I am fitting a linear model to a problem, and a little confused by what is going on. Without the details here are the two plots confusing me:

Residuals vs Fitted

![Residuals vs Fitted][1]

Residuals vs Y

![Residuals vs Y][2]

Now the residuals vs fitted looks good to me. Fairly evenly dispersed, no clear pattern. However, the $y$ vs fitted do not look good. I would have expected there to also not be a clear trend in this relationship. 

This seems basic, but I'm rather lost. I don't want to fit a model that allows large positive errors at high values of $Y$ to make up for large negative errors at low values of $Y$.

Is this just an indication of a poorly fitting model? Or is something else going on here?

EDIT: Asked for fitted vs y (changed to have labels)

![fitted vs y][3]

EDIT2: Just want to point out that this question has already been asked and answered (albeit in a more abstract sense) https://stats.stackexchange.com/questions/5235/what-is-the-expected-correlation-between-residual-and-the-dependent-variable?rq=1 .


  [1]: https://i.sstatic.net/gWcb1.png
  [2]: https://i.sstatic.net/LsRTw.png
  [3]: https://i.sstatic.net/QPl5t.png