Case Study CS3-1 Case Study Deregulation of the Intrastate Trucking Industry Deregulated for x3 = yˆ = 12.192 − 598 x1 − 00598 x2 − 01078 x1 x2 + 086 x12 + 00014 x22 + 677 x4 − 275 x1 x4 − 026 x2 x4 +.013x1 x2 x4 − 782 + 0399 x1 − 021x2 − 00331 x2 ⇒= 11.41− 5581x1 − 02698 x2 − 01408 x1 x2 + 086 x12 + 0014 x22 + 677 x4 − 275 x1 x4 −.026 x2 x4 + 013x1 x2 x4 Regulated for x3 = yˆ = 12.192 − 598 x1 − 00598 x2 − 01078 x1 x2 + 086 x12 + 00014 x22 + 677 x4 − 275 x1 x4 − 026 x2 x4 +.013x1 x2 x4 yˆ regulated − yˆ deregulated = 782 − 0399 x1 + 021x2 + 0033x1 x2 For x4 = 0, x2 = 15, yˆ regulated − yˆderegulated = 1.097 + 0096 x1 Deregulated yˆ = 12.5632 − 086 x12 yˆ = 11.5712 − 8439 x1 + 086 x12 Regulated The difference between the regulated and deregulated prices is given by yˆ regulated − yˆ deregulated = −.992 + 0069 x1 Scatterplot of Predicted Value of LNPRICE vs DISTANCE 12.5 Predicted Value of LNPRICE Regulation 12.0 11.5 11.0 10.5 10.0 9.5 Regulated = DISTANCE Deregulated = Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall Deregulation of the Intrastate Trucking Industry a The interval plot for lnprice with carriers shows that carrier B is significantly different from the other carriers Interval Plot of y-LNPRICE 95% CI for the Mean 11.2 11.1 11.0 y-LNPRICE CS3-2 10.9 10.8 10.7 10.6 10.5 10.4 CARRIER_D CARRIER_C CARRIER_B CARRIER_A 0 1 0 1 1 1 0 1 0 1 MINTAB results shown below indicate that there is a difference in the carriers The regression equation is LNPRICE = 11.9 - 0.287 DISTANCE - 0.0326 WEIGHT + 0.180 ORIGIN_MIA Predictor Constant DISTANCE WEIGHT ORIGIN_MIA Coef 11.8980 -0.28700 -0.032593 0.17980 S = 0.489209 SE Coef 0.0608 0.01674 0.002660 0.04651 R-Sq = 51.0% PRESS = 108.478 T 195.79 -17.14 -12.25 3.87 P 0.000 0.000 0.000 0.000 R-Sq(adj) = 50.7% R-Sq(pred) = 49.99% Analysis of Variance Source Regression Residual Error Total DF 444 447 SS 110.635 106.261 216.895 MS 36.878 0.239 F 154.09 P 0.000 ⎧1 if Carrier A x5 = ⎨ else ⎩0 ⎧1 if Carrier C If we let x6 = ⎨ and add interaction terms for each of these dummy variables else ⎩0 ⎧1 if Carrier D x7 = ⎨ else ⎩0 (except with x12 and x22 ), the model becomes E ( y ) = β + β1 x1 + β x2 + β x1 x2 + β x12 + β x22 + β x3 + β x4 + β x1 x3 + β10 x1 x4 + β12 x2 x3 + β13 x2 x4 + β15 x1 x2 x3 + β16 x1 x2 x4 + β17 x5 + β18 x1 x5 + β19 x2 x5 + β 20 x1 x2 x5 + β 21 x3 x5 + β 22 x4 x5 + β 23 x1 x3 x5 + β 24 x1 x4 x5 + β 25 x2 x3 x5 + β 26 x2 x4 x5 + β 27 x1 x2 x3 x5 + β 28 x1 x2 x4 x5 + β 29 x6 + … β 40 x1 x2 x4 x6 + β 41 x7 + … + β 52 x1 x2 x4 x7 Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall Case Study CS3-3 In running a partial least squares procedure in MINITAB with the above model, the optimal model obtained had the same variables as in Model y_LNPRICE = 12.2 - 0.567 x1_DISTANCE - 0.0167 x2_WEIGHT - 0.373 x3_dereg + 0.600 x4_origin + 0.0748 x1_Sq + 0.000349 x2_Sq - 0.00754 x1x2 + 0.0077 x1x3 - 0.224 x1x4 - 0.0093 x2x3 - 0.0263 x2x4 + 0.00111 x1x2x3 + 0.00864 x1x2x4 However, if variable x5 is defined as a dummy variable for Carrier B, with x5 = x6 = x7 = denoting Carrier A, then the added terms in the model for Carrier B are significant Copyright © 2012 Pearson Education, Inc Publishing as Prentice Hall