How to detect heteroscedasticity and rectify it?

One of the important assumptions of linear regression is that, there should be no heteroscedasticity of residuals. In simpler terms, this means that the variance of residuals should not increase with fitted values of response variable. In this post, I am going to explain why it is important to check for heteroscedasticity, how to detect it in your model? If is present, how to make amends to rectify the problem, with example R codes. This process is sometimes referred to as residual analysis.