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9. [-/2.84 Points) DETAILS ASWSBE 14 15.E.033. Consider a regression study involving a dependent variable y, a quantitative independent variable x , and a categorical independent variable with three possible levels (level 1, level 2, and level 3). (a) How many dummy variables are required to represent the categorical variable? (b) Write a multiple regression equation relating x, and the categorical variable to y. E(y) = $. +B,X, where x, = 1 for level 1, *1 = 2 for level 2, andx, = 3 for level 3. E(Y) = B. +8,*. +82*2 +B3*, where x2 = 1 for level 2 and otherwise and x, = 1 for level 3 and otherwise. O E(Y) = B. +B,*1 +82X2 +B343 +B4* where x2 = 1 for level 1 and otherwise, xz = 1 for level 2 and otherwise, and xa = 1 for level 3 and otherwise. Ely) = Be +$,* +Byx, where x2 = 1 for level 1, x, = 2 for level 2, and x = 3 for level 3. (c) Interpret the parameter B. in your regression equation. OB, is the change in y for a 1 unit change in X. OB, is the change in Ely) for a 1 unit change in x, holding the quantitative variable constant. OB, is the change in y for a 1 unit change in x, holding the categorical variable constant. OB, is the change in Ely) for a 1 unit change in x, holding the categorical variable constant. Interpret the parameter B, in your regression equation. OB, represents the difference in the expected value of y for level 1 and level 2. OB, is not included in the regression equation. OB, represents two times the difference in the expected value of y for level 1 and level 3. OB, is the change in E(Y) for a 1 unit change in x. Interpret the parameter B, in your regression equation. OB, is the change in Ely) for a 1 unit change in x. OB, represents the difference in the expected value of y for level 1 and level 2. 08is not included in the regression equation. OB, represents the difference in the expected value of y for level 1 and level 3. Interpret the parameter B, in your regression equation. OB, represents the difference in the expected value of y for level 2 and level 3. OB, represents the difference in the expected value of y for level 1 and level 3. OB, is the change in Ely) for a 1 unit change in xx. OB, is not included in the regression equation.