regression
What is the difference between binomial and ordinary logistic regression?: They are the same model with the data organised differently. Ungrouped logistic regression has one 0/1 row per individual; binomial (grouped) logistic regression collapses individuals with identical covariates into r successes out of n trials. The coefficients and odds ratios are the same, but grouping makes the residual deviance a valid goodness-of-fit test. Chapter 04 · Binomial Models
Why use Poisson regression instead of a linear model on the counts?: Three failures of the linear model on counts: the fitted mean can go negative (impossible for a count); the variance is not constant but equals the mean, so large counts are noisier; and the integer, right-skewed shape is far from normal. The Poisson GLM fixes all three at once by modelling log(μ) linearly and letting Var = μ. Chapter 05 · Poisson Regression
How is a log-linear model just Poisson regression?: Because each cell count in the contingency table is modelled as a Poisson response with a log link, and the predictors are the table's classifying factors and their interactions. Everything from Poisson regression — the log link, the deviance, goodness-of-fit — carries straight over; the only new idea is reading factor interactions as associations. Chapter 06 · Log-Linear Models
When do I use multinom() versus polr()?: It depends entirely on whether the response categories are ordered. Unordered (nominal) responses — brand, transport mode, holiday type — use the baseline-category logit via nnet::multinom(). Ordered (ordinal) responses — severity, satisfaction, ratings — use the proportional-odds (cumulative-logit) model via MASS::polr(), which exploits the ordering with a single slope. Chapter 07 · Multicategory Models
How do I test whether adding terms improves a GLM?: If the smaller model is nested in the larger, use the likelihood-ratio test: compute ΔD = D_small − D_large and compare it to χ² on the difference in the number of parameters. A significant drop means the extra terms matter. In R this is anova(m0, m1, test="Chi"). Chapter 08 · Model Checking

Study strategy

How to study for the exam

Build everything on Chapter 2, the GLM framework — random component, linear predictor and link — because every later model is that template with a new distribution and link.

Then drill the three recurring exam moves until they are automatic: Name (response type → distribution → canonical link), Test (ΔD = D₀ − D₁ against χ² with the df difference for nested models; D against χ²(n−q) for grouped goodness-of-fit), and Interpret (e^β as an odds ratio, rate ratio, cross-product ratio or cumulative OR).

Practise on real R printouts so you can do the deviance arithmetic and the coefficient sentence at speed — that triple is the whole paper.

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