1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 1 16:18 Tuesday, June 19, 2001 The REG Procedure Correlation Variable X1 X2 X3 X1 1.0000 0.3909 0.4186 X2 0.3909 1.0000 0.8926 X3 0.4186 0.8926 1.0000 X4 0.1306 0.2820 0.4671 X5 0.2276 0.1989 0.3840 Y 0.1786 0.4832 0.6434 Correlation Variable X4 X5 Y X1 0.1306 0.2276 0.1786 X2 0.2820 0.1989 0.4832 X3 0.4671 0.3840 0.6434 X4 1.0000 0.9199 0.7676 X5 0.9199 1.0000 0.8229 Y 0.7676 0.8229 1.0000 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 2 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 4.32851 0.86570 38.39 <.0001 Error 34 0.76677 0.02255 Corrected Total 39 5.09528 Root MSE 0.15017 R-Square 0.8495 Dependent Mean 0.38014 Adj R-Sq 0.8274 Coeff Var 39.50482 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 0.12176 0.03162 3.85 0.0005 X1 1 -0.00005284 0.00001786 -2.96 0.0056 X2 1 0.00004541 0.00015344 0.30 0.7691 X3 1 0.00024949 0.00008831 2.83 0.0079 X4 1 -0.00086660 0.00037613 -2.30 0.0275 X5 1 0.01339 0.00228 5.87 <.0001 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 3 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Std Error Student Obs Y Value Mean Predict Residual Residual Residual 1 0.3574 0.5262 0.0386 -0.1688 0.145 -1.163 2 1.9673 1.6891 0.1281 0.2782 0.0784 3.551 3 0.1862 0.1821 0.0315 0.004059 0.147 0.0276 4 0.3816 0.2917 0.0901 0.0899 0.120 0.748 5 0.1512 0.1270 0.0313 0.0242 0.147 0.165 6 0.1449 0.1298 0.0315 0.0151 0.147 0.103 7 0.4711 0.5602 0.0534 -0.0891 0.140 -0.635 8 0.6512 0.9622 0.0723 -0.3110 0.132 -2.363 9 0.6624 0.4458 0.0312 0.2166 0.147 1.475 10 0.3457 0.1356 0.0309 0.2101 0.147 1.429 11 0.3355 0.2597 0.0264 0.0758 0.148 0.513 12 0.3982 0.3441 0.0262 0.0541 0.148 0.366 13 0.2044 0.2328 0.0272 -0.0284 0.148 -0.192 14 0.2969 0.2132 0.0283 0.0837 0.147 0.567 15 1.1515 0.9202 0.1173 0.2313 0.0938 2.467 16 0.5609 0.3046 0.0447 0.2563 0.143 1.788 17 0.1104 0.1877 0.0289 -0.0773 0.147 -0.524 18 0.0863 0.1465 0.0306 -0.0602 0.147 -0.410 19 0.1952 0.1771 0.0306 0.0181 0.147 0.123 20 0.1688 0.2119 0.0366 -0.0431 0.146 -0.296 21 0.0786 0.2253 0.0292 -0.1467 0.147 -0.996 22 0.0955 0.1463 0.0313 -0.0508 0.147 -0.346 23 0.0486 0.2168 0.0541 -0.1682 0.140 -1.201 24 0.0867 0.1692 0.0305 -0.0825 0.147 -0.561 25 0.1403 0.1880 0.0322 -0.0477 0.147 -0.325 26 0.3786 0.3699 0.0276 0.008657 0.148 0.0586 27 0.0761 0.1465 0.0309 -0.0704 0.147 -0.479 28 0.8927 1.0742 0.0671 -0.1815 0.134 -1.351 29 0.3621 0.3021 0.0254 0.0600 0.148 0.405 30 0.1758 0.1356 0.0430 0.0402 0.144 0.279 31 0.2699 0.1496 0.1439 0.1203 0.0430 2.801 32 0.2762 0.2551 0.0267 0.0211 0.148 0.143 33 0.3240 0.4896 0.0328 -0.1656 0.147 -1.130 34 0.3737 0.5365 0.0430 -0.1628 0.144 -1.132 35 0.9114 0.7766 0.1024 0.1348 0.110 1.227 36 0.2594 0.2876 0.0319 -0.0282 0.147 -0.192 37 0.4284 0.1597 0.0293 0.2687 0.147 1.824 38 0.1905 0.2488 0.0266 -0.0583 0.148 -0.395 39 0.2341 0.3243 0.0261 -0.0902 0.148 -0.610 40 0.7759 0.9562 0.1416 -0.1803 0.0501 -3.599 Output Statistics Cook's Hat Diag Cov Obs -2-1 0 1 2 D RStudent H Ratio DFFITS 1 | **| | 0.016 -1.1696 0.0661 1.0038 -0.3111 2 | |******| 5.615 4.4098 0.7277 0.2726 7.2087 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 4 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Cook's Hat Diag Cov Obs -2-1 0 1 2 D RStudent H Ratio DFFITS 3 | | | 0.000 0.0272 0.0440 1.2511 0.0058 4 | |* | 0.053 0.7435 0.3600 1.6917 0.5576 5 | | | 0.000 0.1626 0.0436 1.2447 0.0347 6 | | | 0.000 0.1011 0.0440 1.2489 0.0217 7 | *| | 0.010 -0.6293 0.1264 1.2747 -0.2394 8 | ****| | 0.281 -2.5467 0.2319 0.5307 -1.3994 9 | |** | 0.016 1.5016 0.0431 0.8408 0.3188 10 | |** | 0.015 1.4525 0.0424 0.8612 0.3055 11 | |* | 0.001 0.5071 0.0310 1.1782 0.0907 12 | | | 0.001 0.3609 0.0304 1.2049 0.0639 13 | | | 0.000 -0.1897 0.0327 1.2286 -0.0349 14 | |* | 0.002 0.5615 0.0354 1.1713 0.1076 15 | |**** | 1.587 2.6824 0.6101 0.9394 3.3553 16 | |*** | 0.052 1.8503 0.0885 0.7258 0.5766 17 | *| | 0.002 -0.5186 0.0369 1.1830 -0.1015 18 | | | 0.001 -0.4047 0.0416 1.2116 -0.0843 19 | | | 0.000 0.1212 0.0414 1.2445 0.0252 20 | | | 0.001 -0.2920 0.0595 1.2522 -0.0734 21 | *| | 0.007 -0.9955 0.0379 1.0410 -0.1976 22 | | | 0.001 -0.3412 0.0435 1.2244 -0.0728 23 | **| | 0.036 -1.2086 0.1300 1.0602 -0.4672 24 | *| | 0.002 -0.5555 0.0412 1.1798 -0.1152 25 | | | 0.001 -0.3205 0.0460 1.2306 -0.0704 26 | | | 0.000 0.0578 0.0337 1.2371 0.0108 27 | | | 0.002 -0.4733 0.0423 1.1993 -0.0995 28 | **| | 0.076 -1.3680 0.1995 1.0733 -0.6829 29 | | | 0.001 0.4002 0.0286 1.1961 0.0686 30 | | | 0.001 0.2756 0.0820 1.2851 0.0824 31 | |***** | 14.680 3.1467 0.9182 3.0284 10.5422 32 | | | 0.000 0.1407 0.0316 1.2307 0.0254 33 | **| | 0.011 -1.1351 0.0477 0.9982 -0.2540 34 | **| | 0.019 -1.1367 0.0821 1.0350 -0.3401 35 | |** | 0.219 1.2369 0.4654 1.7048 1.1540 36 | | | 0.000 -0.1895 0.0452 1.2446 -0.0412 37 | |*** | 0.022 1.8923 0.0380 0.6701 0.3761 38 | | | 0.001 -0.3897 0.0314 1.2014 -0.0702 39 | *| | 0.002 -0.6042 0.0302 1.1546 -0.1066 40 |******| | 17.239 -4.5072 0.8887 0.6043 -12.7355 Output Statistics --------------------------DFBETAS-------------------------- Obs Intercept X1 X2 X3 X4 X5 1 -0.0690 0.1202 -0.0427 0.0232 0.2002 -0.2350 2 -1.2156 -0.5708 -2.7813 3.2707 2.4915 -1.2193 3 0.0046 -0.0001 0.0025 -0.0027 0.0011 -0.0015 4 0.0489 -0.0156 0.5298 -0.4836 0.1025 -0.0252 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 5 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics --------------------------DFBETAS-------------------------- Obs Intercept X1 X2 X3 X4 X5 5 0.0347 -0.0003 -0.0062 0.0027 0.0065 -0.0133 6 0.0206 0.0003 0.0017 -0.0037 0.0069 -0.0098 7 -0.0283 -0.0812 -0.0378 0.0927 -0.1646 0.0945 8 0.3234 -0.3834 -0.0024 0.2738 -0.1778 -0.3192 9 0.1197 0.0110 -0.0164 -0.0001 -0.1563 0.1782 10 0.3048 -0.0168 -0.0575 0.0336 0.0237 -0.0875 11 0.0820 -0.0094 -0.0087 -0.0032 0.0084 -0.0126 12 0.0488 -0.0059 -0.0076 -0.0025 0.0105 -0.0066 13 -0.0326 0.0052 0.0046 -0.0016 0.0016 0.0022 14 0.1011 -0.0177 -0.0182 0.0121 -0.0143 -0.0027 15 -0.4179 -1.3429 0.1335 0.3215 -3.0831 3.2590 16 0.3917 -0.1463 -0.3377 0.4312 -0.1169 -0.0480 17 -0.0996 0.0105 0.0213 -0.0132 -0.0020 0.0197 18 -0.0842 0.0042 0.0168 -0.0100 -0.0109 0.0278 19 0.0248 -0.0014 -0.0079 0.0062 0.0032 -0.0084 20 -0.0635 0.0100 0.0327 -0.0392 0.0001 0.0211 21 -0.1887 0.0223 0.0732 -0.0575 -0.0141 0.0475 22 -0.0724 0.0025 0.0188 -0.0124 -0.0126 0.0275 23 -0.3202 0.0210 0.3493 -0.3404 -0.0971 0.2074 24 -0.1135 0.0027 0.0306 -0.0179 -0.0264 0.0463 25 -0.0610 -0.0062 0.0045 0.0093 -0.0380 0.0405 26 0.0078 -0.0035 -0.0020 0.0031 -0.0044 0.0032 27 -0.0977 -0.0015 0.0156 -0.0025 -0.0298 0.0450 28 0.1372 0.2572 0.0773 -0.1292 0.3254 -0.4889 29 0.0572 -0.0111 0.0019 -0.0051 -0.0086 0.0060 30 0.0574 0.0180 0.0094 -0.0242 0.0634 -0.0637 31 0.1476 9.8270 -1.2086 -1.0157 0.5820 -0.6177 32 0.0242 -0.0040 -0.0045 0.0037 0.0001 -0.0037 33 -0.0835 0.0379 -0.0885 0.1131 -0.0540 -0.0143 34 -0.0277 0.0451 -0.1328 0.1416 0.1579 -0.2303 35 -0.1348 -0.0159 1.0083 -0.8653 0.3728 -0.1016 36 -0.0285 0.0129 0.0048 -0.0059 0.0226 -0.0177 37 0.3665 -0.0206 0.0047 -0.0341 0.0509 -0.1072 38 -0.0630 0.0030 0.0120 -0.0048 0.0090 -0.0014 39 -0.0900 0.0156 0.0280 -0.0164 -0.0062 0.0091 40 0.0719 -0.5155 -1.8211 -3.6889 3.2388 -0.9834 Sum of Residuals 0 Sum of Squared Residuals 0.76677 Predicted Residual SS (PRESS) 6.97367 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 6 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--- Y | | | | | | 0.4 + + | 1 1 | | | | | | 1 | 0.3 + + | | | 1 | | | | | 0.2 + 1 + | 1 1 | | 1 1 | | 11 111 | | 1 1 1 | 0.1 + 1 + | 1 1 1 | | 1 1 1 11 | | 1 1 2 | | | 0.0 + 1 + | 1 | | 1 | | 1 | | | -0.1 + + | 1 | | 1 1 | | | | 1 | -0.2 + + | | | 1 | | | | | -0.3 + + | | | | | | | 1 | -0.4 + + | | | | ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--- -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Intercept 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 7 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot ---+---------+---------+---------+---------+---------+---------+--- Y | | | | | | 0.4 + + | 1 | | | | | | | 0.3 + 1 + | 1 1 | | | | | | 2 | 0.2 + + | | | | | 1 | | | 0.1 + 2 + | 2 | | 1 | | 1 1 | | 3 1 | 0.0 + 1 1 + | 2 | | 1 | | 121 | | 12 | -0.1 + 1 + | 1 | | 11 1 | | 2 | | | -0.2 + 1 + | | | | | | | 1 | -0.3 + + | | | | | 1 | | | -0.4 + + | | | | ---+---------+---------+---------+---------+---------+---------+--- -4000 -2000 0 2000 4000 6000 8000 X1 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 8 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--- Y | | | | 0.3 + + | | | 1 1 | | 1 | | 1 | | 1 | 0.2 + 1 + | | | 1 | | | | | | 1 1 | 0.1 + + | 11 | | 1 | | 1 | | 1 | | 1 2 1 | 0.0 + 1 1 + | | | 2 | | 1 1 1 | | 3 | | 11 1 | -0.1 + 1 + | | | | | 1 1 | | 1 1 1 | | 1 1 | -0.2 + + | | | | | | | | | | -0.3 + + | 1 | | | | | | | | | -0.4 + + | | ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--- -400 -300 -200 -100 0 100 200 300 400 500 600 X2 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 9 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot -+------+------+------+------+------+------+------+------+------+-- 0.5 + + | | | | | 1 | | | 0.4 + + | | | 1 | | | | | 0.3 + + | | | 1 1 | | | | 11 | 0.2 + + | | Y | | | | | | 0.1 + 1 + | 1 1 | | 11 | | 112 | | 1 | 0.0 + 1 1 + | 1 1 | | 1 11 | | 1 121 2 | | 1 1 | -0.1 + + | 1 | | 1 1 1 | | | | 1 | -0.2 + 1 + | 1 | | | | | | | -0.3 + + | | | | | 1 | | | -0.4 + + -+------+------+------+------+------+------+------+------+------+-- -1000 -800 -600 -400 -200 0 200 400 600 800 X3 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 10 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot -+------+------+------+------+------+------+------+------+------+-- 0.5 + + | 1 | | | | | | | 0.4 + + | | | | | | | | 0.3 + + | 1 | | 1 1 | | | | | 0.2 + 1 + | 1 | Y | | | | | | 0.1 + 1 1 + | 1 | | 1 1 1 | | 1 1 | | 1 1 1 | 0.0 + 11 1 + | 1 | | 1 1 | | 1 11 | | 1 1 | -0.1 + 11 1 2 + | 1 1 | | | | 1 | | 1 1 | -0.2 + 1 + | | | | | | | | -0.3 + + | | | 1 | | | | | -0.4 + + -+------+------+------+------+------+------+------+------+------+-- -300 -250 -200 -150 -100 -50 0 50 100 150 X4 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 11 16:18 Tuesday, June 19, 2001 The REG Procedure Model: MODEL1 Partial Regression Residual Plot -----+-------+-------+-------+-------+-------+-------+-------+----- Y | | | | 1.0 + + | | | | | 1 | | | | | 0.8 + + | | | | | | | | | | 0.6 + + | | | | | | | | | | 0.4 + + | | | 1 | | | | | | 1 1 | 0.2 + + | 1 1 | | | | 1 | | 2 211 1 1 | | 1 | 0.0 + 1 2 + | 21 1 | | 1 1 | | 1 11 1 | | 2 | | 1 1 11 1 | -0.2 + 1 1 1 + | | | | | 1 | | | | | -0.4 + + | | -----+-------+-------+-------+-------+-------+-------+-------+----- -20 -10 0 10 20 30 40 50 X5 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 12 16:18 Tuesday, June 19, 2001 The UNIVARIATE Procedure Variable: YPRED (Predicted Value of Y) Moments N 40 Sum Weights 40 Mean 0.38014 Sum Observations 15.2056 Std Deviation 0.33314781 Variance 0.11098747 Skewness 2.19575318 Kurtosis 5.36391443 Uncorrected SS 10.1087679 Corrected SS 4.32851114 Coeff Variation 87.6381893 Std Error Mean 0.05267529 Basic Statistical Measures Location Variability Mean 0.380140 Std Deviation 0.33315 Median 0.251961 Variance 0.11099 Mode . Range 1.56209 Interquartile Range 0.29454 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 7.216666 Pr > |t| <.0001 Sign M 20 Pr >= |M| <.0001 Signed Rank S 410 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.721231 Pr < W <0.0001 Kolmogorov-Smirnov D 0.243025 Pr > D <0.0100 Cramer-von Mises W-Sq 0.718284 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 3.842398 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 1.689056 99% 1.689056 95% 1.018208 90% 0.938196 75% Q3 0.467711 50% Median 0.251961 25% Q1 0.173173 10% 0.140959 5% 0.132714 1% 0.126964 0% Min 0.126964 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 13 16:18 Tuesday, June 19, 2001 The UNIVARIATE Procedure Variable: YPRED (Predicted Value of Y) Extreme Observations ------Lowest------ ------Highest----- Value Obs Value Obs 0.126964 5 0.920156 15 0.129834 6 0.956235 40 0.135594 30 0.962224 8 0.135647 10 1.074191 28 0.146272 22 1.689056 2 Stem Leaf # Boxplot 16 9 1 * 15 14 13 12 11 10 7 1 0 9 266 3 0 8 7 8 1 | 6 | 5 346 3 | 4 59 2 +-----+ 3 00247 5 | + | 2 1123356699 10 *-----* 1 33445555678899 14 +-----+ ----+----+----+----+ Multiply Stem.Leaf by 10**-1 Normal Probability Plot 1.65+ * | | 1.35+ | + | +++ 1.05+ * +++ | ** *+++ | +++ 0.75+ +*+ | +++ | +++ *** 0.45+ +++ ** | +++ **** | ++****** 0.15+ * * * ********** +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 14 16:18 Tuesday, June 19, 2001 Plot of STUDENT*YPRED. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | | A | | 2 + | A A S | t | A A u | d | A e 1 + n | t | A i | AA z | A AA e | B A A d 0 +-------A----A-------------------------------------------- | AA R | BAB e | BA s | A A i | d -1 + A u | A AB a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + ---+------------+------------+------------+------------+-- 0.0 0.5 1.0 1.5 2.0 Predicted Value of Y 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 15 16:18 Tuesday, June 19, 2001 Plot of STUDENT*X1. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | |A | | 2 + |AA S | t |A A u | d | A e 1 + n | t | A i |B z | C e |D d 0 +-B---------------------------------------------------------------- |B R |CAA e |C s |A A i | d -1 +A u |BA A a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + -+------------+------------+------------+------------+------------+ 0 2000 4000 6000 8000 10000 X1 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 16 16:18 Tuesday, June 19, 2001 Plot of STUDENT*X2. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | |A | | 2 + | A A S | t |AA u | d | A e 1 + n | t | A i |B z |AAA e |BB d 0 +---AA------------------------------------------------------------- |B R |D A e |C s |A A i | d -1 +A u |A BA a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + -+------------+------------+------------+------------+------------+ 0 500 1000 1500 2000 2500 X2 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 17 16:18 Tuesday, June 19, 2001 Plot of STUDENT*X3. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | | A | | 2 + | A A S | t | A A u | d | A e 1 + n | t | A i | B z | C e | BAA d 0 +---A--A-------------------------------------------------- | B R | CA A e | BA s | A A i | d -1 + A u | A B A a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + ---+------------+------------+------------+------------+-- 0 1000 2000 3000 4000 X3 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 18 16:18 Tuesday, June 19, 2001 Plot of STUDENT*X4. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | | A | | 2 + | B S | t |A A u | d | A e 1 + n | t | A i | A A z | A AA e | AB A d 0 +--A-A------------------------------------------------------------- | A A R |AB A A e | C s | A A i | d -1 + A u | A A A A a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + -+------------+------------+------------+------------+------------+ 0 200 400 600 800 1000 X4 1 EXAMPLE 7. INFLUENCE DIAGNOSTICS: SOLID WASTED DATA 19 16:18 Tuesday, June 19, 2001 Plot of STUDENT*X5. Legend: A = 1 obs, B = 2 obs, etc. 4 + | | | A | | 3 + | A | | A | | 2 + | B S | t | A A u | d | A e 1 + n | t | A i | A A z | A A A e | AB A d 0 +----A---A---------------------------------------------- | B R | AB B e | AB s | A A i | d -1 + A u | A AAA a | A l | | | -2 + | | A | | | -3 + | | | | A | -4 + ---+---------+---------+---------+---------+---------+-- 0 30 60 90 120 150 X5