Question

multicollinearity

Heteroscedasticity

What are the effects of failing to obey the four key regression assumptions on the

above regression properties?

Answer 1

Consequences of multicollinearity

1. Even extreme multicollinearity (so long as it is not perfect) does not violate OLS assumptions. OLS estimates are still unbiased and BLUE (Best Linear Unbiased Estimators)
2. Nevertheless, the greater the multicollinearity, the greater the standard errors. Note, however, that large standard errors can be caused by things besides multicollinearity.
3. When two IVs are highly and positively correlated, their slope coefficient estimators will tend to be highly and negatively correlated. In other words, if you overestimate the effect of one parameter, you will tend to underestimate the effect of the other. Hence, coefficient estimates tend to be very shaky from one sample to the next.

Consequences of Heteroscedasticity

1. The OLS estimators and regression predictions based on them remains unbiased and consistent.
2. The OLS estimators are no longer the BLUE (Best Linear Unbiased Estimators) because they are no longer efficient, so the regression predictions will be inefficient too.
3. Because of the inconsistency of the covariance matrix of the estimated regression coefficients, the tests of hypotheses, (t-test, F-test) are no longer valid.