The residual plots are part of the post-analysis to assess model adequacy and the assumptions of the regression model. The residual is the predicted or fitted Y minus the observed Y. The residual estimates the statistical error.
The assumptions include that the statistical errors are independent and identically normally distributed with a mean of zero and a constant variance (i.e., variance is independent of Y). The normal quantile plot results from fitting a normal distribution and plotting the fitted quantiles against the residual value. The scaling is unique to each distribution model. The scaling results in a linear relationship between the quantiles and the errors. In the case of the normal quantile plot, the slope of the line is the standard deviation, and the y-intercept is the mean. If you see a pattern that is not linear overall, then the assumption of normal errors is violated. If you see a linear pattern but one or more quantiles are far from the line at the ends of the plot, then you might have outliers.
The residual by predicted plot is used to assess the adequacy of the model. The identity reference line shows where Y = X. You expect the observations to follow this line. A large departure from the line overall suggests lack of fit. A large departure from the line by some observations suggests outliers. This plot also helps assess the constant variance. The plot should exhibit a uniform spread of residuals from low to high predicted values. That is, the magnitude of the residuals does not depend on the response. The appearance of a funnel shape indicates a violation of this assumption. Ordinary least square regression is inappropriate in such cases.
The assumption that all the statistical error is in Y and none of it is in X is not assessed with the residual plots. They also assume the same thing.
