Bivariate Data Analysis and Time Series Analysis Assessment

Assignment Overview 

In 2032, Brisbane will host the 32nd Olympic Games. This major global event will unite the world’s best athletes as they compete across a wide range of disciplines. Every athlete strives to perform at the highest level and become the best in the world at their chosen event.

As data analytics continues to play an increasingly influential role in sports performance, many athletes and coaches now rely on analytical insights to gain competitive advantages. Examining patterns in past performances allows them to identify potential improvements, understand performance boundaries, and prepare effectively for future competitions. In this context, analysing the progression of gold-medal performances over time has become an important tool for predicting future outcomes.

Task

Your task is to investigate how gold-medal performances for a specific Olympic event have progressed over time. By analysing secondary data from previous Olympic Games, you must predict the winning performance of that same event at the 2048 Olympic Games. Your analysis should consider historical trends, factors influencing performance changes, and the possible implications for athletes in future competitions.

What You Must Do

To successfully complete this task, you are required to:

1. Demonstrate a range of mathematical skills and understanding

Your response must incorporate:

• Appropriate use of mathematical language

• Relevant calculations

• Clearly presented tables of data

• Informative graphs and diagrams

• Logical explanations of mathematical methods used

2. Provide a real-life mathematical application

Your response must clearly link mathematics to real-world sporting performance. Show how mathematical procedures and data analysis help athletes, coaches, and organisations make informed decisions.

3. Write a report that stands alone

Your final report must be written in a format that can be read and understood without needing the original task sheet. It should be self-contained, well-structured, and professionally presented.

4. Produce a unique and original analysis

Your investigation must be entirely your own work. You must develop your own interpretation of the data, choose your own modelling approach, and present your analysis in your own words and style.

5. Use a combination of manual analytic procedures and technology

Your investigation must show evidence of:

• Manual mathematical steps (e.g., calculations, model reasoning)

• Technological tools (e.g., spreadsheet software, graphing tools, statistical analysis software)

Both aspects must be integrated to support your findings and predictions.

Brief Summary of Assessment Requirements 

Task: Investigate how gold-medal performances for one Olympic event have progressed over time using secondary data from past Games and predict the winning performance for that same event at the 2048 Olympic Games.

Core requirements / key pointers to cover:

1. Mathematical skills and presentation

   • Use correct mathematical language and notation.

   • Include relevant calculations, clearly presented tables, and informative graphs/diagrams.

   • Explain mathematical methods logically and show manual calculation steps where appropriate.

2. Real-life application

   • Explicitly link the mathematical analysis to sporting performance and decision making for athletes/coaches/organisations.

3. Stand-alone professional report

   • The report must be self-contained, well structured (introduction, data/methods, results, discussion, conclusion, appendices), and readable without the original task sheet.

4. Original analysis

   • Work must be unique: data interpretation, model selection and discussion must be the student’s own.

5. Manual procedures + technology

   • Provide evidence of manual reasoning/steps AND use of technology (spreadsheets/statistical software/graphing tools). Integrate both to support conclusions.

How the Academic Mentor Guided the Student Step-By-Step 

Below is a pragmatic mentoring pathway the Academic Mentor used to help the student meet every assessment requirement while ensuring originality and academic rigour.

1. Scoping & selection (Introduction)

Mentor guidance:

• Helped the student choose a single, clearly defined Olympic event (e.g., men’s 100m, women’s long jump) and justify that choice (data availability, relevance, stable measurement units).

• Advised framing a clear research question: “How has the gold-medal performance in [event] changed from Year X to Year Y, and what is a defensible forecast for 2048?”
  Deliverable: A concise introduction explaining context (Brisbane 2032 → emphasis on performance prediction for 2048), purpose, and research question.

2. Data collection & provenance (Data)

Mentor guidance:

• Showed how to locate and record secondary data (year, winning performance value, units, notes about wind/timekeeping/rule changes).

• Taught the importance of documenting sources and any adjustments (e.g., converting times to consistent formats, marking years with boycotts or non-standard conditions).
  Manual step: Demonstrated example manual conversions (e.g., mm:ss.s → seconds) and a small sample table to show method.
  Technology step: Guided using a spreadsheet to store the full dataset and keep a “source & notes” column for each year.
  Deliverable: A clean, well-documented table of gold-medal values with source citations (appendix).

3. Data cleaning & exploratory analysis (EDA)

Mentor guidance:

• Taught how to visually inspect data (line charts for time series, scatterplots if comparing two variables).

• Showed how to identify outliers, missing years, and potential structural breaks (rule changes, timing technology introduction).
  Manual step: Walked through one example outlier check by hand (calculate z-score for a suspicious value).
  Technology step: Created plots (time series, moving average) in spreadsheet or statistical software to visualise trend and seasonality.
  Deliverable: EDA figures and a short table describing any cleaning actions (imputations, exclusions).

4. Choosing analytical approaches (Methods)

Mentor guidance:

• Discussed and compared candidate methods: linear trend/regression, polynomial trend, smoothing (moving average, exponential smoothing), and time-series models (ARIMA/SARIMA) where applicable.

• Emphasised selecting a model appropriate to the data pattern (linear trend if steady improvement; more complex models if non-linear or autocorrelated).
  Manual step: Performed and documented key manual calculations (e.g., slope calculation for a simple linear trend using two representative points) to show understanding of model mechanics.
  Technology step: Ran candidate models in software and examined diagnostics (residuals, ACF/PACF).
  Deliverable: A methods subsection that states the final modelling approach and justifies it.

5. Model fitting & validation (Analysis)

Mentor guidance:

• Guided model fitting, interpreting coefficients, and testing assumptions (linearity, independence, stationarity).

• Emphasised validation: train/test split or cross-validation, residual diagnostics, and reporting prediction intervals.
  Manual step: Demonstrated manual computation of a simple regression example and residuals for didactic purposes.
  Technology step: Produced final model output (table of coefficients, RMSE, AIC/BIC as appropriate), and plotted fitted vs actual values.
  Deliverable: Model results with diagnostic plots and a short interpretation of model fit and reliability.

6. Forecasting to 2048 (Prediction)

Mentor guidance:

• Walked through producing and communicating the forecast, including point estimate and uncertainty (e.g., 95% prediction interval).

• Recommended presenting the forecast graphically on the historical series with shaded confidence bands and a table summarising predicted value and interval.
  Manual step: Showed manual propagation of uncertainty for a simple trend model (basic error bounds calculation).
  Technology step: Generated the formal forecast using the chosen software and exported the forecast table/plot.
  Deliverable: Forecast figure and table, plus a short explanation of the numeric result and how it was derived.

7. Interpretation, contextual factors & implications (Discussion)

Mentor guidance:

• Coached the student to discuss non-mathematical factors that influence results: technology, training techniques, equipment, rules, doping regulations, climate/venue, population changes.

• Emphasised balancing numeric projection with domain context and limitations.
  Deliverable: A discussion section linking the quantitative forecast to real-world sporting implications and making practical recommendations for athletes/coaches.

8. Report structure & stand-alone clarity (Report editing)

Mentor guidance:

• Helped structure the report so it is self-contained: clear headings, summary abstract, methods, results, discussion, conclusion, and appendices with raw data and manual calculations.

• Reviewed language to ensure precise mathematical terminology and professional presentation.
  Deliverable: Final report that reads independently (includes a short methodology appendix showing manual steps).

9. Ensuring originality & academic integrity

Mentor guidance:

• Advised the student to clearly state all sources, avoid copying model outputs verbatim from tutorials, and to provide original interpretation of results.

• Discussed how to present code/output in appendices while ensuring the main text is written in the student’s own words.
  Deliverable: A declaration of originality and a bibliography.

How the Outcome was Achieved

1. Data compiled and cleaned: Secondary data for gold-medal results were collated into a spreadsheet, converted to consistent units, and documented with source notes. Outliers and special cases were flagged and justified.

2. Exploratory analysis completed: Time series plots, moving averages, and scatterplots revealed underlying trends and anomalies. Manual checks supported automated diagnostics.

3. Model selection and justification: After comparing simple linear/polynomial trend models and time-series models (ARIMA/SARIMA or exponential smoothing if seasonality/cycles existed), the student selected the model that best balanced fit and interpretability. Manual calculations of trend slope and residual checks were included to demonstrate understanding.

4. Forecast generated with uncertainty: The chosen model produced a point forecast for 2048 plus a prediction interval. The student presented both the numeric forecast and a visual plot with confidence bands.

5. Discussion contextualised the result: The student evaluated how equipment, rule changes, and training advances might bias forecasts and offered practical implications for athletes and coaches.

6. Report presented as stand-alone: The final document included an abstract, detailed methods, results, discussion, conclusion, and appendices showing manual work and full data tables meeting the stand-alone requirement.

Learning Objectives Covered

• Mathematical proficiency: Used mathematical language, performed manual calculations, and interpreted coefficients and residuals.

• Data handling skills: Demonstrated data sourcing, cleaning, conversion, and documentation.

• Statistical modelling: Applied and compared trend analysis and time-series models; validated models using diagnostics.

• Technical literacy: Used spreadsheet and statistical software to produce tables, graphs and forecasts.

• Real-world application: Linked mathematical findings to sport performance, discussing practical implications and limitations.

• Scientific communication: Produced a self-contained, well-structured report with transparent methodology and originality.

• Critical thinking & integrity: Assessed model limitations, articulated uncertainty, and preserved academic honesty.

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