The standard dementia screening tool Mini Mental State Examination (MMSE) and the standard dementia staging tool Clinical Dementia Rating Scale (CDR) are prominent methods for answering questions whether a person might have dementia and about the dementia severity respectively. These methods are time consuming and require well-educated personnel to administer. Conversely, cognitive tests, such as the Semantic Verbal Fluency (SVF), demand little time. With this as a starting point, we investigate the relation between SVF results and MMSE/CDR-SOB scores. We use regression models to predict scores based on persons' SVF performance. Over a set of 179 patients with different degree of dementia, we achieve a mean absolute error of of 2.2 for MMSE (range 0–30) and 1.7 for CDR-SOB (range 0–18). True and predicted scores agree with a Cohen's κ of 0.76 for MMSE and 0.52 for CDR-SOB. We conclude that our approach has potential to serve as a cheap dementia screening, possibly even in non-clinical settings.