11  Assignment 10: Wage Analytics — Predicting High vs Low Earners Using Logistic Regression

Binary Classification • Logistic Regression • Model Evaluation • ROC/AUC

12 Overview

The Wage Analytics Division (WAD) has hired you as their new Data Scientist.

Your mission is to determine whether demographic and employment characteristics can be used to predict whether a worker earns a high or low wage.

Using the Wage dataset from the ISLR package, you will:

  • Create a binary wage classification
  • Explore relationships between predictors and wage
  • Build a logistic regression model
  • Evaluate predictive performance on unseen data

Your analysis will help the company understand which characteristics are associated with higher earnings and determine how well a predictive model performs in practice.

13 Learning Objectives

By completing this assignment, you will be able to:

  • Clean and prepare mixed-type real-world data
  • Create a binary outcome variable
  • Conduct t-tests, ANOVA, and Chi-Square tests
  • Perform a train/test split
  • Build and interpret a logistic regression model
  • Evaluate classifier performance using confusion matrices and ROC/AUC
  • Communicate predictive modeling results clearly and professionally

14 Textbook Connection

This assignment builds directly from Chapter 9: Logistic Regression in Reproducible Research Using R.

Students are encouraged to review the chapter before beginning this assignment, as it provides the conceptual foundation and reproducible workflow demonstrated here.

15 Submission Instructions

Submit two files:

  1. Your .qmd file
  2. Your knitted and published .html file

Your document must:

  • Knit without errors
  • Suppress warnings and messages in the final HTML
  • Include clearly labeled sections
  • Include all statistical tests and model outputs
  • Include performance metrics and ROC curve
  • Include a professional final summary
  • Use at least one inline R expression

16 Assignment Tasks

16.1 1. Create the WageCategory Variable

Begin by preparing the dataset.

16.1.1 Required Tasks

  • Load the Wage dataset from the ISLR package

  • Create a new factor variable called WageCategory:

    • If wage > median(wage) → "High"
    • If wage < median(wage) → "Low"

  • Convert WageCategory into a factor variable

16.1.2 Important

  • You must NOT remove wage or logwage
  • Be prepared to explain the concept of target leakage and why it matters in predictive modeling

Briefly explain why creating a binary outcome transforms this into a classification problem.

16.2 2. Data Cleaning

Some categorical variables in the Wage dataset contain numeric prefixes (e.g., "3. Asian").

16.2.1 Required Tasks

  • Remove numeric prefixes from all relevant categorical variables
  • Ensure categorical variables are clean and properly formatted before analysis

Provide a brief explanation of why cleaning categorical labels is important for interpretation and modeling.

16.3 3. Classical Statistical Tests

You will explore relationships between predictors and wage using classical inference methods.

16.3.1 A. t-test

Compare age between High and Low wage earners.

Your write-up must include:

  • Mean age for each wage group
  • t-statistic, degrees of freedom, and p-value
  • A short interpretation of whether age differs between wage categories

16.3.2 B. ANOVA

Using the original numeric wage variable, choose one of the following:

  • wage ~ education
  • wage ~ maritl
  • wage ~ jobclass

Your write-up must include:

  • ANOVA table
  • F-statistic, degrees of freedom, and p-value
  • A brief interpretation of the result

16.3.3 C. Chi-Square Test

Choose one categorical relationship that is different from your ANOVA variable.

You must:

  • Create a contingency table
  • Conduct a Chi-Square test
  • Report χ², df, and p-value
  • Compute and interpret Cramer’s V
  • Describe any patterns observed in the contingency table

Explain what the Chi-Square test tells you about association.

16.4 4. Logistic Regression Model

You will now build a predictive model.

16.4.1 Train/Test Split

  • Perform a 70/30 split using sample.split()
  • Clearly define your training and testing datasets

Explain why separating training and test data is critical in predictive modeling.

16.4.2 Model Specification

  • Build a logistic regression model predicting WageCategory
  • Choose predictors thoughtfully (be cautious of leakage or redundancy)

Your write-up must include:

  • Logistic regression output

  • Odds ratios using exp(coef())

  • A 2–4 sentence interpretation describing:

    • Which predictors are significant
    • Direction of effects
    • Magnitude of effects
    • Any surprising findings

16.5 5. Model Evaluation on Test Data

Using your test dataset, compute:

  • Predicted probabilities
  • Predicted classes (“High” or “Low”)
  • Confusion matrix

Report and interpret:

  • Accuracy
  • Sensitivity
  • Specificity
  • Balanced Accuracy

16.5.1 ROC Curve and AUC

  • Generate an ROC curve
  • Compute AUC

In your interpretation, discuss:

  • How well the model identifies high earners
  • How accuracy compares to the No Information Rate
  • Whether the model performs better than guessing

16.6 6. Final Interpretation

Write a professional 3–5 paragraph summary addressing:

  • Whether age, education, jobclass, or marital status meaningfully relate to wage
  • Which predictors were most influential in the logistic regression
  • How well the model performed on unseen data
  • Which wage group the model predicts best
  • What variables you would add or remove if repeating the analysis
  • One limitation of your modeling approach

Your tone should resemble a professional data science report, not a homework answer.

17 Guidelines for Interpretation

When interpreting regression results, include:

  • Direction (positive or negative relationship)
  • Magnitude (odds ratio interpretation)
  • Statistical significance
  • Plain-language meaning

Example:

Workers with higher education levels have greater odds of being classified as high earners, holding other factors constant.

Avoid technical jargon without explanation.

18 Reflection

In 4–6 sentences, answer:

  1. What is the difference between inference and prediction?
  2. Why is target leakage dangerous in predictive modeling?
  3. What did you learn about evaluating classifier performance?

19 Reproducibility Practice

This assignment emphasizes responsible predictive modeling.

Your document must:

  • Load data programmatically
  • Clean variables reproducibly
  • Use clearly labeled code chunks
  • Avoid hard-coding values in narrative
  • Use inline R expressions where appropriate
  • Suppress warnings and messages in the final HTML
  • Render cleanly without manual edits

The goal is that another analyst could reproduce your entire workflow and validate every statistical claim.

20 Publishing Instructions

  1. Render your .qmd file to HTML.
  2. Confirm warnings and messages do not appear in the final document.
  3. Submit both your .qmd file and your published .html report.