The aim of this paper is the development of driver speed models based on detailed driving data collected from smartphone sensors. More specifically, this research investigates to which extent various driving behaviour parameters (harsh acceleration and deceleration events, driving distance, percentage of driving time per different road types, etc.) interact with each other and how these might potentially serve as driving speed predictors. Real time driving behaviour data collection was carried out using a smartphone application. Data were collected from 100 drivers and a total of 18,853 trips between July and December 2016. Six different linear regression models are developed to predict average driving speed under different driving conditions. One model for each road type (urban, rural and highways), one model for the risky hours period and one for the rest of the day, and a general model. The results indicated that the distance covered by the driver, the number of the harsh events occurred and the average deceleration are the strongest predictors of the average speed of a driver.