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.