Statistics Final Year Topic: Prediction and Coefficient Stability of Ridge Regression with Correlated Predictors

This Statistics final year project uses simulated training and independent test sets with known regression structure to investigate a specific question in regularised regression. The analysis is designed around known generating conditions so that the behaviour of competing statistical procedures can be checked.

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Why choose this project topic?

This study makes ridge collinearity an explicit, reproducible comparison. Working with simulated training and independent test sets with known regression structure lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How does predictor correlation change the prediction error and coefficient stability of ridge and ordinary least-squares regression?

Agree the scenario ranges, sample sizes and reporting measures for ridge collinearity before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated training and independent test sets with known regression structure.
02Implement a reproducible analysis of ridge collinearity with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How does predictor correlation change the prediction error and coefficient stability of ridge and ordinary least-squares regression?

A suggested research approach

Vary predictor correlation while controlling signal and sample size. Select ridge tuning within the training data only and compare test error, coefficient variation and the effect of standardisation. Write the analysis before inspecting favourable runs, record random seeds where simulation is used, and keep generated study data distinct from observed field data.

What you will need

A written design for simulated training and independent test sets with known regression structure
Statistical software supporting regularised regression and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Stable predictions do not make shrunken coefficients unbiased causal effects or uniquely interpretable importance measures.

Statistics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

Chapter 1Introduction
Chapter 2Literature Review
Chapter 3Theory and Methodology
Chapter 4Results and Applications
Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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