Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 30 / 4 / a / Solution

Measurements from the same person share baseline strength and likely share an individual response to training. An ordinary linear model with independent errors treats all 600 readings as independent conditional on week; that fails to represent their within-person correlation. The regression residuals can remain associated even when the population mean is linear in time. A random intercept captures differences in baseline strength, and a random slope can additionally describe differences in progress.