Due to the COVID-19 pandemic, testing what is required to support teachers and students while subject to forced online teaching and learning is relevant in terms of similar situations in the future. To understand the complex relationships of numerous factors with teaching during the lockdown, we used administrative data and survey data from a large Danish university. The analysis employed scores from student evaluations of teaching and the students’ final grades during the first wave of the COVID-19 lockdown in the spring of 2020 as dependent targets in a linear regression model and a random forest model. This led to the identification of linear and non-linear relationships, as well as feature importance and interactions for the two targets. In particular, we found that many factors, such as the age of teachers and their time use, were associated with the scores in student evaluations of teaching and student grades, and that other features, including peer interaction among teachers and student gender, also exerted influence, especially on grades. Finally, we found that for non-linear features, in terms of the age of teachers and students, the average values led to the highest response values for scores in student evaluations of teaching and grades.