What are the dangers of violating the homoscedasticity assumption for linear regression?

Question

As an example, consider the ChickWeight data set in R. The variance obviously grows over time, so if I use a simple linear regression like:

m <- lm(weight ~ Time*Diet, data=ChickWeight)

which aspects of the model will be questionable? Are the problems limited to extrapolating outside the Time range? How tolerant is linear regression to violation of this assumption (i.e., how heteroscedastic does it have to be to cause problems?).

Answer 1

The linear model (or "ordinary least squares") still has its BLUE (Best Linear Unbiased Predictor) properties.

In the face of heteroskedasticity in error terms, you still have unbiased parameter estimates but you loose on the covariance matrix: your inference (i.e. parameter tests) may be off. The common fix is to use a robust method for computing the covariance matrix aka standard errors. Which one you use is somewhat domain-dependent but White's method is a start.

And for completeness, serial correlation of error terms is worse as it will lead to biased parameter estimates.

Answer 2

Absence of homoscedasticity may give unreliable standard error estimates of the parameters. Parameter estimates are unbiased. But the estimates may not efficient(not BLUE). You can find some more in the following link