Interpretation of residual plots Here is a question in the book of Freedman p.189.

 The answers provided are
(a) ( i)&(ii)
(b) not used
(c) something wrong
My biggest confusion is the answer for (c), what is wrong with this residual plot?
The second biggest headache is (a) could be an answer represented by both (i) and (ii). Intuitive it seems ok. But I am unsure how it get calculated as 1000 from (i), (ii).
Hope to hear some helps. I wish an explanation at 1st year level without invoking the term endogeneity/exogenous etc.
 A: Picture (iii) denotes a clear linear relationship, which should have been detected and exploited by the initial linear regression; that lead to these residuals. That is why something went wrong. 
The absolute observed errors in (i) and (ii) lie between 0 and 2000. None comes close to 5000.
Edit:
Let there be $n$ individuals. If the linear regressions follows the form of 
$$y_{i} = \beta_0+\beta_1x_{i}+\epsilon_{i}$$ and $\epsilon_{i}$ follows a linear pattern as well, i.e. $\epsilon_{i}={\beta_\epsilon}_0 + {\beta_\epsilon}_1x_{i}+{\epsilon_2}_{i},$ then plugging this error term into the above linear regression yields $$y_{i} = \beta_0+\beta_1x_{i}+{\beta_\epsilon}_0 + {\beta_\epsilon}_1x_{i}+{\epsilon_2}_{i}.$$ You can easily rearrange the above expression into $$y_{i} = (\beta_0+{{\beta_\epsilon}_0})+(\beta_1+{\beta_\epsilon}_1)x_{i}+ {\epsilon_2}_{i}.$$ Note, this too is linear. The algorithm will find those $\beta$s which minimize the sum of squared errors, and that is the one with no linear part in $\epsilon$.
A: Well, let's think about the broader picture first. What does the residual set graph tell us? It's graphing the relationship between some $x_{i}$, an independent variable used in the regression, and the error $\hat{e}_{i} = \hat{Y}_{i} - Y_{i}$. This graph provides a visual aid to tease out relationships between the unexplained component and the non-stochastic elements of the estimation process. 
Okay, so how is RMSE calculated?
$RMSE = \sqrt[]{\frac{\sum_{n=1}^{N}(\hat{Y_{i}}-Y_{i})^{2}}{N}}$. 
So, just looking at the set of values the residual can take, I see you have values of $\hat{e}_{i}$ which approach the absolute value of 2000. It's harder to decisively say without knowing the number of observations but the RMSE seemingly exceeds 1000 in either case. So, if I had to go with either a or b, I'd choose b. 
The third case is a standard example of something we call endogeneity, i.e. $E[e_{i}|x_{i}] \neq 0$.
Edit: It looks like the image is the set of potential residuals realizations. If so, just plug in the largest set of values for $\hat{e}_{i}$ possible for a low $n$ regression and you will see the RMSE is larger than 1000.
