How Can The Monthly GDP Of The United States Be Used To Model The Monthly Values Of The S&P 500 And NASDAQ For The Last 10 Years, And Which Stock Index Has A Better Fitting Model To Allow For Accurate Predictions?HL
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4
Official IB Result
11/20
General feedback
11/20
0
10
20
No overall summary is available for this report.
6.1·Suggestion
Page 3
The rationale provides context but would be strengthened by explicitly identifying a research gap or novel contribution of this study.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- Clear and logical structure with a defined introduction, body and conclusion
- Coherent progression of sections (introduction → data collection → model testing → evaluation)
- Effective use of headings, table of contents and appendices to guide the reader
- Occasional digressions and verbosity (repeated definitions, raw tables in body) disrupt conciseness
- Minor errors in captions and labels (e.g., “NASDAO” typo) affect professionalism
- Inconsistent bibliography formatting detracts from overall polish
1.1·Weakness
Page 15
Table 1 caption contains a typo (“NASDAO”); ensure accuracy in all headings and labels for professional presentation.
1.2·Suggestion
Page 23
Bibliography entries vary in format (italicization, punctuation). Adopt a single citation style (e.g., APA) for presentation coherence.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria Strands
B.1Mathematical language and notation
Good
B.2Multiple representations
Good
B.3Clarity and consistency
Good
Criteria Feedback
- Use of multiple representations (tables, scatterplots, overlaid regression curves) aids understanding
- Key formulas (e.g. R² = 1 − RSS/TSS) are correctly presented
- Terminology and notation are generally understood
- Frequent notation inconsistencies (mixing ŷ, v, â, missing subscripts) reduce clarity
- Units of measurement (e.g., months since June 2014) are not always specified
- Lack of residual or diagnostic plots limits depth of representation
2.1·Weakness
Page 4
The hypothesis section uses notation correctly but occasionally mixes variable notation. Ensure consistent use of LaTeX notation throughout.
2.2·Strength
Page 5
The formula for is correctly presented, reflecting sound mathematical communication.
2.3·Weakness
Page 5
The definitions of and introduce a different symbol than . Unify the dependent‐variable notation to avoid confusion.
2.4·Suggestion
Page 7
Figure 1 effectively visualizes GDP trend over time, but adding a residual plot would provide deeper insight into model fit.
2.5·Suggestion
Page 10
When introducing the quadratic model, specify that is measured in months since June 2014 so units are clear in the formula.
2.6·Weakness
Page 11
Consistent notation for the dependent variable would enhance clarity (some analyses use , others ).
2.7·Strength
Page 15
The student effectively uses tables and regression graphs to compare multiple models, demonstrating clear mathematical communication.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
C.1Independent thinking
Good
C.2Personal approach
Good
C.3Creativity and initiative
Good
Criteria Feedback
- Clear articulation of personal motivation in economics and financial markets
- Student’s choice of data range and model testing reflects individual initiative
- Development of a percentage-error adjustment shows creative thinking
- Reliance on standard Desmos outputs limits depth of independent methodology
- Creative elements are modest and confined to basic model selection
- Personal approach drives the topic but lacks deeper methodological innovation
3.1·Strength
Page 3
The student’s personal interest in economics and financial markets is clearly articulated, demonstrating authentic personal engagement in the investigation.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
D.1Depth of reflection
Good
D.2Critical analysis
Good
D.3Connection to understanding
Good
Criteria Feedback
- Meaningful reflection on model limitations (overfitting, logistic plateau)
- Basic critical analysis comparing R² and percentage error
- Clear link between findings and understanding of market behavior
- Reflection lacks deeper statistical critique (e.g., confidence intervals, residual analysis)
- Connections to broader mathematical subtleties are not fully explored
- Suggestions for improvement are present but not elaborated with quantitative metrics
4.1·Suggestion
Page 7
Noting the inconsistent decimal places between GDP and S&P data is good, but discuss how this precision difference may affect regression coefficients.
4.2·Suggestion
Page 13
The logistic model’s asymptote assumption may conflict with unlimited stock growth; critically reflect on its long‐term applicability in finance.
4.3·Strength
Page 15
The student rightly recognizes logistic plateau limitations; this evaluation is a strong critical reflection on model suitability.
4.4·Suggestion
Page 17
The mean percentage error table shows quartic fitting slightly worse than quadratic. Discuss overfitting with quantitative metrics beyond mean error.
4.5·Suggestion
Page 17
When forecasting GDP for August 2025 using a linear trend, consider non-linear growth or seasonality instead of assuming a constant slope.
4.6·Strength
Page 21
The evaluation of model assumptions and external factors displays meaningful reflection on the investigation’s limitations.
Criteria E: Use of Mathematics
2/6
0
3
6
Criteria Strands
E.1Relevance and level
Moderate
E.2Accuracy and correctness
Moderate
E.3Knowledge and understanding
Moderate
Criteria Feedback
- Relevant course-level mathematics (regression, R², forecasting) applied appropriately
- Equations and numerical computations are mostly correct
- Justification of model choice shows sound understanding
- Error-adjusted forecasting method is simplistic and lacks statistical rigor
- Chronological ordering errors in data plotting may distort results
- Major statistical tools (confidence intervals, cross-validation) are absent
5.1·Strength
Page 4
The aim and approach justify data selection period well, showing thoughtful design in accounting for pandemic and recession effects.
5.2·Weakness
Page 8
Ordering GDP values numerically instead of chronologically can distort temporal relationships; maintain time sequence when plotting for regression.
5.3·Strength
Page 9
Excluding linear regression is appropriate given data complexity; this model selection shows good mathematical understanding.
5.4·Strength
Page 13
The student justifies model choice and acknowledges overfitting risk in quartic regression, reflecting understanding of model complexity.
5.5·Suggestion
Page 16
Demonstrating a single‐point percentage error is informative, but include error distribution (e.g., standard deviation) for a complete assessment.
5.6·Weakness
Page 17
Adjusting predictions by adding average percentage error is not statistically rigorous. Consider constructing confidence intervals or using cross‐validation instead.
5.7·Weakness
Page 18
Use of average-error adjustment shows initiative but lacks statistical rigor; consider more robust forecasting methods.