Given here are the data from a dependent variable and two independent variables.

The second independent variable is an indicator variable with several categories.

Hence, this variable is represented by x2, x3, and x4. How many categories are needed in total for this independent variable? Use a computer to perform a multiple regression analysis on this data to predict y from the x values. Discuss the output and pay particular attention to the dummy variables.

y x1 x2 x3 x4 11 1.9 1 0 0 3 1.6 0 1 0 2 2.3 0 1 0 5 2.0 0 0 1 9 1.8 0 0 0 14 1.9 1 0 0 10 2.4 1 0 0 8 2.6 0 0 0 4 2.0 0 1 0 9 1.4 0 0 0 11 1.7 1 0 0 4 2.5 0 0 1 6 1.0 1 0 0 10 1.4 0 0 0 3 1.9 0 1 0 4 2.3 0 1 0 9 2.2 0 0 0 6 1.7 0 0 1