Taxi-calling apps are gaining increasing popularity for their efficiency in dispatching idle taxis to passengers in need. To precisely balance the supply and the demand of taxis, it is essential for the online taxicab platforms to predict Unit Original Taxi Demands (UOTD), which refers to the number of taxi-calling requirements submitted per unit time (e.g. every hour) and per unit region (e.g. each POI). Prediction of UOTD is non-trivial for large-scale industrial online taxicab platforms because both accuracy and flexibility are essential. Complex non-linear models such as GBRT and deep learning are generally accurate, yet labor-intensive model redesign is indispensable after scenario changes (e.g. extra constraints due to new regulations). To accurately predict UOTD while remaining flexible to scenario changes, we propose LinUOTD, a unified linear regression model with more than 200 million dimensions of features. The simple model structure eliminates the need of repeatedly model redesign, while the high-dimensional features contribute to accurate UOTD prediction. Furthermore, we design a series of optimization techniques for efficient model training and updating. Evaluations on two large-scale datasets from an industrial online taxicab platform verify that LinUOTD outperforms popular non-linear models in accuracy. We envision our experiences to adopt simple linear models with high-dimensional features in UOTD prediction as a pilot study and can shed insights upon other industrial large-scale spatio-temporal prediction problems.