Question

what is heterocscedasticity ? Why its a problem in regression?How do you recognize it? what are the possible solutions for heterosedasticity ?

Answer 1

What is Heteroscedasticity ?

Heteroscedasticity is a problem because ordinary least squares (OLS) regression assumes that all residuals are drawn from a population that has a constant variance . When you draw the residual vs. x plot, and you see a varying residual with respect to x then you have heteroscedasticity. In other words, the a not-contant variation of residuals means that you can't assume homoscedasticity.

Why is a problem:

This situation represents heteroscedasticity because the size of the error varies across values of the independent variable. ... A more serious problem associated with heteroscedasticity is the fact that the standard errors are biased. This means linear regression can't be used in such cases

How to rectify it? i.e.what are the solutions?

1. Re-build the model with new predictors. - this also means including new ones which may try to explain the not constant variance in the data

2. Variable transformation such as Box-Cox transformation. - this means that existing variables if transformed using a function will now have a linear relationship with the dependent variable, and may therefore remove the heteroscedasticity.