Methods and apparatus for predicting colorant usage by printing devices are provided. A prediction server can receive a request to predict colorant usage for a first printing device. The prediction server can determine first plurality of functions to predict colorant usage for the first printing device. The first plurality of functions can include at least one linear function and at least one non-linear function. The first plurality of functions can be based on colorant-usage rates indicating historical rates of change in colorant used by the first printing device. The prediction server can determine a prediction of colorant usage for the first printing device using the first plurality of functions. The prediction server can provide an output involving the prediction of colorant usage for the first printing device, where the prediction of colorant usage can include a confidence interval related to the prediction.