MH3510: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's regression analysis course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH3510.
Sia generates MH3510 practice questions, walks through regression models and simple regression: least squares step by step, and quizzes you on the material the exam weights most heavily.
Worked example
A simple linear regression on 22 observations gives SSR (regression) = 300 and SSE (error) = 200. What is R², and is the slope significant at the 5% level (F critical value with 1 and 20 degrees of freedom ≈ 4.35)?
Total sum of squares is SSR + SSE = 500, so R² = SSR/SST = 300/500 = 0.6.
F = MSR/MSE = 30, far above 4.35, so the slope is significant at 5%.
Option B uses SSR/SSE without the degrees of freedom; option C reports 1 − R²; option D divides by the wrong totals.
The trap: Forgetting the degrees of freedom. The F ratio compares mean squares, not sums of squares, and the error degrees of freedom are n − 2 in simple regression. classic slip!
One exam decides 60% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH3510 is, and where it sits
MH3510 Regression Analysis is a year-3 statistics course at NTU's Division of Mathematical Sciences. The OBTL+ document, in the new format for AY2026-2027, sets the aim as a rigorous grasp of regression models for summarising relationships among variables, with the ability to build regression models for real data using R.
Six intended learning outcomes define it: build multiple regression models, describe the principle of least squares, identify important predictors, conduct one-way and two-way ANOVA, explore and analyse real data sets in R, and interpret the results. The content runs from simple linear regression through the matrix formulation, multivariate normal random vectors, full versus reduced models, one-way and two-way classification models, dummy variables and ANCOVA, to model selection and diagnostics.
Assessment is a team presentation 20%, a mid-term test 20% and a final examination 60%. The course is 4 AU with 52 contact hours delivered through lectures, tutorials with weekly problem sets, and team-based learning; it is offered in Semester 1 and requires MH2500 plus MH3500 or MH2510. The course author is Jeremie Houssineau.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH3510 hard, and how much time does it take?
MH3510 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You are comfortable with matrices and want to see regression written in them.
- You do the weekly problem sets; the document says feedback comes through them.
- You can explain an ANOVA table line by line.
- You contribute visibly in team sessions — peer evaluation is real.
You may struggle if
- You treat R output as the answer rather than something to interpret; ILO 6 is interpretation.
- You skip the matrix week; multiple regression is built on it.
- You memorise formulas for one-way ANOVA without understanding the decomposition.
- You free-ride in the team; peer evaluation can lower your mark below the team's.
- Derive the least squares estimator in matrix form yourself and check it against the simple case.
- For every model, write the full-versus-reduced test as a sentence before computing the F statistic.
- Practise reading residual and leverage plots and naming the assumption each one checks.
- Rehearse the presentation rubric: accuracy, thoroughness, presentation, originality.
Syllabus
The 13 topics, week by week
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Regression models and terminology
Week 1; ILOs 1-3Response and predictor variables; the purpose of regression.
T2 · Simple regression: least squares
Week 2; ILOs 1-3Deriving least squares estimators; basic hypothesis tests.
T3 · Simple regression: inference
Week 3; ILOs 1-3Interpreting coefficients; assessing model significance; confidence intervals.
T4 · Simple regression: problems
Week 4; ILOs 1-3Least squares fitting, inference and interpretation in practice.
T5 · Matrices and random vectors
Week 5; ILO 3Matrix algebra, expectation and covariance of random vectors, multivariate normal distribution.
T6 · Multiple regression: estimation
Week 6; ILOs 1-4Least squares in matrix form; ANOVA-based model assessment.
T7 · Multiple regression: inference
Week 7; ILOs 1-4Full versus reduced models; hypothesis tests.
T8 · Multiple regression: comparison
Week 8; ILOs 1-4ANOVA decomposition and model comparison.
T9 · One-way and two-way ANOVA
Week 9; ILOs 3-4Model assumptions, treatment effects, interaction.
T10 · ANOVA hypothesis testing
Week 10; ILOs 3-4Main and interaction effects; contrasts.
T11 · ANOVA in practice
Week 11; ILOs 3-4Factorial structure and interaction analysis on examples.
T12 · Universal linear modelling
Week 12; ILOs 5-6Dummy variables, ANCOVA, one unified framework; model selection.
T13 · Diagnostics
Week 13; ILOs 5-6Residual plots, leverage, standardised residuals; justifying a model.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Continuous assessment: presentation in a team-based learning context (selected teams present at the end of a session; marked with a rubric and peer evaluation) | 20% | Team presentation in a team-based learning session, marked against a rubric with peer evaluation; individual marks may vary with contribution. During the semester. Continuous assessment. |
| Continuous assessment: mid-term test (ILOs 1-3) | 20% | Standard mid-term test on ILOs 1-3. Mid-semester. Continuous assessment; no make-up. |
| Final examination (all ILOs) | 60% | Final examination on all six ILOs; point-based marking. Examination period. Summative assessment. |
- The three components sum to 100 and no examination hurdle is published. There is no make-up quiz or mid-term; with a medical certificate the missed component is not counted towards the final grade. Team marks may vary individually through peer evaluation.
- Sixty percent in the final examination across all six ILOs, with a 20% mid-term on the first three (regression building, least squares, predictor selection). The team presentation is the only judgement-marked component and carries peer evaluation.
This is an exam-cram course. With the exams at 60% of the grade and the final examination (all ilos) alone at 60%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: During the examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Derive least squares estimators for simple regression.
- Test the significance of a slope and build a confidence interval.
- Interpret a coefficient in context.
- Explain the ANOVA decomposition for simple regression.
Before the final heaviest topics
- Fit and test a multiple regression in matrix form.
- Compare full and reduced models with an F test.
- Conduct one-way and two-way ANOVA with interaction.
- Select a model and check it with residual diagnostics.
The mistakes that cost marks
Significance without context. A small p-value is not an interpretation; say what the coefficient means for the response.
Ignoring interaction. In two-way ANOVA the interaction term must be tested before reading main effects.
Skipping diagnostics. A model with a good R² and a patterned residual plot is a wrong model.
Teaching team
Who teaches MH3510
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH3510.
Teaching team as listed in the course materials reviewed. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH3510.
Formula & concept sheet
The vocabulary and formulas you must own
- Least squares
- Choosing coefficients that minimise the sum of squared residuals.
- Residual
- The difference between an observed response and the fitted value.
- ANOVA table
- The decomposition of total variation into model and error components.
- F test
- A test comparing nested (full and reduced) models.
- Multiple regression
- A linear model with several predictors, usually written in matrix form.
- Multivariate normal
- The joint distribution underlying inference for random vectors.
- One-way ANOVA
- Comparing means across levels of one factor.
- Interaction
- When the effect of one factor depends on the level of another.
- Dummy variable
- A 0/1 predictor that puts categorical factors into a regression.
- Leverage
- A measure of how far a point's predictors are from the others, flagging influential observations.
Set texts
The prescribed reading
The syllabus references map straight onto these.
Applied Linear Regression Models
.
Where it fits
Prerequisites, related courses & why it matters
Prerequisites: MH2500 and MH3500, or MH2500 and MH2510. 4 AU; 52 contact hours; offered in Semester 1.
Your MH3510 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH3510: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is MH3510 hard?
It rates moderate, at the harder end. The matrix formulation and ANOVA theory are demanding, and 80% of the grade is two sittings, but there is no exam hurdle.
What is the assessment breakdown?
Team presentation 20%, mid-term test 20% and final examination 60%, per the OBTL+ document.
What are the prerequisites?
MH2500 and MH3500, or MH2500 and MH2510.
Is R required?
Yes. Exploring and analysing real data sets using R is the fifth learning outcome.
How does the team presentation work?
During team-based learning sessions some teams are asked to present their work; the presentation is marked against a rubric covering accuracy, thoroughness, presentation and originality, with a peer evaluation form that can move individual marks.
What does it lead to?
NTU's time series and multivariate analysis courses list MH3510 among their prerequisites.
Study MH3510 with Sia
Work through regression models, simple regression: least squares, simple regression: inference and the rest of the course with a tutor that knows it and quizzes you on the topics the assessments weight most heavily.
Start studying with Sia
