Originally, we were going to build high dimensional statistical learning systems crunching large datasets on GPUs in Haskell.
90% of clients cannot feed me the data, so I end up building them a data warehouse first; in some cases we even redo their data model. 100% of clients have datasets too small to justify getting out of R and single CPUs, so our Haskell ML libraries are, so far, on the wishlist only (I think Tweag has had more success there, but I still have feeble hope that one day...) Hence the RM focus as well as ML. The ML side is sort of picking up this month.
That being said, I'm not actually that well versed in ML. Just the guy running the company. I've built (and read) just enough to know how it works, how it applies to clients and who to hire to get the job done properly...
A value with x close to the mean, but extremely high y would barely move the line as a whole up or down as you vary y. The gradient would not be much affected.
A value with extremely high x does not need to move much to change the gradient of the line. You might even change the sign of the gradient.
Both are outliers but the second has higher leverage than the first.
Edit: illustration: http://imgur.com/vVKwjHh (right hand side are high leverage)