Assumptions

What is the consequence of a violation of constant (and finite) error variance?

SE bias (and thus type 1 error and inferences)

What is the consequence of violation of uncorrelated errors?

SE bias (and thus type 1 error and inferences)

What is teh consequence of violation of strictly exogenous predictors?

Parameter bias

What is the consequence of violation of normally distributed errors?

Small sample inferences may be biased

How do you detect violation of constant (and finite) error variance?

Residual plots, breusch-Pagan test

How do you detect violation of uncorrelated errors?

Autocorrelation, Intraclass correlation coefficient (ICC)

How do you detect violation of strictly exogenous predictors?

Think about it in advance

How do you detect violation of normally distributed errors?

Kurtosis, skewness, Shapiro wilk, kolmogorov-smirnov

How do you treat violation of constant (and finite) error variance?

Weighted least squares, HC variance estimator, adjusting model may also help (check nonlinear trends with RESET (regression equation specification error test); remove influential observations

How do you treat violation of uncorrelated errors?

Adjust model, multilevel modeling, HC variance etsimator

How do you treat violation of strictly exogenous predictors?

Add omitted variables to the model

How do you treat violation of normally distributed errors?

Rely on central limit theorem for larger sample size, bootstrapping for moderate sample size, remove influential observations