Final Project: Regression Analysis
Overview
This project builds on your understanding of regression analysis and challenges you to apply these techniques to real-world data. The aim is to critically analyze variables, create regression models, and make data-driven decisions while interpreting outputs to draw meaningful conclusions. The final deliverable will include your analyses, insights, and a reflective piece.
Learning Goals and Tasks
Learning Goal 1: Speculating Variable Importance
1a) Which variable in the dataset do you believe is the most important for predicting post-graduate earnings? Justify your choice with real-world reasoning and examples.
1b) Which variable do you believe is the second-most important for predicting post-graduate earnings? Provide a detailed explanation for your choice.
1c) Identify a potential interaction between two variables that could influence post-graduate earnings. Discuss the real-world implications of this interaction.
Learning Goal 2: Simple Linear Regression
2a) Run a simple linear regression using university price as the predictor and average earnings after graduation as the dependent variable. Analyze the output by answering:
i. Is price significant at the 5% significance level?
ii. How do you expect post-graduate pay to change with a $1 increase in university price?
iii. How effective is the regression in explaining variability in earnings? Refer to the R-squared value. Is this value low or high in your opinion? Why?
iv. Are there any noticeable patterns or issues in the residuals? What do they suggest about your model?
2b) Consider transforming either the predictor or dependent variable (e.g., using logarithms or other transformations). Would this improve the model? Justify your decision based on the data.
2c) Select another variable from the dataset that you find interesting. Run a simple linear regression with this variable as the predictor and average earnings as the dependent variable. Analyze the regression in the same way as in Question 2a, and discuss how this variable compares to university price as a predictor of post-graduate earnings.
i. Is that variable significant at the 5% significance level?
ii. How do you expect post-graduate pay to change with a 1 unit increase in your variable?
iii. How effective is the regression in explaining variability in earnings? Refer to the R-squared value. Is this value low or high in your opinion? Why?
iv. Are there any noticeable patterns or issues in the residuals? What do they suggest about your model?
Learning Goal 3: Data Preparation and New Variables
Review the dataset and identify opportunities to create new variables. Using techniques such as IF statements, addition, multiplication, or division, construct at least one new variable to enhance your analysis.
3) Describe the new variable(s) you created. Why did you create them? How did you create them? How do they improve the dataset’s usefulness for regression analysis?
Learning Goal 4: Multiple Regression
Build a multiple regression model incorporating at least:
• Two numerical variables.
• One dummy variable representing a categorical variable.
• One interaction term between two variables.
• Your newly created variable.
4a) Assess the quality of your multiple regression model:
i. Is the overall regression significant? How do you know?
ii. Which variables are significant predictors, and what does their significance tell you about their impact on post-graduate earnings?
iii. How well does the model explain the data (R-squared and adjusted R-squared)?
4b) Compare the results of your multiple regression to the simple linear regressions from Questions 2a and 2c. What additional insights does the multiple regression provide? Are there limitations to the model?
Learning Goal 5: University Comparisons
5a) Select your top-choice and bottom-choice universities (excluding USC) when you were applying for college. Search online for their costs and average exam scores, as well as USC’s. Submit those figures for this question, and where you found them.
5b) Using your regression model from Question 4a, predict post-graduate earnings for students from both your top- and bottom-choice universities.
5c) Compare these predicted earnings to the predicted earnings for USC students. Are the predictions consistent with your expectations? Explain why or why not.
5d) Reflect on the results. What do these predictions suggest about the factors influencing post- graduate earnings? Are there any surprises in your findings?
Learning Goal 6: Reflection on Strengths and Preparation for the Future
6a) Reflect on your personal strengths in completing this project. What aspects of the project came naturally to you? What are you most proud of in your work, and why?
6b) Identify areas where you feel you could improve. Were there any specific parts of the project that felt particularly challenging or tedious? How might you overcome these challenges in the future?
6c) Consider how this project has prepared you for future job opportunities. How did working on this project help you think about using data to solve real-world problems? How will you communicate your strengths and the skills you demonstrated in this project to future employers?
Deliverables
Report: A written document with the following points. It should be written narratively, like a journal article, addressing the points above.
1. Answers to all questions above, including detailed justifications and analyses.
2. Clear presentation of regression outputs, residuals, and any transformations made.
3. Visualizations to support your findings, where appropriate.
4. A discussion of assumptions and limitations for your models.
5. Learning goal 6 should be on a separate page as everything else --- it is for you to use when applying for things.
Submission Details
• Format: Submit a PDF report with Excel output included.
• Grading Criteria:
o Clarity and depth of analysis.
o Justification and reasoning.
o Presentation and accuracy of results.
o Style. it should be formatted as a narrative piece, as if written for an academic journal.
o Quality of the reflection piece.