Consistent estimates of variances:

With heteroscedasticity, the biased and inconsistent estimates of the variances of the OLS  parameter estimates causes statistical  inferences  to be invalid. White (1980) has suggested a method for  obtaining consistent  estimates  Of  variance and covariance of OLS estimates which provides valid  statistical tests for large samples. The heteroscedasticity-consistent  estimator (HCE)  is based on  the principle of maximum likelihood.

In the two-variable regression model  

generates a biased estimate of thevariance of  P. An unbiased estimator is

The heteroscedasticity-consistent estimator uses equation as its basis, replacing  the unknown σ² with  the squares of  the  residuals ε.  With HCE estimation, the R²  for the regression will be the same, but all estimates  of standard errors and related statistics will change because  they are now consistent estimates. While  the use of the HCE estimator does generate consistent variance estimates, it does not provide the most efficient  parameter estimates. For efficient estimation, one of  the weighted least squares estimatioh procedures must be used.