Logistics Regression

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Logistics Regression
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Background

• Y is a 0 or 1 yes or no true or false
  etc.
• Simple Linear and Multiple Regression are not
  suitable
• Need a new method

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Odds

• Let P P(Y 1)
• O(Y1) P/(1-P)
• Example p .2 ( 1 P) .8
• O(Y 1) .2/.8 .25 or 1 to 4

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Logistic Model
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Problems

• Non normal error terms
• Non constant variance
• Constraints on parameters

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Logit
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Example Table 14.1

• What is the predicted probability of success when
  x 25?
• What is the predicted probability of success when
  x 14?
• What is the interpretation of beta1?

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Example Task Success
SLR Fit
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Logistic Fit
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Interpretation of beta1
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Beta1
What does the .161 mean? What does the 1.175
mean? Compare a person with 10 months to a
person with 25 months, what is The odds ratio?
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Likelihood Function
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-2loglikelihood

• Measure of Goodness of Fit.
• We start with a model with just the constant term
  and compute the -2loglikelihood
• We compute the -2loglikelihood for the model
  with more terms
• We compute the difference between which is a
  Chi-square.
• We would like -2loglikelihood to go to zero.

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Hypothesis Testing
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Other Topics

• Estimation
• Subset selection
• Interpretation
• Multi-collinearity
• Problem Points