1 EXAMPLE 14. MULTICOLLINEARITY IN LINEAR REGRESSION: MANHOURS DATA 1 14:02 Tuesday, July 31, 2001 The REG Procedure Correlation Variable X1 X2 X3 X4 X1 1.0000 0.6192 0.3652 0.3874 X2 0.6192 1.0000 0.4794 0.4732 X3 0.3652 0.4794 1.0000 0.4213 X4 0.3874 0.4732 0.4213 1.0000 X5 0.4884 0.5524 0.4016 0.6861 X6 0.6200 0.8495 0.4989 0.5938 X7 0.6763 0.8608 0.5142 0.6619 Y 0.6404 0.9044 0.5017 0.5717 Correlation Variable X5 X6 X7 Y X1 0.4884 0.6200 0.6763 0.6404 X2 0.5524 0.8495 0.8608 0.9044 X3 0.4016 0.4989 0.5142 0.5017 X4 0.6861 0.5938 0.6619 0.5717 X5 1.0000 0.6763 0.7589 0.7355 X6 0.6763 1.0000 0.9782 0.8926 X7 0.7589 0.9782 1.0000 0.9431 Y 0.7355 0.8926 0.9431 1.0000 1 EXAMPLE 14. MULTICOLLINEARITY IN LINEAR REGRESSION: MANHOURS DATA 2 14:02 Tuesday, July 31, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 7 87382503 12483215 60.17 <.0001 Error 17 3526698 207453 Corrected Total 24 90909201 Root MSE 455.46991 R-Square 0.9612 Dependent Mean 2109.38640 Adj R-Sq 0.9452 Coeff Var 21.59253 Parameter Estimates Parameter Standard Variance Variable DF Estimate Error t Value Pr > |t| Inflation Intercept 1 148.22057 221.62695 0.67 0.5126 0 X1 1 -1.28739 0.80574 -1.60 0.1285 2.16554 X2 1 1.80962 0.51525 3.51 0.0027 4.50015 X3 1 0.59040 1.80009 0.33 0.7469 1.40588 X4 1 -21.48169 10.22264 -2.10 0.0508 2.35297 X5 1 5.61940 14.75619 0.38 0.7081 3.65333 X6 1 -14.51467 4.22615 -3.43 0.0032 37.18483 X7 1 29.36026 6.37037 4.61 0.0003 63.71277 Collinearity Diagnostics Condition --Proportion of Variation- Number Eigenvalue Index Intercept X1 1 6.47557 1.00000 0.00284 0.00488 2 0.59402 3.30171 0.10641 0.11148 3 0.35633 4.26295 0.05160 0.23051 4 0.26813 4.91432 0.00023479 0.46421 5 0.14222 6.74783 0.02875 0.00961 6 0.08287 8.83957 0.48032 0.00019656 7 0.07623 9.21649 0.32788 0.00009173 8 0.00462 37.44753 0.00197 0.17903 Collinearity Diagnostics -----------------Proportion of Variation---------------- Number X2 X3 X4 X5 1 0.00245 0.00239 0.00351 0.00278 2 0.02073 0.04068 0.01131 0.00047297 3 0.00639 0.02441 0.11318 0.12293 4 0.13195 0.00139 0.04691 0.04803 1 EXAMPLE 14. MULTICOLLINEARITY IN LINEAR REGRESSION: MANHOURS DATA 3 14:02 Tuesday, July 31, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Collinearity Diagnostics -----------------Proportion of Variation---------------- Number X2 X3 X4 X5 5 0.00646 0.00205 0.68848 0.43419 6 0.18706 0.58444 0.00132 0.04168 7 0.55610 0.34398 0.02815 0.04481 8 0.08886 0.00067620 0.10714 0.30511 Collinearity Diagnostics --Proportion of Variation- Number X6 X7 1 0.00027979 0.00016038 2 0.00089748 0.00042622 3 0.00011771 0.00017714 4 0.00552 0.00092335 5 0.00000124 0.00003383 6 0.02491 0.00541 7 0.03419 0.00582 8 0.93409 0.98705 Collinearity Diagnostics(intercept adjusted) Condition --Proportion of Variation- Number Eigenvalue Index X1 X2 1 4.67149 1.00000 0.01125 0.00760 2 0.74212 2.50894 0.14878 0.03839 3 0.67585 2.62908 0.00725 0.00017926 4 0.45074 3.21934 0.63920 0.07786 5 0.29779 3.96070 0.01310 0.01594 6 0.15199 5.54391 0.00069639 0.77221 7 0.01002 21.58967 0.17972 0.08783 Collinearity Diagnostics(intercept adjusted) -----------------Proportion of Variation---------------- Number X3 X4 X5 X6 1 0.01257 0.01056 0.00814 0.00107 2 0.02669 0.23545 0.05946 0.00088482 3 0.90999 0.01671 0.03251 0.00020215 4 0.02057 0.02208 0.01092 0.00732 5 0.02738 0.58982 0.50047 0.00003313 6 0.00216 0.01963 0.08283 0.05525 7 0.00063602 0.10574 0.30567 0.93523 1 EXAMPLE 14. MULTICOLLINEARITY IN LINEAR REGRESSION: MANHOURS DATA 4 14:02 Tuesday, July 31, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Collinearity Diagnostics(intercept adjusted) -Proportion of Variation- Number X7 1 0.00067938 2 0.00017083 3 0.00028512 4 0.00143 5 0.00003146 6 0.01093 7 0.98647