DTS206TC Applied Linear Statistical Models

Coursework

Due: Sunday March. 16th, 2024 @ 11:59pm

Weight: 40%

Maximum score: 100 points

Learning Outcomes Assessed

• 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. Carryout and interpret linear regressions and analyses of variance, and derive basic theoretical results.

Submission Policy

1. Submission Format

• 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.

2. File Naming

• 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.

3. All submissions must be written in English.

4. Please do NOT include the data in the folder if the data is more than 80M. If you would like to share the data, please upload it to any e-Drive and paste the share link in the report (as reference or footnote).

5.  Coverpage should be inserted in the report.

6. Page limit: No more than 16 pages.

Late Policy

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.

Avoid Plagiarism

• Do not submit work from other students.

• Do not share code/work to other students.

• Do not copy code/work from other students.

• Do not use content generated by AI tools.

1 Coursework Overview

This coursework aims to provide students with practical experience in data analysis, linear regression, and ANOVA analysis using the R programming language. The task will involve exploring a dataset of your choice, performing various statistical analyses, and interpreting the results with a focus on understanding and applying the key principles of linear regression models,ANOVA, and diagnostics. The overall goal is to demonstrate your ability to use R to perform a thorough analysis, assess the fit of the model, and address any issues or violations of regression assumptions through appropriate diagnostic and remedial measures.

The coursework is divided into the following key sections:

2   Data Analysis & Visualization (15 marks)

1. Describe the dataset and the variables of interest (5 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 dependent and 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.

2. Perform. Exploratory Data Analysis (EDA) using R functions/packages (5 Marks)

• 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.

3. Visualize the relationships between variables using scatter plots, histograms, etc. (5 Marks)

• 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)

1. Perform. Simple Linear Regression Analysis (5 Marks)

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

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

2. Specify the Regression Model, Explaining the Choice of Independent and Dependent Variables (5 Marks)

• Write the equation of the regression model.

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

3. Interpret the Regression Coefficients (5 Marks)

• 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.

4. Assess the Goodness-of-Fit of the Model (R2, Adjusted R2) (5 Marks)

•  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)

1. Construct the ANOVA Table (5 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 regression model results.

2. Interpret the ANOVA table (5 Marks)

• 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.

3. Applying the F-Test (5 Marks)

• 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)

1. Perform. Diagnostic Checks for Linear Regression Models (8 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.

2. Identify and Address Violations of Assumptions (7 Marks)

• 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%)

1. Structure and Organization (15 Marks)

•  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.

2. Analytical Depth and Accuracy (10 Marks)

• 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.

    3. Technical Demonstration and Originality (5 Marks)

•  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.