The present study is a secondary analysis of a randomized control trial that had established the causal impact of MyTeachingPartner (MTP) coaching for improving the quality of teacher-student interactions. This study reports auxiliary analyses of the extent to which MTP was associated indirectly with classroom engagement and literacy outcomes for pre-kindergarten (pre-K) students as a function of the association of dosage of MTP cycles with teacher-student interactions. The number of coaching cycles a teacher completed was examined as a predictor of teacher-student interactions, as were corresponding direct or indirect associations with students' early literacy outcomes. The significant indirect effects detected provided support for the premise that coaching can improve student outcomes as a function of improvements in teachers' behaviors with students. When exposed to more cycles of feedback regarding interactions, teachers demonstrated improvements in their emotionally supportive interactions with students, which in turn predicted greater increases in students' positive classroom engagement. No significant indirect associations were detected for literacy outcomes. This linkage of coaching inputs, teacher-student interaction, and students' increased engagement confirms the hypothesized effects and theory of change associated with MTP and of coaching more generally. (author abstract)