The present study has developed regression models to study the impact of side friction factors on speeds of vehicles in urban roads. The factors that were considered are on-street parking, pedestrian movement, water stagnation, encroachment, poor road condition and wrong side driving. Three locations from Vellore and Chikmagalur cities in India were selected and vehicle speeds, side friction parameters and flow were collected through videographic survey for 6 hours duration. It was found that the speeds of vehicles were in the range of only 11-23 km/h due to side friction. The study has proposed a "simple arithmetic operand" method to overcome the multicollinearity problem and it predicts well, the speeds with mean absolute percentage error (MAPE) between 8-29 %. The arithmetic operand method proposed in the present study can be applied in other fields as well to overcome the multicollinearity problem.