Logistic Regression

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Logistic Regression
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Theory

• Linear regression numerical responseLogistic
  regression binary categorical response
• eg. has the disease, or unaffected by the disease
• Interested to find the attributes that are
  associated with the onset of the disease
• Or interested to predict the probability of
  getting the disease, given a set of attributes

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Theory

• Linear regression numerical responseLogistic
  regression binary categorical response
• eg. has the disease, or unaffected by the disease
• Interested to find the attributes that are
  associated with the onset of the disease
• Or interested to predict the probability of
  getting the disease, given a set of attributes
• Fits the model
• Effectively a linear model for log odds

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Lung Cancer
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Logistic Regression

• Assess whether a variable is significantly
  associated with the response
• Quantify the association, in terms of odds ratio

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Logistic Regression

• Assess whether a variable is significantly
  associated with the response
• Quantify the association, in terms of odds ratio
• Consider the equation
• 0.03 1.4 Smoke 0.02 Gender
  0.01 (Age 20)
• where p probability of getting lung cancer
• with baseline of a non-smoking female of age 20
• Keep everything else constant to interpret the
  effects of each variable

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• 0.03 1.4 Smoke 0.02 Gender
  0.01 (Age 20)
• Non-smoking male of age 20 is exp(0.02) 1.02
  times more likely than a non-smoking female of
  age 20 to get lung cancer
• Smoking female of age 20 is exp(1.4) 4.06 times
  more likely than non-smoking female of age 20
• Non-smoking female of age 50 is exp(30 ? 0.01)
  1.35 times more likely than non-smoking female of
  age 20
• Combining the effects
• Smoking male of age 50 is
  exp(1.4 0.02 0.01 ? 30) 5.58times more
  likely than a non-smoking female of age 20

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Note the encodings!
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Interpret based on encodings
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Summary

• Large suite of statistical tools for analysing
  data
• Important to choose the appropriate tools for
  the kind of data available.
• Most statistical tests require particular
  assumptions to be valid need to check these
  assumptions.