The linearity assumption in a regression model states that the conditional expectation value
of the response variable is linear in the model parameters. For a predictor vector
,
the standard multiple linear regression model
assumes
 |
Linearity here is with respect to the unknown parameters 
, not necessarily the raw predictors. For example, transformed
predictors and polynomials can
enter the model while it remains linear in its coefficients. Systematic curvature
in a residual vs. predictor plot can
indicate a failure of the assumption; transformations or a different regression
model may then be appropriate.
The linearity assumption is distinct from assumptions that the errors are independent, have constant variance (homoscedasticity), or are normally distributed. Those additional conditions are used for particular estimators or inferential procedures.
