Research on predictors of achievement in science is often targeted on more traditional content-based assessments and single student characteristics. At the same time, the development of skills in the field of scientific inquiry constitutes a focal point of interest for science education. Against this background, the purpose of this study was to investigate to which extent multiple student characteristics contribute to skills of scientific inquiry. Based on a theoretical framework describing nine epistemological acts, we constructed and administered a multiple-choice test that assesses these skills in lower and upper secondary school level (n?=?780). The test items contained problem-solving situations that occur during chemical investigations in school and had to be solved by choosing an appropriate inquiry procedure. We collected further data on 12 cognitive, motivational, and sociodemographic variables such as conceptual knowledge, enjoyment of chemistry, or language spoken at home. Plausible values were drawn to quantify students' inquiry skills. The results show that students' characteristics predict their inquiry skills to a large extent (55%), whereas 9 out of 12 variables contribute significantly on a multivariate level. The influence of sociodemographic traits such as gender or the social background becomes non-significant after controlling for cognitive and motivational variables. Furthermore, the performance advance of students from upper secondary school level can be explained by controlling for cognitive covariates. We discuss our findings with regard to curricular aspects and raise the question whether the inquiry skills can be considered as an autonomous trait in science education research.