7.6 Assumptions

  • 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.
  • 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.