Network function virtualization (NFV) proposes to replace physical middleboxes with more flexible virtual network functions (VNFs). To dynamically adjust to ever-changing traffic demands, VNFs have to be instantiated and their allocated resources have to be adjusted on demand. Deciding the amount of allocated resources is non-trivial. Existing optimization approaches often assume fixed resource requirements for each VNF instance. However, this can easily lead to either waste of resources or bad service quality if too many or too few resources are allocated. To solve this problem, we train machine learning models on real VNF data, containing measurements of performance and resource requirements. For each VNF, the trained models can then accurately predict the required resources to handle a certain traffic load. We integrate these machine learning models into an algorithm for joint VNF scaling and placement and evaluate their impact on resulting VNF placements. Our evaluation based on real-world data shows that using suitable machine learning models effectively avoids over- and under-allocation of resources, leading to up to 12 times lower resource consumption and better service quality with up to 4.5 times lower total delay than using standard fixed resource allocation.