sequential selection methods 1 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Forward Selection: Step 1 Statistics for Entry DF = 1,29 Model Variable Tolerance R-Square F Value Pr > F x1 1.000000 0.0928 2.97 0.0957 x2 1.000000 0.0265 0.79 0.3817 x3 1.000000 0.7434 84.01 <.0001 x4 1.000000 0.1595 5.50 0.0260 x5 1.000000 0.1584 5.46 0.0266 x6 1.000000 0.0560 1.72 0.1997 Variable x3 Entered: R-Square = 0.7434 and C(p) = 13.6988 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 632.90010 632.90010 84.01 <.0001 Error 29 218.48144 7.53384 Corrected Total 30 851.38154 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 82.42177 3.85530 3443.36654 457.05 <.0001 x3 -3.31056 0.36119 632.90010 84.01 <.0001 Bounds on condition number: 1, 1 ------------------------------------------------------------------------ Forward Selection: Step 2 sequential selection methods 2 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Forward Selection: Step 2 Statistics for Entry DF = 1,28 Model Variable Tolerance R-Square F Value Pr > F x1 0.964375 0.7642 2.48 0.1267 x2 0.979406 0.7449 0.17 0.6827 x4 0.797156 0.7435 0.02 0.8981 x5 0.901625 0.7614 2.12 0.1567 x6 0.948877 0.7452 0.20 0.6563 No other variable met the 0.1000 significance level for entry into the model. Summary of Forward Selection Variable Number Partial Model Step Entered Vars In R-Square R-Square C(p) F Value Pr > F 1 x3 1 0.7434 0.7434 13.6988 84.01 <.0001 sequential selection methods 3 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL2 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Backward Elimination: Step 0 All Variables Entered: R-Square = 0.8487 and C(p) = 7.0000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 722.54361 120.42393 22.43 <.0001 Error 24 128.83794 5.36825 Corrected Total 30 851.38154 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 102.93448 12.40326 369.72831 68.87 <.0001 x1 -0.22697 0.09984 27.74577 5.17 0.0322 x2 -0.07418 0.05459 9.91059 1.85 0.1869 x3 -2.62865 0.38456 250.82210 46.72 <.0001 x4 -0.02153 0.06605 0.57051 0.11 0.7473 x5 -0.36963 0.11985 51.05806 9.51 0.0051 x6 0.30322 0.13650 26.49142 4.93 0.0360 Bounds on condition number: 8.7438, 137.13 ------------------------------------------------------------------------ Backward Elimination: Step 1 Statistics for Removal DF = 1,24 Partial Model Variable R-Square R-Square F Value Pr > F x1 0.0326 0.8161 5.17 0.0322 x2 0.0116 0.8370 1.85 0.1869 x3 0.2946 0.5541 46.72 <.0001 x4 0.0007 0.8480 0.11 0.7473 x5 0.0600 0.7887 9.51 0.0051 x6 0.0311 0.8176 4.93 0.0360 sequential selection methods 4 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL2 Dependent Variable: y Backward Elimination: Step 1 Variable x4 Removed: R-Square = 0.8480 and C(p) = 5.1063 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 721.97309 144.39462 27.90 <.0001 Error 25 129.40845 5.17634 Corrected Total 30 851.38154 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 102.20428 11.97929 376.78935 72.79 <.0001 x1 -0.21962 0.09550 27.37429 5.29 0.0301 x2 -0.07230 0.05331 9.52157 1.84 0.1871 x3 -2.68252 0.34099 320.35968 61.89 <.0001 x5 -0.37340 0.11714 52.59624 10.16 0.0038 x6 0.30491 0.13394 26.82640 5.18 0.0316 Bounds on condition number: 8.7312, 104.83 ------------------------------------------------------------------------ Backward Elimination: Step 2 Statistics for Removal DF = 1,25 Partial Model Variable R-Square R-Square F Value Pr > F x1 0.0322 0.8158 5.29 0.0301 x2 0.0112 0.8368 1.84 0.1871 x3 0.3763 0.4717 61.89 <.0001 x5 0.0618 0.7862 10.16 0.0038 x6 0.0315 0.8165 5.18 0.0316 Variable x2 Removed: R-Square = 0.8368 and C(p) = 4.8800 sequential selection methods 5 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL2 Dependent Variable: y Backward Elimination: Step 2 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 712.45153 178.11288 33.33 <.0001 Error 26 138.93002 5.34346 Corrected Total 30 851.38154 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 98.14789 11.78569 370.57373 69.35 <.0001 x1 -0.19773 0.09564 22.84231 4.27 0.0488 x3 -2.76758 0.34054 352.93570 66.05 <.0001 x5 -0.34811 0.11750 46.90089 8.78 0.0064 x6 0.27051 0.13362 21.90067 4.10 0.0533 Bounds on condition number: 8.4182, 76.851 ------------------------------------------------------------------------ Backward Elimination: Step 3 Statistics for Removal DF = 1,26 Partial Model Variable R-Square R-Square F Value Pr > F x1 0.0268 0.8100 4.27 0.0488 x3 0.4145 0.4223 66.05 <.0001 x5 0.0551 0.7817 8.78 0.0064 x6 0.0257 0.8111 4.10 0.0533 All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Variable Number Partial Model Step Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 x4 5 0.0007 0.8480 5.1063 0.11 0.7473 2 x2 4 0.0112 0.8368 4.8800 1.84 0.1871 sequential selection methods 6 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL3 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Stepwise Selection: Step 1 Statistics for Entry DF = 1,29 Model Variable Tolerance R-Square F Value Pr > F x1 1.000000 0.0928 2.97 0.0957 x2 1.000000 0.0265 0.79 0.3817 x3 1.000000 0.7434 84.01 <.0001 x4 1.000000 0.1595 5.50 0.0260 x5 1.000000 0.1584 5.46 0.0266 x6 1.000000 0.0560 1.72 0.1997 Variable x3 Entered: R-Square = 0.7434 and C(p) = 13.6988 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 632.90010 632.90010 84.01 <.0001 Error 29 218.48144 7.53384 Corrected Total 30 851.38154 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 82.42177 3.85530 3443.36654 457.05 <.0001 x3 -3.31056 0.36119 632.90010 84.01 <.0001 Bounds on condition number: 1, 1 ------------------------------------------------------------------------ Stepwise Selection: Step 2 sequential selection methods 7 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL3 Dependent Variable: y Stepwise Selection: Step 2 Statistics for Entry DF = 1,28 Model Variable Tolerance R-Square F Value Pr > F x1 0.964375 0.7642 2.48 0.1267 x2 0.979406 0.7449 0.17 0.6827 x4 0.797156 0.7435 0.02 0.8981 x5 0.901625 0.7614 2.12 0.1567 x6 0.948877 0.7452 0.20 0.6563 All variables left in the model are significant at the 0.1000 level. No other variable met the 0.1000 significance level for entry into the model. Summary of Stepwise Selection Variable Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value 1 x3 1 0.7434 0.7434 13.6988 84.01 Summary of Stepwise Selection Step Pr > F 1 <.0001 model with x0 and x3 8 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 632.90010 632.90010 84.01 <.0001 Error 29 218.48144 7.53384 Corrected Total 30 851.38154 Root MSE 2.74478 R-Square 0.7434 Dependent Mean 47.37581 Adj R-Sq 0.7345 Coeff Var 5.79364 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 82.42177 3.85530 21.38 <.0001 69578 x3 1 -3.31056 0.36119 -9.17 <.0001 632.90010 Parameter Estimates Variable DF Type II SS Intercept 1 3443.36654 x3 1 632.90010 model with x0 and x3 9 15:37 Sunday, March 3, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | | A 6 + | | | | | A 4 + | A A | | | A A R | e 2 + s | A A i | A A d | A A u | A A a | A l 0 +--------------------------------A--------------------------------- | A A | A A | A | A | A -2 + A A | | A A | | | A A -4 + | | | A | A | -6 + | -+------------+------------+------------+------------+------------+ 35 40 45 50 55 60 Predicted Value of y model with x0 and x3 10 15:37 Sunday, March 3, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | | A 6 + | | | | | A 4 + | A A | | | A A R | e 2 + s | A A i | A A d | A A u | A A a | A l 0 +----------------------------A------------------------------------ | A A | A A | A | A | A -2 + A A | | A A | | | A A -4 + | | | A | A | -6 + | ---+---------+---------+---------+---------+---------+---------+-- 8 9 10 11 12 13 14 x3 model with x0 and x3 11 15:37 Sunday, March 3, 2013 Obs y x3 yhat resid 1 44.609 11.37 44.7808 -0.17176 2 54.297 8.65 53.7855 0.51153 3 49.874 9.22 51.8985 -2.02445 4 45.681 11.95 42.8606 2.82036 5 39.442 13.08 39.1197 0.32229 6 50.541 10.13 48.8858 1.65515 7 44.754 11.12 45.6084 -0.85440 8 51.855 10.33 48.2237 3.63126 9 40.836 10.95 46.1712 -5.33519 10 46.774 10.25 48.4886 -1.71458 11 39.407 12.63 40.6095 -1.20246 12 45.441 9.63 50.5411 -5.10012 13 45.118 11.08 45.7408 -0.62282 14 45.790 10.47 47.7603 -1.97026 15 48.673 9.40 51.3026 -2.62955 16 47.467 10.50 47.6609 -0.19394 17 45.313 10.07 49.0845 -3.77148 18 59.571 8.17 55.3745 4.19646 19 44.811 11.63 43.9200 0.89099 20 49.091 10.85 46.5022 2.58875 21 60.055 8.63 53.8517 6.20332 22 37.388 14.03 35.9747 1.41332 23 47.273 10.60 47.3299 -0.05689 24 49.156 8.95 52.7923 -3.63630 25 46.672 10.00 49.3162 -2.64422 26 50.388 10.08 49.0514 1.33663 27 46.080 11.17 45.4429 0.63713 28 54.625 8.92 52.8916 1.73338 29 39.203 12.88 39.7818 -0.57882 30 50.545 9.93 49.5480 0.99704 31 47.920 11.50 44.3504 3.56961 model with x0 and x3 12 15:37 Sunday, March 3, 2013 The UNIVARIATE Procedure Variable: resid (Residual) Moments N 31 Sum Weights 31 Mean 0 Sum Observations 0 Std Deviation 2.69865056 Variance 7.28271483 Skewness 0.02923134 Kurtosis -0.0504736 Uncorrected SS 218.481445 Corrected SS 218.481445 Coeff Variation . Std Error Mean 0.48469195 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 2.69865 Median -0.05689 Variance 7.28271 Mode . Range 11.53851 Interquartile Range 3.62541 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 0 Pr >= |S| 1.0000 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.990663 Pr < W 0.9932 Kolmogorov-Smirnov D 0.066786 Pr > D >0.1500 Cramer-von Mises W-Sq 0.014905 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.112735 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 6.2033201 99% 6.2033201 95% 4.1964646 90% 3.5696140 75% Q3 1.6551531 50% Median -0.0568858 25% Q1 -1.9702580 10% -3.6363022 5% -5.1001245 1% -5.3351915 0% Min -5.3351915 model with x0 and x3 13 15:37 Sunday, March 3, 2013 The UNIVARIATE Procedure Variable: resid (Residual) Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -5.33519 9 2.82036 4 -5.10012 12 3.56961 31 -3.77148 17 3.63126 8 -3.63630 24 4.19646 18 -2.64422 25 6.20332 21 Stem Leaf # Boxplot 6 2 1 | 5 | 4 2 1 | 3 66 2 | 2 68 2 | 1 03477 5 +-----+ 0 3569 4 | + | -0 966221 6 *-----* -1 72 2 | | -2 6600 4 +-----+ -3 86 2 | -4 | -5 31 2 | ----+----+----+----+ Normal Probability Plot 6.5+ * +++ | ++++ | +*++ | *+* | +**+ | +**** 0.5+ +**** | ***** | ***+ | +*** | *+* | ++++ -5.5+ +*++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 model with x0 and x3 14 15:37 Sunday, March 3, 2013 Obs resid normsc 1 -0.17176 -0.08030 2 0.51153 0.16112 3 -2.02445 -0.79950 4 2.82036 1.04505 5 0.32229 0.08030 6 1.65515 0.69349 7 -0.85440 -0.41246 8 3.63126 1.37866 9 -5.33519 -2.05375 10 -1.71458 -0.59477 11 -1.20246 -0.50153 12 -5.10012 -1.62576 13 -0.62282 -0.32656 14 -1.97026 -0.69349 15 -2.62955 -0.91537 16 -0.19394 -0.16112 17 -3.77148 -1.37866 18 4.19646 1.62576 19 0.89099 0.32656 20 2.58875 0.91537 21 6.20332 2.05375 22 1.41332 0.59477 23 -0.05689 0.00000 24 -3.63630 -1.19522 25 -2.64422 -1.04505 26 1.33663 0.50153 27 0.63713 0.24301 28 1.73338 0.79950 29 -0.57882 -0.24301 30 0.99704 0.41246 31 3.56961 1.19522 model with x0 and x3 15 15:37 Sunday, March 3, 2013 Plot of resid*normsc. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | | A 6 + | | | | | A 4 + | A A | | | AA R | e 2 + s | AA i | AA d | AA u | B a | A l 0 + A | AA | AA | A | A | A -2 + AA | | AA | | | A A -4 + | | | A | A | -6 + | ---+---------+---------+---------+---------+---------+---------+-- -3 -2 -1 0 1 2 3 Rank for Variable resid model with x0 x1 and x3 16 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 650.66573 325.33287 45.38 <.0001 Error 28 200.71581 7.16842 Corrected Total 30 851.38154 Root MSE 2.67739 R-Square 0.7642 Dependent Mean 47.37581 Adj R-Sq 0.7474 Coeff Var 5.65139 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 88.46229 5.37264 16.47 <.0001 69578 x3 1 -3.20395 0.35877 -8.93 <.0001 632.90010 x1 1 -0.15037 0.09551 -1.57 0.1267 17.76563 Parameter Estimates Variable DF Type II SS Intercept 1 1943.41071 x3 1 571.67751 x1 1 17.76563 Sequential Parameter Estimates Intercept x3 x1 47.375806 0 0 82.421773 -3.310555 0 88.462287 -3.203951 -0.150366 model with x0 x1 and x3 17 15:37 Sunday, March 3, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A | A | 4 + | A | A | | | A | A 2 + A | A | AA R | A e | s | A A A i | A d 0 +-----------AA----------------------------------------------------- u | A A a | A l | A | | A A | A -2 + A | A | | | A | A | -4 + | A | | A A | | | -6 + | -+------------+------------+------------+------------+------------+ 35 40 45 50 55 60 Predicted Value of y model with x0 x1 and x3 18 15:37 Sunday, March 3, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A | A | 4 + | A | A | | | A | A 2 + A | A | A A R | A e | s | A A A i | A d 0 +------------------------------------------------A--A------------- u | A A a | A l | A | | A A | A -2 + A | A | | | A | A | -4 + | A | | A A | | | -6 + | ---+---------+---------+---------+---------+---------+---------+-- 8 9 10 11 12 13 14 x3 model with x0 x1 and x3 19 15:37 Sunday, March 3, 2013 Plot of resid*x1. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A | A | 4 + | A | A | | | A | A 2 + A | A | A A R | A e | s | A A A i | A d 0 +--------------------------------------------------A--------A-- u | A A a | A l | A | | A A | A -2 + A | A | | | A | A | -4 + | A | | A A | | | -6 + | ---+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-- 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 x1 model with x0 x1 and x3 20 15:37 Sunday, March 3, 2013 Obs y x1 x3 yhat resid 1 44.609 44 11.37 45.4173 -0.80828 2 54.297 44 8.65 54.1320 0.16497 3 49.874 38 9.22 53.2080 -3.33397 4 45.681 40 11.95 44.1605 1.52055 5 39.442 44 13.08 39.9385 -0.49652 6 50.541 44 10.13 49.3902 1.15082 7 44.754 45 11.12 46.0679 -1.31390 8 51.855 54 10.33 47.2457 4.60927 9 40.836 51 10.95 45.7104 -4.87438 10 46.774 48 10.25 48.4042 -1.63024 11 39.407 57 12.63 39.4255 -0.01855 12 45.441 52 9.63 49.7892 -4.34823 13 45.118 51 11.08 45.2939 -0.17587 14 45.790 51 10.47 47.2483 -1.45828 15 48.673 49 9.40 50.9772 -2.30423 16 47.467 52 10.50 47.0018 0.46521 17 45.313 40 10.07 50.1839 -4.87088 18 59.571 42 8.17 55.9707 3.60035 19 44.811 47 11.63 44.1332 0.67784 20 49.091 43 10.85 47.2337 1.85730 21 60.055 38 8.63 55.0983 4.95670 22 37.388 45 14.03 36.7444 0.64359 23 47.273 47 10.60 47.4332 -0.16023 24 49.156 49 8.95 52.4190 -3.26301 25 46.672 51 10.00 48.7541 -2.08213 26 50.388 49 10.08 48.7985 1.58945 27 46.080 54 11.17 44.5544 1.52559 28 54.625 50 8.92 52.3648 2.26023 29 39.203 54 12.88 39.0757 0.12734 30 50.545 57 9.93 48.0762 2.46878 31 47.920 48 11.50 44.3993 3.52070 model with x0 x3 and x5 21 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 648.26218 324.13109 44.68 <.0001 Error 28 203.11936 7.25426 Corrected Total 30 851.38154 Root MSE 2.69337 R-Square 0.7614 Dependent Mean 47.37581 Adj R-Sq 0.7444 Coeff Var 5.68513 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 93.08877 8.24882 11.29 <.0001 69578 x3 1 -3.14019 0.37326 -8.41 <.0001 632.90010 x5 1 -0.07351 0.05051 -1.46 0.1567 15.36208 Parameter Estimates Variable DF Type II SS Intercept 1 923.85514 x3 1 513.41745 x5 1 15.36208 Sequential Parameter Estimates Intercept x3 x5 47.375806 0 0 82.421773 -3.310555 0 93.088766 -3.140188 -0.073509 model with x0 x3 and x5 22 15:37 Sunday, March 3, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | A | 6 + | | | | | A 4 + | | A A | A | R | e 2 + A A s | A i | A A d | u | a | A A A l 0 +---------------------------------A-----------------A-------------- | A A A | A A A | A | A A A | -2 + | A | A A | A | | -4 + | | | | A | A -6 + | -+------------+------------+------------+------------+------------+ 35 40 45 50 55 60 Predicted Value of y model with x0 x3 and x5 23 15:37 Sunday, March 3, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | A | 6 + | | | | | A 4 + | | A A | A | R | e 2 + A A s | A i | A A d | u | a | A A A l 0 +---------A-----------------A------------------------------------- | A AA | AA A | A | A A A | -2 + | A | A A | A | | -4 + | | | | A | A -6 + | ---+---------+---------+---------+---------+---------+---------+-- 8 9 10 11 12 13 14 x3 model with x0 x3 and x5 24 15:37 Sunday, March 3, 2013 Plot of resid*x5. Legend: A = 1 obs, B = 2 obs, etc. | | 8 + | | | | A | 6 + | | | | | A 4 + | | A A | A | R | e 2 + A A s | A i | A A d | u | a | A A A l 0 +---------------A-----------------A----------------------- | A A A | A A A | A | A A A | -2 + | A | A A | A | | -4 + | | | | A | A -6 + | ---+------------+------------+------------+------------+-- 146 156 166 176 186 x5 model with x0 x3 and x5 25 15:37 Sunday, March 3, 2013 Obs y x3 x5 yhat resid 1 44.609 11.37 178 44.3001 0.30886 2 54.297 8.65 156 54.4587 -0.16166 3 49.874 9.22 178 51.0515 -1.17755 4 45.681 11.95 176 42.6259 3.05515 5 39.442 13.08 174 39.2245 0.21754 6 50.541 10.13 168 48.9291 1.61193 7 44.754 11.12 176 45.2322 -0.47821 8 51.855 10.33 166 48.4481 3.40695 9 40.836 10.95 168 46.3541 -5.51812 10 46.774 10.25 162 48.9933 -2.21931 11 39.407 12.63 174 40.6375 -1.23055 12 45.441 9.63 164 50.7932 -5.35220 13 45.118 11.08 172 45.6519 -0.53386 14 45.790 10.47 186 46.5382 -0.74824 15 48.673 9.40 186 49.8982 -1.22524 16 47.467 10.50 170 47.6202 -0.15318 17 45.313 10.07 185 47.8678 -2.55482 18 59.571 8.17 166 55.2309 4.34014 19 44.811 11.63 176 43.6307 1.18029 20 49.091 10.85 162 47.1092 1.98181 21 60.055 8.63 170 53.4923 6.56267 22 37.388 14.03 186 35.3592 2.02883 23 47.273 10.60 162 47.8942 -0.62124 24 49.156 8.95 180 51.7524 -2.59638 25 46.672 10.00 162 49.7784 -3.10635 26 50.388 10.08 168 49.0861 1.30192 27 46.080 11.17 156 46.5454 -0.46539 28 54.625 8.92 146 54.3459 0.27909 29 39.203 12.88 168 40.2936 -1.09056 30 50.545 9.93 148 51.0273 -0.48230 31 47.920 11.50 170 44.4800 3.44000 model with x0 x1 x3 and x5 26 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 690.55086 230.18362 38.64 <.0001 Error 27 160.83069 5.95669 Corrected Total 30 851.38154 Root MSE 2.44063 R-Square 0.8111 Dependent Mean 47.37581 Adj R-Sq 0.7901 Coeff Var 5.15165 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 111.71806 10.23509 10.92 <.0001 69578 x3 1 -2.82538 0.35828 -7.89 <.0001 632.90010 x5 1 -0.13091 0.05059 -2.59 0.0154 15.36208 x1 1 -0.25640 0.09623 -2.66 0.0129 42.28867 Parameter Estimates Variable DF Type II SS Intercept 1 709.69014 x3 1 370.43529 x5 1 39.88512 x1 1 42.28867 Sequential Parameter Estimates Intercept x3 x5 x1 47.375806 0 0 0 82.421773 -3.310555 0 0 93.088766 -3.140188 -0.073509 0 111.718064 -2.825379 -0.130909 -0.256398 model with x0 x1 x3 and x5 27 15:37 Sunday, March 3, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A A | | 4 + | | A | A | | | 2 + | A | R | A A B A e | A AA s | i | A A A A d 0 +---------------------------------------------------A-------------- u | A A a | l | A | A A A A | | -2 + | | B | A | | A | -4 + | A | | A | | | -6 + | -+------------+------------+------------+------------+------------+ 35 40 45 50 55 60 Predicted Value of y model with x0 x1 x3 and x5 28 15:37 Sunday, March 3, 2013 Plot of resid*x1. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A A | | 4 + | | A | A | | | 2 + | A | R | A A A A A e | A B s | i | A A A A d 0 +--------------------------------------A----------------------- u | A A a | l | A | B A A | | -2 + | | A A | A | | A | -4 + | A | | A | | | -6 + | ---+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-- 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 x1 model with x0 x1 x3 and x5 29 15:37 Sunday, March 3, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A A | | 4 + | | A | A | | | 2 + | A | R | B A A A e | A A A s | i | A A AA d 0 +-----------A----------------------------------------------------- u | A A a | l | A | A A A A | | -2 + | | A A | A | | A | -4 + | A | | A | | | -6 + | ---+---------+---------+---------+---------+---------+---------+-- 8 9 10 11 12 13 14 x3 model with x0 x1 x3 and x5 30 15:37 Sunday, March 3, 2013 Plot of resid*x5. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A A | | 4 + | | A | A | | | 2 + | A | R | A B B e | A A A s | i | A A A A d 0 +--A------------------------------------------------------ u | A A a | l | A | A A A A | | -2 + | | B | A | | A | -4 + | A | | A | | | -6 + | ---+------------+------------+------------+------------+-- 146 156 166 176 186 x5 model with x0 x1 x3 and x5 31 15:37 Sunday, March 3, 2013 Obs y x1 x3 x5 yhat resid 1 44.609 44 11.37 178 45.0102 -0.40124 2 54.297 44 8.65 156 55.5753 -1.27826 3 49.874 38 9.22 178 52.6232 -2.74919 4 45.681 40 11.95 176 44.6589 1.02207 5 39.442 44 13.08 174 40.7025 -1.26047 6 50.541 44 10.13 168 49.8228 0.71821 7 44.754 45 11.12 176 45.7220 -0.96800 8 51.855 54 10.33 166 46.9556 4.89945 9 40.836 51 10.95 168 45.7112 -4.87520 10 46.774 48 10.25 162 49.2436 -2.46961 11 39.407 57 12.63 174 38.6407 0.76628 12 45.441 52 9.63 164 49.7079 -4.26693 13 45.118 51 11.08 172 44.8203 0.29774 14 45.790 51 10.47 186 44.7110 1.07898 15 48.673 49 9.40 186 48.2470 0.42603 16 47.467 52 10.50 170 46.4644 1.00260 17 45.313 40 10.07 185 48.7925 -3.47946 18 59.571 42 8.17 166 56.1351 3.43585 19 44.811 47 11.63 176 43.7683 1.04274 20 49.091 43 10.85 162 48.8304 0.26063 21 60.055 38 8.63 170 55.3374 4.71757 22 37.388 45 14.03 186 36.1911 1.19694 23 47.273 47 10.60 162 48.5111 -1.23812 24 49.156 49 8.95 180 50.3038 -1.14784 25 46.672 51 10.00 162 49.1808 -2.50876 26 50.388 49 10.08 168 48.6821 1.70593 27 46.080 54 11.17 156 45.8913 0.18868 28 54.625 50 8.92 146 54.5831 0.04190 29 39.203 54 12.88 168 39.4890 -0.28602 30 50.545 57 9.93 148 49.6729 0.87213 31 47.920 48 11.50 170 44.6646 3.25539 model with x0 x1 x3 and x5 32 15:37 Sunday, March 3, 2013 The UNIVARIATE Procedure Variable: resid (Residual) Moments N 31 Sum Weights 31 Mean 0 Sum Observations 0 Std Deviation 2.31538829 Variance 5.36102295 Skewness 0.04193167 Kurtosis 0.25490592 Uncorrected SS 160.830689 Corrected SS 160.830689 Coeff Variation . Std Error Mean 0.41585601 Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation 2.31539 Median 0.260629 Variance 5.36102 Mode . Range 9.77464 Interquartile Range 2.30321 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 2.5 Pr >= |M| 0.4731 Signed Rank S 0 Pr >= |S| 1.0000 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.967347 Pr < W 0.4492 Kolmogorov-Smirnov D 0.141305 Pr > D 0.1137 Cramer-von Mises W-Sq 0.080636 Pr > W-Sq 0.2033 Anderson-Darling A-Sq 0.457667 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 4.899447 99% 4.899447 95% 4.717566 90% 3.255386 75% Q3 1.042739 50% Median 0.260629 25% Q1 -1.260474 10% -2.749191 5% -4.266932 1% -4.875195 0% Min -4.875195 model with x0 x1 x3 and x5 33 15:37 Sunday, March 3, 2013 The UNIVARIATE Procedure Variable: resid (Residual) Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -4.87520 9 1.70593 26 -4.26693 12 3.25539 31 -3.47946 17 3.43585 18 -2.74919 3 4.71757 21 -2.50876 25 4.89945 8 Stem Leaf # Boxplot 4 79 2 0 3 34 2 | 2 | 1 000127 6 +-----+ 0 02334789 8 *--+--* -0 43 2 | | -1 33210 5 +-----+ -2 755 3 | -3 5 1 | -4 93 2 0 ----+----+----+----+ Normal Probability Plot 4.5+ * +++* | *+*+++ | ++++ 1.5+ ****** | ******* | ***+ -1.5+ **** | *+** | +++*+ -4.5+ *+++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 model with x0 x1 x3 and x5 34 15:37 Sunday, March 3, 2013 Obs resid normsc 1 -0.40124 -0.32656 2 -1.27826 -0.79950 3 -2.74919 -1.19522 4 1.02207 0.59477 5 -1.26047 -0.69349 6 0.71821 0.24301 7 -0.96800 -0.41246 8 4.89945 2.05375 9 -4.87520 -2.05375 10 -2.46961 -0.91537 11 0.76628 0.32656 12 -4.26693 -1.62576 13 0.29774 0.08030 14 1.07898 0.79950 15 0.42603 0.16112 16 1.00260 0.50153 17 -3.47946 -1.37866 18 3.43585 1.37866 19 1.04274 0.69349 20 0.26063 0.00000 21 4.71757 1.62576 22 1.19694 0.91537 23 -1.23812 -0.59477 24 -1.14784 -0.50153 25 -2.50876 -1.04505 26 1.70593 1.04505 27 0.18868 -0.08030 28 0.04190 -0.16112 29 -0.28602 -0.24301 30 0.87213 0.41246 31 3.25539 1.19522 model with x0 x1 x3 and x5 35 15:37 Sunday, March 3, 2013 Plot of resid*normsc. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | A A | | 4 + | | A | A | | | 2 + | A | R | AAAAA e | AAA s | i | AAAA d 0 + A u | AA a | l | A | AAAA | | -2 + | | AA | A | | A | -4 + | A | | A | | | -6 + | ---+---------+---------+---------+---------+---------+---------+-- -3 -2 -1 0 1 2 3 Rank for Variable resid model with x0 x3 x5 and x6 36 15:37 Sunday, March 3, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 31 Number of Observations Used 31 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 689.60921 229.86974 38.37 <.0001 Error 27 161.77233 5.99157 Corrected Total 30 851.38154 Root MSE 2.44777 R-Square 0.8100 Dependent Mean 47.37581 Adj R-Sq 0.7889 Coeff Var 5.16670 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 80.90079 8.81619 9.18 <.0001 69578 x3 1 -2.97019 0.34534 -8.60 <.0001 632.90010 x5 1 -0.37511 0.12365 -3.03 0.0053 15.36208 x6 1 0.35422 0.13484 2.63 0.0140 41.34703 Parameter Estimates Variable DF Type II SS Intercept 1 504.52712 x3 1 443.20281 x5 1 55.14175 x6 1 41.34703 Sequential Parameter Estimates Intercept x3 x5 x6 47.375806 0 0 0 82.421773 -3.310555 0 0 93.088766 -3.140188 -0.073509 0 80.900790 -2.970187 -0.375114 0.354219 model with x0 x3 x5 and x6 37 15:37 Sunday, March 3, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | | | A 4 + | A | | A | A | A A A | 2 + A | | R | e | A A s | A B i | A d 0 +------A--------------------------------------------A-------------- u | A A a | A l | A | A A A | A | AA -2 + A | | | | A A | | -4 + A | | | | | A | -6 + | -+------------+------------+------------+------------+------------+ 35 40 45 50 55 60 Predicted Value of y model with x0 x3 x5 and x6 38 15:37 Sunday, March 3, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | | | A 4 + | A | | A | A | A A A | 2 + A | | R | e | A A s | AA A i | A d 0 +-----------A--------------------------------------------------A-- u | A A a | A l | A | A A A | A | A A -2 + A | | | | A A | | -4 + A | | | | | A | -6 + | ---+---------+---------+---------+---------+---------+---------+-- 8 9 10 11 12 13 14 x3 model with x0 x3 x5 and x6 39 15:37 Sunday, March 3, 2013 Plot of resid*x5. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | | | A 4 + | A | | A | A | B A | 2 + A | | R | e | A A s | A A A i | A d 0 +--A---------------------------------------------------A-- u | A A a | A l | A | A A A | A | A A -2 + A | | | | A A | | -4 + A | | | | | A | -6 + | ---+------------+------------+------------+------------+-- 146 156 166 176 186 x5 model with x0 x3 x5 and x6 40 15:37 Sunday, March 3, 2013 Plot of resid*x6. Legend: A = 1 obs, B = 2 obs, etc. | | 6 + | | | | | | A 4 + | A | | A | A | A A A | 2 + A | | R | e | A A s | A A A i | A d 0 +-------A-----------------------------------------------A---------- u | A A a | A l | A | A A A | A | A A -2 + A | | | | A A | | -4 + A | | | | | A | -6 + | -+------------+------------+------------+------------+------------+ 150 160 170 180 190 200 x6 model with x0 x3 x5 and x6 41 15:37 Sunday, March 3, 2013 Obs y x3 x5 x6 yhat resid 1 44.609 11.37 178 182 44.8273 -0.21828 2 54.297 8.65 156 168 56.1996 -1.90264 3 49.874 9.22 178 180 50.5047 -0.63074 4 45.681 11.95 176 180 43.1464 2.53464 5 39.442 13.08 174 176 39.1234 0.31860 6 50.541 10.13 168 168 47.3024 3.23861 7 44.754 11.12 176 176 44.1947 0.55926 8 51.855 10.33 166 170 48.1670 3.68798 9 40.836 10.95 168 172 46.2837 -5.44771 10 46.774 10.25 162 164 47.7798 -1.00578 11 39.407 12.63 174 176 40.4600 -1.05299 12 45.441 9.63 164 166 49.5795 -4.13850 13 45.118 11.08 172 172 44.3971 0.72087 14 45.790 10.47 186 188 46.6248 -0.83485 15 48.673 9.40 186 188 49.8029 -1.12995 16 47.467 10.50 170 172 46.8701 0.59693 17 45.313 10.07 185 185 47.1254 -1.81238 18 59.571 8.17 166 172 55.2911 4.27994 19 44.811 11.63 176 176 42.6799 2.13105 20 49.091 10.85 162 170 48.1230 0.96802 21 60.055 8.63 170 186 57.3834 2.67162 22 37.388 14.03 186 192 37.4679 -0.07986 23 47.273 10.60 162 164 46.7402 0.53279 24 49.156 8.95 180 185 52.3276 -3.17156 25 46.672 10.00 162 168 49.9392 -3.26720 26 50.388 10.08 168 168 47.4509 2.93710 27 46.080 11.17 156 165 47.6521 -1.57211 28 54.625 8.92 146 155 54.5440 0.08102 29 39.203 12.88 168 172 40.5513 -1.34825 30 50.545 9.93 148 155 50.7939 -0.24887 31 47.920 11.50 170 176 45.3168 2.60324