We would like to build a linear regression model for Uber to estimate the trip fare using the trip distance (positive real numbers in km) and the origin (the city is partitioned into 4 regions so that any origin belongs to one of them). (a) Write the linear regression model when the region 1 is chosen as the base category. Explain the meaning of the dummy variables. (b) We estimate the model in (a) and find the coefficients of the dummy variables for region 2 and 3 are 0.25 and 0.2 respectively. Now we build another model in which region 2 is chosen as the base category. What are the estimated coefficients of the dummy variables for region 1 and 3 in the new model?