Yesterday I was talking with two of my workmates, one of them mentioned that when applying regression methods is not a very good idea to include a lot of similar points as those can cause leverage of the regression. This leverage was supposed to bias a line or model towards the tendency of the data where the distance is shorter, such as in the red line of the following image (assuming that the point added in the blue line is representative and was ignored for the red one regression):
I was curious about methods to avoid leverage, but instead of finding about leverage in general I found about leverage points.
According to Carnegie Mellon community, any point that significantly influences the model fit has leverage. In the same page, they suggest a residuals vs leverage plot to find possible outliers biasing the model.