Logistic Regression

Linear regression – numerical response Logistic 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 response Logistic 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 Theory

Lung Cancer An 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 Smoke Gender (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

Smoke Gender (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(  30) = 5.58 times more likely than a non-smoking female of age 20

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.