DTS206TC Applied Linear Statistical Models
Coursework

• A. Demonstrate knowledge and understanding of basic principles of R programming language.

• B. Demonstrate understanding of the significance of linear regression models and ANOVA tables.

• C. Show understanding of the rationale and assumptions of linear regression models.

• E. Carry out and interpret linear regressions and analyses of variance, and derive basic theoretical results.

• Each student must submit both report and codes:

(a) The final report in PDF format.

(b) The code in .R format. If multiple code files are to be submitted, please create a code folder.

• The files and folders should be named as follows: StudentID_report.pdf, StudentID_code.R, or StudentID_codes.zip if you are submitting a folder with code.

5% of the total marks available for the assessment shall be deducted from the assessment mark for each working day after the submission date, up to a maximum of five working days.

1 Coursework Overview

The coursework is divided into the following key sections:

2 Data Analysis & Visualization (15 marks)

• Provide a clear description of the dataset you have chosen for your analysis. Include relevant details such as the source of the data, the variables it contains, and the key characteristics of the data. Highlight which variables are of particular interest in your analysis.

• Include the dataset name and source, and a summary of the variables (both dependentand independent variables), and a brief discussion of why you have chosen these variables for analysis.

• For example, you can use datasets from sources like the UCI Machine Learning Repository or Kaggle competitions, such as the Boston Housing Dataset or the Student Performance Dataset. These are just a few examples; feel free to choose a dataset that aligns with your interests.

• Perform EDA to understand the structure of your data, identify any patterns, and detect potential issues (such as missing values or outliers).

• Summary statistics (mean, median, standard deviation, etc.).

• Identify any missing values or outliers.

• Use R functions (e.g., summary(), str(), head(), summary(), etc.) to gain insights into the dataset.

• Use appropriate graphical techniques (e.g., scatter plots for continuous variables, histograms for distribution of individual variables).

• Plot relationships between independent and dependent variables.

• Discuss the insights gained from the visualizations.

3 Linear Regression (20 Marks)

• Use R to fit a linear regression model (e.g., lm() function).

• Ensure the choice of dependent and independent variables is well-justified.

• Write the equation of the regression model.

• Explain the rationale behind selecting each variable for the model (e.g., why certain variablesare considered independent and others dependent).

• Provide an interpretation of the regression coefficients, including their magnitude, direction, and significance.

• Explain the meaning of the slope and intercept in the context of the problem.

• Provide interpretations of each coefficient in relation to the dependent variable.

• Calculate and interpret R2 and adjusted R2 .

• Assess how well the model fits the data and whether any improvements are necessary.

4 ANOVA Analysis (15 Marks)

• Construct the ANOVA table using R, ensuring it accurately displays all key metrics (SSR, SSE, SSTO, df, F-value, etc.).

• Ensure the format is correct and all calculations are accurate, consistent with the regressionmodel results.

• Explain the meaning of each metric in ANOVA Table.

• Briefly explain how to compute SSR, SSE, and SSTO, and describe their significance in ANOVA.

• Discuss the significance of factors on the dependent variable, and determine whether the independent variables significantly impact the dependent variable.

• Explain the basic principle of the F-test, including how F-values are calculated and their application in ANOVA.

• Based on the F-test results, assess the overall significance of the independent variables in the regression model, and explain how this affects the conclusions of the study.

5 Diagnostics & Remedial Measures (15 Marks)

• Residuals vs Fitted: Check for linearity (patterns indicate non-linearity).

• Residuals vs Leverage: Check for homoscedasticity (fluctuations indicate heteroscedasticity).

• Residuals vs Time: Check for independence (trends suggest violation).

• Q-Q Plot: Assess normality (deviations indicate non-normality).

• Histogram: Verify if distribution is bell-shaped.

• Discuss Violations. Describe observed issues (e.g., non-linearity, heteroscedasticity) and their impact.

• Implement appropriate remedial measures to address any issues identified.

6 Conclusion (5 Marks)

• Provide a clear summary of the linear regression results, including model performance and key coefficients.

• Discuss the implications of the results and any insights gained from the analysis.

7 Report Writing (30%)

• Clear and Concise Manner, with Appropriate Headings and Subheadings.

• Clarity and Organization of the Report. The report should be cohesive, with ideas flowing logically. Transitions between sections should be smooth.

• The report should maintain a high standard of academic professionalism, with formal language, correct grammar, and proper formatting.

• Provide a thorough, well-explained regression analysis. This includes data analysis, model specification, assumption checks, and interpretation of results.

• All R code should run correctly, producing accurate outputs.

• Include relevant R code snippets demonstrating the analysis and visualization steps.

• The code should be well-commented to explain the methodology and logic behind it.

• The report should demonstrate independent thought and creativity. Any external resources should be properly cited.

Marking Criteria