Assumptions
The normal linear model is:
y = β0 + β1x + ε
ε ~ normal (0 , σ)
The following four requirements are implicit in the model but may be violated, as illustrated by the examples.
Linearity The response may change nonlinearly with x. |
Constant standard deviation The response may be more variable at some x than others. |
Normal distribution for errors The errors may have skew distributions. |
Independent errors When the observations are ordered in time, successive errors may be correlated. |
Residual plots
The above problems may be evident in a scatterplot of the raw data, but a residual plot often highlights any problems.