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LINEAR REGRESSION
Jeff Goldsmith, PhD
Department of Biostatistics
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• Linear regression is one approach to modeling
Modeling
R for Data Science
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• Like … seriously. I use regression for everything
• Regression covers simple stuff (t-tests) to complex stuff (automated variable
selection via penalization)
– Yes, I use regression for t-tests
Regression is my favorite
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•
Linear models
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• Outcome is continuous; predictors can be anything
• Continuous predictors are added directly
• Categorical predictors require dummy indicator variables
– For each non-reference group, a binary (0 / 1) variable indicating group
membership for each subject is created and used in the model
Predictors
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•
Testing
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• Many model assumptions (constant variance, model specification, etc) can be
examined using residuals
– Look at overall distribution (centered at 0? Skewed? Outliers?
– Look at residuals vs predictors (any non-linearity? Trends? Non-constant
residual variance?)
Diagnostics
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Generalized linear models
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• lm for linear models
• glm for generalized linear models
• Arguments include
– Formula: y ~ x1 + x2
– Data
• Output is complex, and also kind of a mess
– Use the broom package!
Linear models in R