Logistic Regression. Linear regression – numerical response Logistic regression – binary...

Logistic Regression

• 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

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

...1

log 332211

XbXbXbap

p

Theory

Lung CancerAn age effect?Associated with smoking?

Logistic Regression• Assess whether a variable is significantly

associated with the response• Quantify the association, in terms of odds ratio

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

pp

1log

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

pp

1log

Note the encodings!

Interpret based on encodings

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.