EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 1 14:53 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 45.59240 45.59240 57.54 <.0001 Error 23 18.22340 0.79232 Corrected Total 24 63.81580 Root MSE 0.89012 R-Square 0.7144 Dependent Mean 9.42400 Adj R-Sq 0.7020 Coeff Var 9.44529 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 13.62299 0.58146 23.43 <.0001 X 1 -0.07983 0.01052 -7.59 <.0001 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 2 14:53 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Obs Y Value Mean Predict 95% CL Mean 1 10.9800 10.8050 0.2546 10.2783 11.3318 2 11.1300 11.2521 0.2996 10.6323 11.8719 3 12.5100 11.1643 0.2904 10.5636 11.7650 4 8.4000 8.9291 0.1896 8.5368 9.3213 5 9.2700 8.7215 0.2007 8.3064 9.1366 6 8.7300 7.9312 0.2654 7.3823 8.4802 7 6.3600 7.6837 0.2904 7.0830 8.2844 8 8.5000 7.5001 0.3099 6.8591 8.1411 9 7.8200 7.9791 0.2607 7.4398 8.5184 10 9.1400 9.0328 0.1853 8.6494 9.4162 11 8.2400 9.9189 0.1896 9.5267 10.3112 12 12.1900 11.3159 0.3064 10.6820 11.9498 13 11.8800 11.3798 0.3133 10.7317 12.0280 14 9.5700 10.5017 0.2278 10.0305 10.9729 15 10.9400 9.8870 0.1882 9.4977 10.2763 16 9.5800 9.7513 0.1832 9.3724 10.1302 17 10.0900 8.8891 0.1915 8.4930 9.2853 18 8.1100 8.0350 0.2554 7.5067 8.5633 19 6.8300 8.0350 0.2554 7.5067 8.5633 20 8.8800 7.6758 0.2912 7.0733 8.2782 21 7.6800 7.8673 0.2717 7.3054 8.4293 22 8.4700 8.9849 0.1872 8.5977 9.3722 23 8.8600 10.0626 0.1969 9.6553 10.4700 24 10.3600 10.9567 0.2693 10.3996 11.5138 25 11.0800 11.3399 0.3090 10.7007 11.9791 Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 1 8.8898 12.7203 0.1750 0.853 0.205 2 9.3092 13.1950 -0.1221 0.838 -0.146 3 9.2274 13.1011 1.3457 0.841 1.599 4 7.0464 10.8117 -0.5291 0.870 -0.608 5 6.8339 10.6091 0.5485 0.867 0.632 6 6.0098 9.8527 0.7988 0.850 0.940 7 5.7469 9.6206 -1.3237 0.841 -1.573 8 5.5504 9.4499 0.9999 0.834 1.198 9 6.0604 9.8978 -0.1591 0.851 -0.187 10 7.1520 10.9137 0.1072 0.871 0.123 11 8.0363 11.8016 -1.6789 0.870 -1.930 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 3 14:53 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 12 9.3685 13.2634 0.8741 0.836 1.046 13 9.4277 13.3319 0.5002 0.833 0.600 14 8.6010 12.4024 -0.9317 0.860 -1.083 15 8.0049 11.7691 1.0530 0.870 1.210 16 7.8713 11.6312 -0.1713 0.871 -0.197 17 7.0057 10.7726 1.2009 0.869 1.381 18 6.1193 9.9506 0.0750 0.853 0.0880 19 6.1193 9.9506 -1.2050 0.853 -1.413 20 5.7383 9.6132 1.2042 0.841 1.432 21 5.9421 9.7926 -0.1873 0.848 -0.221 22 7.1033 10.8666 -0.5149 0.870 -0.592 23 8.1767 11.9485 -1.2026 0.868 -1.385 24 9.0329 12.8805 -0.5967 0.848 -0.703 25 9.3907 13.2890 -0.2599 0.835 -0.311 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | | | 0.002 2 | | | 0.001 3 | |*** | 0.152 4 | *| | 0.009 5 | |* | 0.011 6 | |* | 0.043 7 | ***| | 0.147 8 | |** | 0.099 9 | | | 0.002 10 | | | 0.000 11 | ***| | 0.089 12 | |** | 0.074 13 | |* | 0.025 14 | **| | 0.041 15 | |** | 0.034 16 | | | 0.001 17 | |** | 0.046 18 | | | 0.000 19 | **| | 0.090 20 | |** | 0.123 21 | | | 0.003 22 | *| | 0.008 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 4 14:53 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Cook's Obs -2-1 0 1 2 D 23 | **| | 0.049 24 | *| | 0.025 25 | | | 0.007 Sum of Residuals 0 Sum of Squared Residuals 18.22340 Predicted Residual SS (PRESS) 21.49377 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 5 14:53 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 25 Sum Weights 25 Mean 0 Sum Observations 0 Std Deviation 0.87138295 Variance 0.75930825 Skewness -0.1591464 Kurtosis -0.900184 Uncorrected SS 18.223398 Corrected SS 18.223398 Coeff Variation . Std Error Mean 0.17427659 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 0.87138 Median -0.12208 Variance 0.75931 Mode . Range 3.02467 Interquartile Range 1.32786 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -0.5 Pr >= |M| 1.0000 Signed Rank S -4.5 Pr >= |S| 0.9065 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.959594 Pr < W 0.4064 Kolmogorov-Smirnov D 0.10035 Pr > D >0.1500 Cramer-von Mises W-Sq 0.040449 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.305083 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 1.345734 99% 1.345734 95% 1.204248 90% 1.200852 75% Q3 0.798797 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 6 14:53 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Quantiles (Definition 5) Quantile Estimate 50% Median -0.122077 25% Q1 -0.529062 10% -1.204981 5% -1.323734 1% -1.678938 0% Min -1.678938 Extreme Observations ------Lowest------ ------Highest----- Value Obs Value Obs -1.678938 11 0.999872 8 -1.323734 7 1.052994 15 -1.204981 19 1.200852 17 -1.202630 23 1.204248 20 -0.931687 14 1.345734 3 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -1.6789378985 1 4.0 4.0 0.0750192636 1 4.0 56.0 -1.3237344858 1 4.0 8.0 0.1071605972 1 4.0 60.0 -1.2049807364 1 4.0 12.0 0.1749636057 1 4.0 64.0 -1.2026295465 1 4.0 16.0 0.5001970139 1 4.0 68.0 -0.9316873597 1 4.0 20.0 0.5484925011 1 4.0 72.0 -0.5967109116 1 4.0 24.0 0.7987965649 1 4.0 76.0 -0.5290621015 1 4.0 28.0 0.8740599685 1 4.0 80.0 -0.5149421868 1 4.0 32.0 0.9998715088 1 4.0 84.0 -0.2598886395 1 4.0 36.0 1.0529935788 1 4.0 88.0 -0.1873404804 1 4.0 40.0 1.2008522452 1 4.0 92.0 -0.1712976426 1 4.0 44.0 1.2042483835 1 4.0 96.0 -0.1591006511 1 4.0 48.0 1.3457344858 1 4.0 100.0 -0.1220770768 1 4.0 52.0 EXAMPLE 3. SIMPLE INVERSE LINEAR REGRESSION: STEAM DATA 7 14:53 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 1 01223 5 | 0 5589 4 +-----+ 0 112 3 | + | -0 32221 5 *-----* -0 9655 4 +-----+ -1 322 3 | -1 7 1 | ----+----+----+----+ Normal Probability Plot 1.25+ *+*+*++ * | ***+**++ | +***++ -0.25+ +***** | ++**+** | ++*+*+* -1.75+ ++*++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2