Logistic Regression

1
Logistic Regression

• An Introduction

2
Uses

• Designed for survival analysis- binary response
• For predicting a chance, probability, proportion
  or percentage. Results are in the form of an odds
  ratio.
• Response is bounded with 0 p 1.
• Provides knowledge of the relationships and
  strengths among the variables (e.g., smoking 10
  packs a day puts you at a higher risk for
  developing cancer than working in an asbestos
  mine).

3
Examples

• Use college ACT or SAT scores to predict whether
  individuals would receive a grade of B or better
  in a given math course (to help with placement.)
• Use various demographic and credit history
  variables to predict if individuals will be good
  or bad credit risks.
• Use various demographic and purchasing
  information to predict if individuals will
  purchase from a catalogue sent to their homes.
• Others?

4
Maximum Likelihood Estimation

• Complex calculation statistical programs will
  run these analyses

5
Interpreting ßs

• The ß coefficients estimate the change in the
  log-odds when xi is increased by 1 unit, holding
  all other xs in the model constant.
• Antilog of the coefficient estimates
  the odds-ratio
• estimates the percentage increase
  (or decrease) in the odds for every 1-unit
  increase in xi

6
Testing Model Adequacy

• This is a Chi Square Distribution
• In Minitab, look for the G and corresponding
  p-values.