In the context of OLS regression I understand that a residual plot (vs fitted values) is conventionally viewed to test for constant variance and assess model specification. Why are the residuals plotted against the fits, and not the $Y$ values? How is the information different from these two plots?
I am working on a model that produced the following residual plots:
So the plot vs the fitted values looks good at quick glance, but the second plot against the $Y$ value has a pattern. I'm wondering why such a pronounced pattern wouldn't also manifest in the residual vs fit plot....
I'm not looking for help in diagnosing issues with the model, but just trying to understand the differences (generally) between (1) residual vs fit plot & (2) residual vs $Y$ plot.
For what it's worth, I'm sure the error pattern in the second chart is due to omitted variable(s) which influence the DV. I'm currently working on obtaining that data, which I expect will help the overall fit and specification. I am working with real estate data: DV=Sales Price. IVs: Sq.ft of house, # garage spaces, year built, year built$^2$.