Regression assumptions
Linear regression assumes a straight-line relationship, independent errors, errors with constant spread, and roughly normal errors. Remember it as LINE: Linear, Independent, Normal, Equal spread.
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Analogy
A recipe that only works if the ingredients are what it expects. Check the data before trusting the answer.
Example
Curved residual pattern: not linearFunnel shape: spread not equalRuns above and below: errors linkedSkewed residual histogram: not normal
In practice
Residual plots and histograms of residuals are the main way to check these assumptions.
Practice
Flashcards
- What does LINE stand for?Linear, Independent, Normal, Equal spread.
Questions people ask
What is an influential point in regression?
It is a point that changes the fitted line a lot if removed, usually one far from the others in x. An outlier in y alone changes the line less. Check unusual points, ask why they occurred, and report results with and without them.
What can I do if the assumptions are violated?
Try transforming the variables, for example with a logarithm, to straighten curves and stabilise spread. Add missing predictors, or fit a curve. For correlated errors, such as in time series, use methods designed for that structure, because ordinary least squares then understates uncertainty.