Solution (source code)

= Solution

Model 1's residuals have a systematic curved pattern and a spread that grows strongly with fitted time. This indicates an incorrect linear mean on the original scale and <heteroscedasticity>; several observations are also influential or outlying. The constant-variance assumption is therefore implausible.

Logging time greatly stabilizes the spread and removes most of the mean pattern, so model 2 is much more compatible with constant conditional variance and linearity. A few conspicuous residuals remain. A residual-versus-fitted plot alone does not check <independent random variables>[independence] or fully establish <normal distribution>[normality].