You are planning a multiple linear regression analysis to predict profitability for companies in the region. One of the variables— type of company— is categorical. You plan to use dummy variables to introduce this factor into the model. There are five “type of company” categories: financial, basic manufacturing, engineering, retail, and fabrication. 

a. Define an appropriate set of dummy (binary) variables.

b. illustrate how you would interpret the coefficients produced by a regression software package for this set of dummy variables. Use hypothetical examples to demonstrate your interpretation.