Lesson 5: Multiple Regression Variable Selection

September 29, 2025

Review:

• Intro to Multiple Regression

Presentation:

• Variable Selection Procedures
  • Variable Selection
  • Backward Elimination then Forward Selection
  • Demonstrate with East Pueblo RE Sales 2014-2016
• Modeling Objective:
  • Achieve highest R^2 possible
    • For some data this may be below 0.50
    • Don’t sacrifice too much significance for small gains in R^2
  • Achieve high F-statistic
    • Fewer variables = generally preferable (keep it simple)
    • Significance of F (p-value) should be <0.05, lower is better
    • Individual variables should have p-value < 0.05
    • Occasionally it’s appropriate to make exceptions
  • Find a good balance between F and R^2

Activity:

• Produce a model to estimate MLB winning percentage
  • Use 2013 MLB Team statistics
  • Produce a Final Model, aiming to maximize both R^2 and F-Statistic
• Compile 2025 MLB Team data and build a new model
  • Here’s a head start with all MLB teams and 2025 Wins, Losses and Payroll
  • Use Baseball Reference to add other variables (e.g., ERA, RBIs, etc)
  • Produce a Final Model, aiming to maximize both R^2 and F-Statistic