7.4 Assumptions

Many of the assumptions for regression are on the form of the residuals, which can’t be assessed until after the model has been fit.

Assumptions to check before modeling

• Randomness / Independence
  • Very serious
  • Can use hierarchical models for clustered samples
  • No real good way to “test” for independence. Need to know how the sample was obtained.
• Linear relationship
  • Slight departures OK
  • Can use transformations to achieve it
  • Graphical assessment: Simple scatterplot of \(y\) vs \(x\). Looking for linearity in the relationship. Should be done prior to any analysis.

Assumptions to check after modeling

• Homogeneity of variance (same \(\sigma^{2}\))
  • Not extremely serious
  • Can use transformations to achieve it
  • Graphical assessment: Plot the residuals against the x variable, add a lowess line. This assumption is upheld if there is no relationship/trend between the residuals and the predictor.
• Normal residuals
  • Slight departures OK
  • Can use transformations to achieve it
  • Graphical assessment: normal qqplot of the model residuals.