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.