Is robust regression less sensitive towards outlier and how?



I recently read about robust regression techniques and that it is less sensitive towards outlier compared to methods like least squares. Please help me to explore this method more and how it is efficient in dealing with outlier and influential observations?

Would appreciate, if you help me with the R or Python library which have the module to perform robust regression.




In case of a standard linear regression the coefficients are computed by minimizing the sum of residuals. Here in robust regression a weight is multiplied with each residual depending on the weightage given to each point( sum(weight*residuals)). So we can assign low weights for outliers and high weights for influential points by defining some weight function accordingly. If you look closely standard linear regression is a special case of robust regression where weight of any point is 1.

This link will help you with doing this in R.