(c) Now specify ‘ring’ as a variate instead of a factor. Fit this new model to the data by mixed modelling. Do the results confirm that there is a linear trend from Ring 1 to Ring 4? Does this trend vary significantly depending on the oil type?

Note that when this change is made to the model, DFring is reduced from 3 to 1, and DFoil.ring from6 to 2.