Which plot to check for heteroscedasticity in a multiple regression model I have a linear model like:
Reg.Model = lm(Y~X1+X2+X3, data=DF)

If I want to check for the presence of heteroscedasticity using a plot, should I plot the residuals with the estimated Y, or the observed Y?  That is, in R:
plot(Reg.Model$residuals, Reg.Model$fitted.values)

or
plot(Reg.Model$residuals, Y)

 A: You don't typically want to use a plot with the observed $Y$ values, because there can be a 'tilt' in the relationship, and that can make things harder to see.  In this case, I'm not sure it makes much difference, but because of that general principle, the default is to use fitted / predicted values.
In addition, we typically put the residuals on the vertical axis, not the horizontal axis, as @SalMangiafico notes.  That way, you are looking for changes in vertical spread, not horizontal.  That will also mirror the way we typically think of the variables (i.e., we put the Y variable on the Y axis, and X on X).
If you use R's inbuilt ?plot.lm function, you can get another plot, the scale-location plot, which can make the detection of heteroscedasticity even easier.
To see these three points, it may help to read my answer to: What does having “constant variance” in a linear regression model mean?, in particular, the three sets of plots at the bottom.  In the top row, the 'tilt' makes heteroscedasticity harder to see.  The middle row is what you have in mind, albeit with the residuals on the Y axis.  The bottom row shows the scale-location plots.
