The superimposed LOESS curve (Locally weighted scatterplot smoothing: a non-parametric technique that graphically represents a curve of best fit without assumptions of data distribution (Cleveland and Devlin, 1988) is not necessary but can facilitate the detection of linearity violation (technical note: an Excel® linear regression add-in allows the construction of residuals vs fitted plots, without the LOESS function, which can be found in R). Where the relation is not linear in form, it is not possible to perform a simple linear regression; one of several other options would be more appropriate, as described below.