A chemical company has three plants. Due to a shortage of labor and the intense heat involved in production, only one plant is operated at a time, and operations are shifted every few days to another plant. The company wants to estimate the relationship between daily production Y and the independent variable, labor force present X1. Since the company knows that differnces may exist among the different plants, it proposes a qualitative variable X2 also be used. The variable is defined as X2=1 if plant A is used, 2 if plant B is used, and 3 if plant C is used during the day.
a. Would you use this regression model? Why or Why not?
b. Please write the regression model that you would use and write descriptions for all variables and coefficients.