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Logistic Regression

Logistic regression is an essential statistical method for predicting binary responses like success/failure or yes/no outcomes. Results are in the form of odds ratios, providing insights into relationships between variables. Learn how to use it with ACT/SAT scores for grade prediction, credit history for risk assessment, and purchase behavior analysis. Extract information about β coefficients and odds ratios to understand the impact of variables. Testing model adequacy is crucial, using Chi-Square Distribution in tools like Minitab for assessing the goodness of fit.

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Logistic Regression

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  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 βs • The β coefficients estimate the change in the log-odds when xi is increased by 1 unit, holding all other x’s 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.

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