Effective use of learning analytics systems has been purported to confer various benefits to learners in terms of both attainment and retention. There is, however, little agreement on which data are meaningful or useful. Whilst measures of engagement might correlate with outcomes, thereby retrospectively 'predicting' them, there are fewer studies which attempt to predict using 'live' system data in a face-to-face teaching environment. This study reports an analysis of week by week data from a learning analytics system which monitored 1,602 first year UK undergraduates. Uniquely, although students could view their own data, no formal interventions took place. Results showed that students who obtained the highest end-of-year marks were more likely to be in a higher engagement quintile as early as the first 3-4 weeks, and that early engagement was highly predictive of future engagement. Students who started in a higher engagement quintile, but their engagement decreased, were more likely to have higher marks than those that started in a lower quintile and then increased their engagement. Early measures of engagement are therefore predictive of future behaviour and of future outcomes, a finding which has important implications for universities wishing to improve student outcomes.