Consider a regression study involving a dependent variable y, a quantitative independent variable x1, 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? x J (b) Write a multiple regression equation relating x1 and the categorical variable to 3/. O E(y} = ,80 + lxl + [32x2 where X2 = 1 for level 1, x2 = 2 for level 2, and x2 = 3 for level 3. O E(y} = ,80 + 51x1 + [32x2 + 3x3 where x2 = 1 for level 2 and 0 otherwise and x3 = 1 for level 3 and 0 otherwise. 0 E(y} = {30 + lxl where x1 = 1 for level 1, x1 = 2 for level 2, and x1 = 3 for level 3. 0 E0!) = [30 + lxl + [32x2 + 63x3 + i34x4 where x2 = 1 for level 1 and 0 otherwise, x3 = 1 for level 2 and III otherwise, and x4 = 1 for level 3 and 0 otherwise. (c) Interpret the parameter ,61 in your regression equation. 0 (31 is the change in y for a 1 unit change in x1. 0 (5'1 is the change in EU!) for a 1 unit change in x1 holding the categorical variable O (5'1 is the change in E{y] for a 1 unit change in x2 holding the quantitative variabl O 31 is the change in y for a 1 unit change in x1 holding the categorical variable to Interpret the parameter ,82 in your regression equation. 0 (32 is the change in y} for a 1 unit change in x1. 0 '32 represents the difference in the expected value of y for level 1 and level 2. O (32 is not included in the regression equation. 0 (32 represents two times the difference in the expected value of y for level 1 and Interpret the parameter ,63 in your regression equation. O 53 represents the difference in the expected value of y for level 1 and level 2. O 53 represents the difference in the expected value of y for level 1 and level 3. O 433 is not included in the regression equation. 0 (33 is the change in EU!) for a 1 unit change in x1. Interpret the parameter .84 in your regression equation. 0 '34 represents the difference in the expected value of y for level 2 and level 3. O '34 is not included in the regression equation. O E4 represents the difference in the expected value of y for level 1 and level 3. O 54 is the change in EU!) for a 1 unit change in x1