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Financial Mathematics
Financial Mathematics: Portfolio Analysis, Risk and Volatility Modelling
This Financial Mathematics coursework focuses on the quantitative analysis of financial assets, portfolio construction, investment risk and volatility modelling. Students are required to work with historical daily share-price data for five stocks previously selected in their portfolio. The data should cover a sufficiently long period, with at least one year of observations, and should provide positive average returns. Students must briefly describe each selected company and the nature of its business before conducting the financial analysis. The first part of the coursework requires students to calculate the expected return and volatility of each of the five companies and analyse the correlations between their asset returns. These calculations provide the foundation for evaluating the risk and return characteristics of the individual assets and their potential contribution to a diversified portfolio. The second part focuses on portfolio optimisation. Students must use an appropriate Solver function to determine portfolio risk and the percentage investment allocated to each asset for a selected target return. The process must be repeated for different target returns to generate an efficient frontier curve. This analysis demonstrates the relationship between expected portfolio returns and the associated levels of portfolio risk. The third part requires students to calculate Sharpe ratios for a range of expected portfolio returns and volatilities obtained through the portfolio analysis. Using a risk-free investment with a guaranteed return of 1.5%, students must determine the equation of the Capital Market Line and discuss its economic significance in relation to investment decisions and portfolio performance. The fourth part applies linear regression analysis to calculate the beta of each asset in the portfolio and discuss the significance of beta as a measure of systematic risk. Students must also estimate the portfolio's Value at Risk at the 5% level and discuss the contribution of each individual asset to the estimated portfolio VaR. The fifth part focuses on financial volatility modelling using R. Students must estimate the volatility of a selected individual asset using ARCH/GARCH models and their extensions, identify the most appropriate model and provide an explanation supporting the model selection. Finally, students must present their findings in non-technical language suitable for a potential investor. The conclusion should identify the implications of the analysis for selecting an efficient portfolio and discuss other relevant performance measurements. The coursework requires clear explanations of the methods and formulae used in Excel worksheets and R outputs, while unnecessary explanations of portfolio theory and the Capital Asset Pricing Model should be avoided.
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Calculus and Optimisation: Python Implementation of Gradient Descent, Derivatives and Polynomial Regression
This Calculus and Optimisation technical exercise demonstrates the implementation of mathematical and machine-learning concepts using Python. The document is organised as a set of code fragments that must logically work together to perform symbolic calculus, numerical optimisation, physical modelling and polynomial regression. The material uses libraries including NumPy, SymPy, Matplotlib and Scikit-learn, linking mathematical theory with practical computational implementation. Jigsaw_Puzzle_Calculus_Original… A central component is the implementation of gradient descent for linear regression. The supplied function calculates predictions, evaluates prediction errors, computes gradients and updates model parameters iteratively using a configurable learning rate. Mean squared error is recorded during optimisation, and a tolerance-based stopping condition is used to terminate the algorithm when successive cost values change by only a very small amount. Jigsaw_Puzzle_Calculus_Original… Synthetic linear-regression data is generated using a fixed NumPy random seed to support reproducible experimentation. A bias column is added to the feature matrix, initial parameter values are randomly generated, and the custom gradient-descent function is then executed to estimate the intercept and slope of the relationship. Jigsaw_Puzzle_Calculus_Original… The document also demonstrates symbolic differentiation and optimisation using SymPy. A cubic polynomial is defined and differentiated to obtain both its first and second derivatives. Critical points are identified by solving where the first derivative equals zero, while the second derivative is evaluated at each critical point to determine whether the point represents a local minimum, local maximum or saddle point. Jigsaw_Puzzle_Calculus_Original… Jigsaw_Puzzle_Calculus_Original… A further section applies mathematical formulas to projectile motion. Using a specified initial velocity, launch angle and gravitational acceleration, the code calculates both maximum projectile height and horizontal range. This component illustrates how calculus-related mathematical relationships can be translated directly into executable computational models. Jigsaw_Puzzle_Calculus_Original… The final major element explores polynomial regression. Synthetic nonlinear data is generated from a cosine-based function with added random noise. Scikit-learn pipelines are then used to compare polynomial models of degrees 1, 4 and 15. The models are fitted to the synthetic dataset and visualised against the underlying true function, allowing comparison of model complexity and illustrating concepts such as underfitting and overfitting. Jigsaw_Puzzle_Calculus_Original… Jigsaw_Puzzle_Calculus_Original… Overall, the exercise integrates calculus, optimisation, numerical methods and machine-learning modelling through Python. It provides practical experience with differentiation, critical-point analysis, iterative optimisation, mathematical simulation, regression modelling and visualisation. Important: because this file does not identify a university, assessment weighting, academic level, reference style or required word count, those fields should remain Not specified / Not applicable rather than being invented.
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Statistical Programming / Data Science / Business Analytics
Statistical Programming with R: Data Analysis, Probability, Regression and Business Decision-Making
This Statistical Programming assessment evaluates students' ability to apply statistical techniques and R programming to practical data-science and business decision-making problems. The individual assessment combines descriptive statistics, data preparation, visualisation, probability, regression, correlation and sampling, requiring students to demonstrate both conceptual statistical understanding and practical implementation in RStudio. The module learning outcomes emphasise the application of statistical methods to large and real-world datasets, critical evaluation of analytical techniques and awareness of legal, cultural and ethical issues associated with data analysis and dissemination. KL7012 - Statistical Programmin… The early tasks examine fundamental statistical reasoning. Students interpret weight-loss data comparing exercise classes with gym-only workouts using sample size, mean, mode and standard deviation, and explain an appropriate method for dealing with missing data, including its advantages and disadvantages. KL7012 - Statistical Programmin… A substantial practical component uses a cystic fibrosis dataset containing variables such as age, sex, height, weight, body-mass-related measurements, forced expiratory volume, residual volume, functional residual capacity, total lung capacity and maximum expiratory pressure. Students import the data into an R data frame, generate descriptive summaries and interpret the results. They then use scatterplots to investigate relationships between variables and sex-stratified boxplots to identify possible outliers. KL7012 - Statistical Programmin… The assessment also covers major probability models. Students apply probability concepts to healthcare survival, helpdesk email arrivals and fuel-demand scenarios, while also discussing how changing assumptions or real-world conditions can affect interpretation. These exercises assess understanding of statistical distributions and their application to operational and managerial decision-making. KL7012 - Statistical Programmin… Further analytical tasks examine linear regression and correlation. Students analyse the relationship between temperature and converted sugar in a chemical process, use a regression model to estimate the expected response at a specified temperature, and interpret relevant summary statistics. They also calculate and evaluate the suitability of a correlation coefficient for examining the relationship between advertising activity and product purchases. KL7012 - Statistical Programmin… The final and most substantial task involves a real-world M1 traffic-speed investigation for a manufacturing organisation. Students must design an appropriate sampling strategy, collect data from the specified Traffic England source, conduct statistical analysis in RStudio and develop evidence-based conclusions. The statistical report for this task is limited to 1,500 words and should include sampling methodology, collected data, statistical analysis, results, conclusions and relevant background research, supported by appropriate graphs, tables and charts. Raw data and RStudio calculations must be included in an appendix. KL7012 - Statistical Programmin… Overall, the assessment integrates statistical theory with R-based practical analysis, covering descriptive statistics, probability, visualisation, missing-data treatment, regression, correlation, sampling and critical interpretation of results in healthcare, operational and business contexts.
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Principles of Data Science
2,000 words
Principles of Data Science – Data Analysis Portfolio
This portfolio assignment for the Principles of Data Science module at Coventry University requires students to analyse the Global Life-Work Balance Index 2025 dataset using statistical and data science techniques in R. The dataset ranks 60 countries according to life-work balance using factors including statutory annual leave, paid maternity leave, sick leave, healthcare, public safety, public happiness, LGBTQ inclusivity and average working hours per employee. The assignment has a 2,000-word equivalent limit, excluding the reference list and output. The portfolio consists of two main tasks. Task 1 is a group task involving multivariate data analysis. Students must use R to perform Principal Component Analysis (PCA) and Cluster Analysis on the dataset. For PCA, students analyse quantitative variables, produce and interpret relevant visualisations such as screeplots, biplots and loadings plots, and investigate the effects of Region and Healthcare System. The PCA analysis also requires comparison of the overall dataset with countries from Europe. The cluster analysis component requires students to cluster both countries and variables using different distance metrics and hierarchical clustering methods. Students compare methods such as Manhattan and Euclidean distances and single linkage and Ward’s method, present comparisons in compact tables, and interpret relevant dendrograms. They must then compare the conclusions obtained from PCA and Cluster Analysis, identifying common insights and apparent conflicts and discussing the extent to which the results are explainable rather than simply interpretable. Task 2 is an individual task focusing on Exploratory Data Analysis and Linear Models. Students create a scatter matrix using ggpairs(), investigate strongly correlated variables, and identify quantitative variables that may help predict Region for European and Asian countries. They then develop and critically assess linear regression models for predicting Score, including models based on employment variables and broader quantitative predictors. Model comparison and selection use concepts including AIC, while diagnostic plots are used to identify countries requiring further investigation. The individual task also requires students to use European Life-Work Balance Index 2023 data to make predictions for European countries not included in the 2025 dataset and to construct a Residuals versus Fitted Values plot. Finally, students must combine the conclusions from their individual linear modelling work with the PCA and Cluster Analysis findings to identify specific discoveries about the variables and countries in the dataset. R code, output and relevant plots must be included directly within the reports. The assignment encourages use of the R tidyverse and requires appropriate referencing of sources. The brief specifies APA-style referencing for the individual and group work. It also states that generative AI may be used for inspiration but not for generating answers or analysing the datasets, and any permitted AI use must be acknowledged and documented.
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Machine Learning / Data Science
Linear Regression and Stability of the Moore–Penrose Pseudoinverse Using Python
This machine learning practical and assessment activity develops an understanding of linear regression, Ordinary Least Squares and the Moore–Penrose pseudoinverse using Python. The work progresses from generating synthetic regression datasets to implementing regression algorithms manually, applying established machine learning libraries, analysing real datasets and evaluating the stability of estimated regression coefficients. The laboratory component begins with the generation of synthetic linear regression data using NumPy, including explanatory variables, random noise and an outcome variable. Students then implement simple linear regression without relying on machine learning libraries, using the least-squares solution to estimate the intercept and slope. The resulting observations and fitted regression line are visualised using Matplotlib. The work is subsequently extended to multiple linear regression, where several independent variables are used and coefficients are first calculated manually before the same problem is solved using Scikit-learn. The laboratory also introduces application of regression to the Scikit-learn Diabetes dataset, including feature and target standardisation, model fitting, prediction, correlation analysis and interpretation of regression coefficients. It also highlights the importance of residual analysis when assessing whether a linear model is appropriate. The associated weekly challenge focuses on the stability of linear regression solutions estimated using the Moore–Penrose pseudoinverse. Using a house-price dataset containing variables such as property size, number of bedrooms, distance from the city centre and property age, students construct the design matrix, standardise features and the response variable, and calculate regression coefficients using the pseudoinverse. Students then investigate model robustness by repeatedly fitting the regression model to random subsamples of different sizes and analysing the mean and standard deviation of each coefficient. Tables, boxplots or error-bar visualisations can be used to compare coefficient variability. The final discussion considers which variables are most influential, which coefficients are most stable, how sample size affects stability and whether coefficient interpretation remains reliable across different samples. The final work is submitted as a single PDF exported from Jupyter Notebook or Google Colab, combining documented Python code, experimental results, plots and written interpretation in a professionally organised notebook. Overview word count: approximately 360 wor
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