EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 1 14:28 Tuesday, August 14, 2001 The REG Procedure Correlation Variable X1 Y X1 1.0000 0.9469 Y 0.9469 1.0000 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 2 14:28 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 67085 67085 190.75 <.0001 Error 22 7737.20563 351.69116 Corrected Total 23 74822 Root MSE 18.75343 R-Square 0.8966 Dependent Mean 134.00000 Adj R-Sq 0.8919 Coeff Var 13.99510 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 37.21273 7.98525 4.66 0.0001 X1 1 9.96950 0.72184 13.81 <.0001 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 3 14:28 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 23.0000 47.1822 7.3599 31.9187 62.4457 2 29.0000 57.1517 6.7538 43.1452 71.1583 3 49.0000 67.1212 6.1727 54.3198 79.9226 4 64.0000 77.0907 5.6243 65.4267 88.7548 5 74.0000 77.0907 5.6243 65.4267 88.7548 6 87.0000 87.0603 5.1191 76.4440 97.6765 7 96.0000 97.0298 4.6711 87.3425 106.7170 8 97.0000 97.0298 4.6711 87.3425 106.7170 9 109.0000 106.9993 4.2983 98.0850 115.9135 10 119.0000 116.9688 4.0217 108.6282 125.3094 11 149.0000 126.9383 3.8620 118.9289 134.9476 12 145.0000 126.9383 3.8620 118.9289 134.9476 13 154.0000 136.9078 3.8338 128.9569 144.8586 14 166.0000 136.9078 3.8338 128.9569 144.8586 15 162.0000 146.8773 3.9399 138.7063 155.0482 16 174.0000 146.8773 3.9399 138.7063 155.0482 17 180.0000 156.8468 4.1702 148.1984 165.4952 18 176.0000 156.8468 4.1702 148.1984 165.4952 19 179.0000 176.7858 4.9245 166.5730 186.9986 20 193.0000 196.7248 5.9397 184.4066 209.0429 21 193.0000 206.6943 6.5083 193.1970 220.1916 22 195.0000 216.6638 7.1047 201.9295 231.3981 23 198.0000 216.6638 7.1047 201.9295 231.3981 24 205.0000 236.6028 8.3572 219.2710 253.9346 Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 1 5.4021 88.9624 -24.1822 17.249 -1.402 2 15.8142 98.4893 -28.1517 17.495 -1.609 3 26.1764 108.0661 -18.1212 17.708 -1.023 4 36.4871 117.6944 -13.0907 17.890 -0.732 5 36.4871 117.6944 -3.0907 17.890 -0.173 6 46.7451 127.3754 -0.0603 18.041 -0.0033 7 56.9492 137.1103 -1.0298 18.162 -0.0567 8 56.9492 137.1103 -0.0298 18.162 -0.0016 9 67.0985 146.9000 2.0007 18.254 0.110 10 77.1922 156.7453 2.0312 18.317 0.111 11 87.2299 166.6466 22.0617 18.351 1.202 12 87.2299 166.6466 18.0617 18.351 0.984 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 4 14:28 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 13 97.2111 176.6044 17.0922 18.357 0.931 14 97.2111 176.6044 29.0922 18.357 1.585 15 107.1360 186.6186 15.1227 18.335 0.825 16 107.1360 186.6186 27.1227 18.335 1.479 17 117.0046 196.6890 23.1532 18.284 1.266 18 117.0046 196.6890 19.1532 18.284 1.048 19 136.5750 216.9966 2.2142 18.095 0.122 20 155.9284 237.5212 -3.7248 17.788 -0.209 21 165.5266 247.8621 -13.6943 17.588 -0.779 22 175.0741 258.2535 -21.6638 17.356 -1.248 23 175.0741 258.2535 -18.6638 17.356 -1.075 24 194.0235 279.1821 -31.6028 16.788 -1.882 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | **| | 0.179 2 | ***| | 0.193 3 | **| | 0.064 4 | *| | 0.026 5 | | | 0.001 6 | | | 0.000 7 | | | 0.000 8 | | | 0.000 9 | | | 0.000 10 | | | 0.000 11 | |** | 0.032 12 | |* | 0.021 13 | |* | 0.019 14 | |*** | 0.055 15 | |* | 0.016 16 | |** | 0.051 17 | |** | 0.042 18 | |** | 0.029 19 | | | 0.001 20 | | | 0.002 21 | *| | 0.042 22 | **| | 0.131 23 | **| | 0.097 24 | ***| | 0.439 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 5 14:28 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Sum of Residuals 0 Sum of Squared Residuals 7737.20563 Predicted Residual SS (PRESS) 9621.32161 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 6 14:28 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 24 Sum Weights 24 Mean 0 Sum Observations 0 Std Deviation 18.3412171 Variance 336.400245 Skewness -0.0492426 Kurtosis -1.1187486 Uncorrected SS 7737.20563 Corrected SS 7737.20563 Coeff Variation . Std Error Mean 3.74388526 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 18.34122 Median -0.04500 Variance 336.40024 Mode . Range 60.69504 Interquartile Range 33.48475 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -1 Pr >= |M| 0.8388 Signed Rank S -2 Pr >= |S| 0.9559 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.948754 Pr < W 0.2546 Kolmogorov-Smirnov D 0.128512 Pr > D >0.1500 Cramer-von Mises W-Sq 0.0685 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.428014 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 29.0922279 99% 29.0922279 95% 27.1227236 90% 23.1532193 75% Q3 17.5769801 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 7 14:28 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Quantiles (Definition 5) Quantile Estimate 50% Median -0.0450028 25% Q1 -15.9077721 10% -24.1822335 5% -28.1517378 1% -31.6028150 0% Min -31.6028150 Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -31.6028 24 19.1532 18 -28.1517 2 22.0617 11 -24.1822 1 23.1532 17 -21.6638 22 27.1227 16 -18.6638 23 29.0922 14 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -31.6028149886 1 4.2 4.2 -0.0297549231 1 4.2 54.2 -28.1517377616 1 4.2 8.3 2.0007407865 1 4.2 58.3 -24.1822334712 1 4.2 12.5 2.0312364961 1 4.2 62.5 -21.6638064078 1 4.2 16.7 2.2142107538 1 4.2 66.7 -18.6638064078 1 4.2 20.8 15.1227236249 1 4.2 70.8 -18.1212420520 1 4.2 25.0 17.0922279153 1 4.2 75.0 -13.6943021174 1 4.2 29.2 18.0617322057 1 4.2 79.2 -13.0907463424 1 4.2 33.3 19.1532193345 1 4.2 83.3 -3.7247978270 1 4.2 37.5 22.0617322057 1 4.2 87.5 -3.0907463424 1 4.2 41.7 23.1532193345 1 4.2 91.7 -1.0297549231 1 4.2 45.8 27.1227236249 1 4.2 95.8 -0.0602506328 1 4.2 50.0 29.0922279153 1 4.2 100.0 EXAMPLE 1. SIMPLE LINEAR REGRESSION: SERVICE CALLS DATA 8 14:28 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 2 2379 4 | 1 5789 4 +-----+ 0 222 3 | + | -0 43100 5 *-----* -1 9843 4 +-----+ -2 842 3 | -3 2 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 Normal Probability Plot 25+ *+*++*+ * | ***+*+ | ++***+ -5+ +**** * | +*+*** | +*++*+* -35+ ++*++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2