Shown here are the data for y and three predictors, x1, x2, and x3. A multiple regression analysis has been done on these data; the Minitab results are given. Comment on the outcome of the analysis in light of the data.

y x1 x2 x3 94 21 1 204 97 25 0 198 93 22 1 184 95 27 0 200 90 29 1 182 91 20 1 159 91 18 1 147 94 25 0 196 98 26 0 228 99 24 0 242 90 28 1 162 92 23 1 180 96 25 0 219

13.32 Minitab residual diagnostic output from the multiple regression analysis for the data given in Problem 13.30 follows. Discuss any potential problems with meeting the regression assumptions for this regression analysis based on the residual graphics.

Regression Analysis: Y versus X1, X2, X3 The regression equation is Y 87.9 0.256 X1 -2.71 X2 + 0.0706 X3 Predictor Coef SE Coef T P Constant 87.890 3.445 25.51 0.000 X1 -0.25612 0.08317 -3.08 0.013 X2 -2.7137 0.7306 -3.71 0.005 X3 0.07061 0.01353 5.22 0.001 S 0.850311 = R-Sq 94.1% R-Sq (adj) 92.1% Analysis of Variance. Source DF SS MS F p Regression 3 103.185 34.395 47.57 0.000 Residual Error 9 6.507 0.723 Total 12 109.692