QBUS2820 Predictive Analytics
The Complete Exam Bible · S2 2026QBUS2820 Overview
- University of Sydney unit
- Semester 2 2026
- Two-hour written final
Predictive Analytics develops a disciplined route from a business question to a tested prediction and then to a decision. The Semester 2 2026 materials begin with supervised and unsupervised learning, regression and classification, prediction versus inference, loss functions, the regression function, underfitting and overfitting.
- Assessment A 40% written final follows three individual coursework tasks.
- Hardest step Protect validation data while tuning models and thresholds.
- How to prepare Recompute methods, then interpret every result in context.
How QBUS2820 is assessed
| Component | Weight | Format |
|---|---|---|
| Individual assignment 0 Short answer assessment on statistical learning concepts (Weeks 1-2). No simple extension permitted. | 10% | Out-of-class quiz Early Feedback Task, Week 02, AI allowed |
| Individual assignment 1 Report | 25% | Data analysis, Week 08, AI allowed |
| Individual assignment 2 Report | 25% | Data analysis, Week 13, AI allowed |
| Final exam Written exam | 40% | Written exam, formal exam period, 2 hours, AI prohibited |
What QBUS2820 covers
The captured Semester 2 2026 teaching sequence moves from statistical learning foundations through linear and nearest-neighbour regression, model evaluation and selection, ridge and lasso regularisation, then classification probabilities, loss and ROC analysis.
Predictive Modelling Foundations
Learning targets, loss, prediction, inference and model flexibilityPredictive modelling converts a business question into a response, predictors, a learning task, a loss and a validated decision. This chapter distinguishes supervised from unsupervised learning, regression from classification, and prediction from inference.
- Business questions and prediction targets
- Supervised and unsupervised learning
- Regression and classification responses
- Prediction compared with inference
- Loss and expected prediction error
- Regression functions and additive noise
Least Squares and Linear Regression
Residuals, coefficient interpretation, categorical terms and interactionsLinear regression expresses a conditional mean through an intercept and slopes, then chooses coefficients by minimising squared residuals.
- Simple linear regression equations
- Least-squares coefficient fitting
- Fitted values and residual signs
- Multiple regression interpretation
- Categorical indicator variables
- Interaction effects and hierarchy
Likelihood and Regression Inference
Maximum likelihood, confidence intervals, coefficient tests and model testsLikelihood ranks parameter values by how strongly each supports the observed sample under a probability model. Log-likelihood converts products into sums and makes differentiation practical.
- Joint likelihood for independent cases
- Log-likelihood transformations
- Score equations and maximisation
- Coefficient standard errors
- Confidence interval construction
- Tests against nonzero benchmarks
K-Nearest Neighbours Regression
Distance, scaling, neighbourhood size and dimensionalityK-nearest neighbours regression predicts locally by averaging the responses attached to the closest training inputs.
- Neighbour averaging at a target
- Euclidean distance and scaling
- Mahalanobis distance
- Small and large K
- Cross-validated K selection
- Curse of dimensionality
Prediction Error, Bias and Variance
Training, validation and test error with honest evaluation boundariesPredictive quality is defined on future cases, not on the observations used to fit a model.
- Training and test error
- Expected prediction error
- Bias squared
- Prediction variance
- Irreducible error
- Underfitting and overfitting
Model and Variable Selection
AIC, BIC, cross-validation and subset search proceduresModel selection chooses among fitted structures, while variable selection determines which predictors enter those structures.
- Candidate model definition
- AIC penalties
- BIC penalties
- K-fold cross-validation
- Best-subset selection
- Forward stepwise search
Ridge Regression
Multicollinearity, squared penalties, scaling and lambda selectionRidge regression stabilises a linear model by adding a squared-coefficient penalty to residual sum of squares. It is especially useful when predictors are highly correlated and ordinary least-squares slopes change sharply across samples.
- Multicollinearity and instability
- Squared coefficient penalties
- Lambda and shrinkage paths
- Bias and variance trade-off
- Predictor standardisation
- Cross-validated lambda choice
Lasso and Elastic Net
Sparse coefficients, grouped predictors and mixed penaltiesLasso uses an absolute-value coefficient penalty, allowing the fitted solution to land exactly on zero for some predictors. This creates sparse models but can produce unstable selections among correlated variables.
- Absolute coefficient penalties
- Sparse fitted solutions
- Lasso constraint geometry
- Correlated predictor instability
- Elastic net mixing
- Group lasso penalties
Classification and Logistic Regression
Bayes decisions, KNN classes, logistic probabilities and oddsClassification predicts categories by estimating probabilities or applying decision boundaries. This chapter introduces the Bayes classifier, KNN class voting, binary logistic regression, log-odds, odds ratios and multinomial extensions.
- Conditional class probabilities
- Bayes classifier decisions
- KNN class voting
- Logistic probability curves
- Log-odds equations
- Odds ratio interpretation
Classification Loss and ROC Analysis
Confusion matrices, asymmetric costs, thresholds and ROC curvesClassification evaluation starts with the four confusion-matrix cells and the identity of the positive class. Sensitivity, specificity, false-positive rate and false-negative rate describe different error directions.
- Confusion matrix cells
- Sensitivity and specificity
- False-positive and false-negative rates
- Misclassification error
- Unequal error costs
- Loss matrices and expected value
They then build linear regression from least squares and maximum likelihood, add uncertainty and coefficient tests, and contrast the global parametric line with local K-nearest neighbours prediction. The middle of the guide focuses on the part of modelling that most often separates a plausible analysis from a reliable one: estimating future error.
Training, validation and test sets are assigned distinct roles; bias and variance explain why maximum flexibility is not the goal; AIC, BIC and cross-validation provide explicit selection rules; and subset searches define which predictor combinations are considered. Ridge regression, lasso, group lasso and elastic net then show how penalties stabilise correlated models or create sparse ones.
The final block turns to classification. Bayes decisions, KNN classification and logistic regression produce class probabilities, while confusion matrices, sensitivity, specificity, loss matrices and ROC curves determine how probabilities become actions. The official 2026 unit page lists an early-feedback task worth 10%, two data-analysis reports worth 25% each, and a two-hour written final exam worth 40%.
The lecture capture explicitly identifies maximum likelihood estimation as examinable. The Week 1 material also warns that the unit requires independent work and a higher-than-average workload, reflecting its combination of mathematics, Python implementation and business communication.
This guide answers that demand with original calculations, method comparisons and decision checks grounded in the available Weeks 1 to 9 teaching files.
Worked example · free
Choose a fraud threshold from expected loss
- +1The marks shown in this example are a revision aid, not a published University assessment scheme. Sensitivity = 32/(32+8) = 0.80.
- +1Specificity = 912/(912+48) = 0.95.
- +1Missed-fraud cost = 8 × $500 = $4,000.
- +1Flagged cases = 32 + 48 = 80, so review cost = 80 × $10 = $800.
- +1Total direct cost = $4,800; compare this value with other validated thresholds rather than choosing by accuracy alone.
Key terms
- Prediction Loss
- A numerical penalty for the difference between an observed outcome and a model prediction.
- Regression Function
- The conditional mean of a numerical response given the predictors and the squared-error prediction target.
- Residual
- An observed response minus its fitted value, with the sign showing whether the model underpredicted or overpredicted.
- Likelihood
- A function that compares parameter values by how strongly each supports the observed sample under the probability model.
- Cross-Validation
- A resampling method that rotates held-out folds to estimate predictive performance and choose tuning values.
- Bias
- Systematic distance between the average fitted rule and the true prediction target.
- Variance
- Sensitivity of a fitted rule to changes in the training sample.
- Ridge Regression
- Penalised regression that shrinks slopes with a squared-coefficient penalty to improve stability.
- Lasso
- Penalised regression using absolute coefficient values, allowing some fitted slopes to become exactly zero.
- Logistic Regression
- A classification model that expresses log-odds as a linear function and maps the result to probability.
- Sensitivity
- The proportion of actual positive cases correctly classified as positive.
- ROC Curve
- A plot of sensitivity against false-positive rate as a classification threshold changes.
QBUS2820 FAQ
What assessment tasks make up the unit?
The official 2026 unit page lists a 10% early-feedback short-answer task, two individual data-analysis reports worth 25% each, and a 40% written final exam. The reports are due in Weeks 8 and 13, while the exam sits in the formal examination period.
How demanding is the course?
The Week 1 lecture describes independent work and a higher-than-average workload within university guidelines. The evidence supports that factual warning, not a rating. The workload combines mathematical derivations, Python implementation, data analysis and clear communication of business decisions.
How much mathematics should I expect?
Expect probability, likelihood, matrix notation, regression algebra, bias and variance, information criteria, regularisation penalties, logistic probabilities and classification metrics. The strongest preparation is to reproduce each derivation or calculation, then explain what the number means for a prediction or decision.
How is Python used in the learning sequence?
The materials position Python as the bridge between statistical knowledge and practical workflow. Tutorials develop data manipulation, visualisation and model implementation. Code should support an auditable analysis: split data correctly, fit preprocessing only on training cases, validate choices and communicate the result.
Are past exam papers included?
The captured folder contains no past exam, practice final or sample exam. It does include two solved problem sets, which demonstrate question types and complete mathematical working for likelihood, regression inference, transformations, multicollinearity and regularisation. This guide uses original questions based on those types.
What should I prioritise before the final?
The official record specifies a two-hour written final worth 40%, and the Week 2 page explicitly says maximum likelihood estimation will be tested. Rehearse symbolic setup, clean arithmetic, interpretation, validation logic, regularisation comparisons, logistic probability and confusion-matrix calculations, then verify operational instructions on Canvas.
Questions students ask in each QBUS2820 chapter
- How do I identify the learning type?
- Check whether an observed response is available. No response suggests unsupervised learning. A numerical response gives regression, while a categorical response gives classification. Then state whether the goal is future prediction or explanation of predictor effects. Chapter 01 · Predictive Modelling Foundations
- How should I interpret a slope?
- State the response change, predictor unit and conditioning phrase. In multiple regression, the slope is the fitted response change for one predictor unit while the other included predictors are held fixed. Chapter 02 · Least Squares and Linear Regression
- Why use the log-likelihood?
- The logarithm is increasing, so it preserves the parameter value that maximises likelihood. It also converts products over independent observations into sums and makes derivatives easier to calculate. Chapter 03 · Likelihood and Regression Inference
- Why must predictors be scaled?
- Distance depends on numerical units. Without scaling, a large-unit predictor can dominate the neighbour search even when it is not more informative. Fit scaling values on training cases only. Chapter 04 · K-Nearest Neighbours Regression
- Why can test error rise with flexibility?
- A more flexible model can follow noise in its training sample. Bias may fall, but prediction variance can rise enough to increase future loss, creating a U-shaped test-error pattern. Chapter 05 · Prediction Error, Bias and Variance
- Should I always choose the smallest AIC?
- Choose the smallest AIC only among genuinely comparable candidate fits. If prediction is the operational target, confirm the choice with an honest held-out design and check whether the gain is stable. Chapter 06 · Model and Variable Selection
- Why does ridge help with correlated predictors?
- The squared penalty discourages unstable large coefficient combinations. Ridge accepts some bias but can sharply reduce variance, producing more reliable predictions when ordinary least-squares slopes compete across correlated inputs. Chapter 07 · Ridge Regression
- Why can lasso set coefficients to zero?
- The absolute-value constraint has corners on coefficient axes. A likelihood or residual contour can first touch a corner, producing an optimum with an exact zero slope. Chapter 08 · Lasso and Elastic Net
- Why use logistic regression instead of a line?
- The logistic link keeps fitted probabilities between zero and one and expresses predictor effects linearly on log-odds. A plain linear probability fit can produce impossible values. Chapter 09 · Classification and Logistic Regression
- Why can accuracy be misleading?
- When one class is rare, predicting the majority class can achieve high accuracy while detecting none of the important cases. Report class-specific rates and decision loss. Chapter 10 · Classification Loss and ROC Analysis
How to study for the exam
Study each method as a decision chain rather than a formula list. Begin by naming the response, predictors, learning type and loss. Reproduce the fitted calculation by hand, then identify which data were used to fit, tune and evaluate it. For regression, practise residual signs, coefficient units, likelihood derivatives, intervals and test statistics.
For KNN and regularisation, explain how scaling and tuning change the fitted rule. For classification, calculate the probability before applying a threshold, write all four confusion-matrix cells before computing rates, and select a threshold from consequences rather than accuracy alone.
Keep one modelling audit sheet with the split design, preprocessing boundary, candidate set, tuning rule, final held-out loss and intended business action. The source capture includes solved problem sets but no past final, so use those solutions to learn visible working and use the original practice chapter to test transfer.
In the final week, confirm the current exam instructions on Canvas and rehearse short calculations under a two-hour time budget without inventing a section structure the public unit page does not state.
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