## 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.