'. [I1 Points] The following estimated regression equation based on 10 observations was presented. )7 : 29.1270 + 0.5906X1 + 0.3930X2 (a) Develop a point estimate of the mean value ofy when x1 = 180 and x2 = 310. :l (b) Develop a point estimate for an individual value of y when x1 : 180 and x2 : 310. :l ASWSBE14 15.E.033. 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? :I (b) Write a multiple regression equation relating x1 and the categorical variable to y. 0 y] : 160 + [31x1 + 32x2 + 3x3 + 54x4 where x2 : 1 for level 1 and 0 otherwise, X3 : 1 for level 2 and 0 otherwise, and x4 : 1 for level 3 and 0 otherwise. 0 E(y) : [90 + [31x1 where x1 : 1 for level 1, x1 : 2 for level 2, and x1 : 3 for level 3. O E(y] : 180 + {31x1 + 32x2 + 33x3 where X2 : 1 for level 2 and 0 otherwise and X3 : 1 for level 3 and 0 otherwise. 0 E(y] : [90 + [31x1 + 32x2 where X2 : 1 for level 1, x2 : 2 for level 2, and x2 : 3 for level 3. (c) Interpret the parameter 31 in your regression equation. 0 BI is the change in y for a 1 unit change in X1. 0 131 is the change in y for a 1 unit change in x1 holding the categorical variable constant. 0 131 is the change in y) for a 1 unit change in X2 holding the quantitative variable constant. 0 131 is the change in y) for a 1 unit change in X1 holding the categorical variable constant. Interpret the parameter 32 in your regression equation. O 132 is the change in Hy) for a 1 unit change in X1. 0 132 represents two times the difference in the expected value ofyfor level 1 and level 3. O [32 is not included in the regression equation. 0 [22 represents the difference in the expected value ofy for level 1 and level 2. Interpret the parameter [is in your regression equation. 0 133 represents the difference in the expected value ofy for level 1. and level 2. O {33 represents the difference in the expected value ofy for level 1 and level 3. O {33 is not included in the regression equation. 0 E3 is the change in Ety] for a 1 unit change in x1. Interpret the parameter B4 in your regression equation. 0 134 represents the difference in the expected value ofy for level 1 and level 3. O 134 represents the difference in the expected value ofy for level 2 and level 3. A n =s LLA .L_e_c ls rr..\\ (a, s 4 .mu .stm :s