Linear regression

Author

Olga Dethlefsen

Linear models allows us to answer questions such as:

is there a relationship between exposure and outcome, e.g. height and weight?
how strong is the relationship between the two variables?
what will be a predicted value of the outcome given a new set of exposure values?
how accurately can we predict outcome?
which variables are associated with the response, e.g. is it only height that explains weight or could it be height and age that are both associated with the response?

Learning outcomes

to understand what a linear model is and be familiar with the terminology
to be able to state linear model in the general vector-matrix notation
to be able to use the general vector-matrix notation to numerically estimate model parameters
to be able to use lm() function for model fitting, parameter estimation, hypothesis testing and prediction
to be able to evaluate model fit by interpreting \(R^2\) and \(R^2(adj)\) values
to be able to check model assumptions
to be able to use glm() for extending linear models into generalized linear models