Residual Plots - Banding I came across a question on residual plots asking to consider the plot $(x_i,e_i)$ for $i=1,\cdots,n$. Discuss the conclusion that may be drawn if the plot $A)$ is approximately a horizontal band $B)$ fans out to the right $C)$ is approximately curved band It may be a trivial question, but what is banding? what is meant by horizontal band, curved band and fanning out to the right? What are the different types of these that could be asked and what do they mean? Thanks :)

In this case, band is a vague term used to refer to the general shape of the scatterplot. If (A) is true, then there is little or no evidence to refute the usual regression assumptions (i.e. $\epsilon_i$ are independent and identically distributed according to a normal distribution with mean 0 and variance $\sigma^2_\epsilon$.

If (B) is true, then this suggests that the variance of the error terms is dependent on $x$. You might speculate that $\sigma^2_\epsilon$ isn't constant but rather an increasing function of $x$.

If (c) is true, then the fundamental assumption that $Y_i = \beta_0 + \beta_1 X_i + \epsilon_i$ isn't true. If you see a curve in the residual plot, then that may suggest that the mean of $Y$ has a curved (possibly quadratic) relationship with $X$.