Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 30 / 1 / e

The simple linear regression assumes a straight conditional mean, $E(Y_i\mid x_i)={\beta }_0+{\beta }_1{x}_i$, so that errors are centred at zero throughout the predictor range. The displayed regression residuals are predominantly positive at both ends and negative in the middle. This is a residual curvature diagnostic: the fitted straight line misses a curved conditional mean. The main concern is the shape of the mean function. The plot alone does not establish failure of the normal distribution assumption or a particular error variance model.