Can outlier data points included while fitting regression modeling?

Question

I have few data points which is somewhat different from all other data points. But these data points are genuine and makes business sense. While building regression modeling, can we include those points or should ignore it. How can I justify it to people with no modeling background on my decision on exclusion or inclusion of outlier points for modeling.

Answer 1

You should certainly not delete points just because they are outliers. But you can't then apply a model that assumes there are no outliers. Instead, change your method from OLS regression (which is what I assume you are using) to another method that doesn't have problems with outliers. I like quantile regression, personally, but robust regression is also good for these purposes.