Many service stations offer self service gasoline at reduced prices when customers pay with cash rather than credit. Suppose an oil company wants to model the mean monthly gasoline sales, E(y), of its affiliated stations as a function of the type of service they offer: cash only, cash or credit (same price), cash or credit (cash at reduced price).

a. How many dummy variables will be needed to describe the qualitative independent variable type of service?

b. Write the main effects model relating E(y) to the type of service. Describe the coding of the dummy variables.