The SAS System The TRANSREG Procedure Transformation Information for BoxCox(x1) Lambda R-Square Log Like -3.00 0.00 -2066.61 -2.75 0.00 -1882.90 -2.50 0.00 -1699.99 -2.25 0.00 -1518.07 -2.00 0.00 -1337.37 -1.75 0.00 -1158.22 -1.50 0.00 -981.08 -1.25 0.00 -806.69 -1.00 0.00 -636.27 -0.75 0.00 -472.02 -0.50 0.00 -318.54 -0.25 0.00 -188.23 0.00 0.00 -107.09 0.25 0.00 -76.37 0.50 + 0.00 -68.22 < 0.75 0.00 -69.22 * 1.00 0.00 -75.36 1.25 0.00 -85.09 1.50 0.00 -97.61 1.75 0.00 -112.41 2.00 0.00 -129.17 2.25 0.00 -147.60 2.50 0.00 -167.51 2.75 0.00 -188.72 3.00 0.00 -211.09 < - Best Lambda * - Confidence Interval + - Convenient Lambda The SAS System The TRANSREG Procedure TRANSREG Univariate Algorithm Iteration History for BoxCox(x1) Iteration Average Maximum Criterion Number Change Change R-Square Change Note ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Constant 1 0.00000 0.00000 0.00000 Converged ERROR: Constant transformations during the last iteration. Iteration History Footnotes Iteration Number Note Explanation ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Constant A constant transformation was avoided for x1. 1 Converged Algorithm converged. The SAS System The TRANSREG Procedure Transformation Information for BoxCox(x2) Lambda R-Square Log Like -3.00 0.00 7.7392 -2.75 0.00 13.0612 -2.50 0.00 17.9783 -2.25 0.00 22.4591 -2.00 0.00 26.4702 -1.75 0.00 29.9759 -1.50 0.00 32.9387 -1.25 0.00 35.3190 -1.00 0.00 37.0760 * -0.75 0.00 38.1681 * -0.50 0.00 38.5534 < -0.25 0.00 38.1914 * 0.00 + 0.00 37.0438 * 0.25 0.00 35.0759 0.50 0.00 32.2585 0.75 0.00 28.5694 1.00 0.00 23.9944 1.25 0.00 18.5290 1.50 0.00 12.1782 1.75 0.00 4.9570 2.00 0.00 -3.1103 2.25 0.00 -11.9915 2.50 0.00 -21.6478 2.75 0.00 -32.0355 3.00 0.00 -43.1080 < - Best Lambda * - Confidence Interval + - Convenient Lambda The SAS System The TRANSREG Procedure TRANSREG Univariate Algorithm Iteration History for BoxCox(x2) Iteration Average Maximum Criterion Number Change Change R-Square Change Note ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Constant 1 0.00000 0.00000 0.00000 Converged ERROR: Constant transformations during the last iteration. Iteration History Footnotes Iteration Number Note Explanation ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Constant A constant transformation was avoided for x2. 1 Converged Algorithm converged. The SAS System The UNIVARIATE Procedure Variable: x7 Moments N 98 Sum Weights 98 Mean 1.77566696 Sum Observations 174.015362 Std Deviation 0.62719859 Variance 0.39337807 Skewness -0.3515402 Kurtosis -0.0012065 Uncorrected SS 347.151 Corrected SS 38.1576723 Coeff Variation 35.3218594 Std Error Mean 0.06335662 Basic Statistical Measures Location Variability Mean 1.775667 Std Deviation 0.62720 Median 1.844961 Variance 0.39338 Mode 0.942868 Range 3.20272 Interquartile Range 0.90709 NOTE: The mode displayed is the smallest of 7 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 28.02654 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.988131 Pr < W 0.5328 Kolmogorov-Smirnov D 0.060409 Pr > D >0.1500 Cramer-von Mises W-Sq 0.056358 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.363474 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 3.2343469 99% 3.2343469 95% 2.7202941 90% 2.5045958 75% Q3 2.2764007 50% Median 1.8449614 25% Q1 1.3693064 10% 0.9428680 The SAS System The UNIVARIATE Procedure Variable: x7 Quantiles (Definition 5) Quantile Estimate 5% 0.5422177 1% 0.0316228 0% Min 0.0316228 Extreme Observations -------Lowest------ -----Highest----- Value Obs Value Obs 0.0316228 25 2.72029 72 0.3535534 95 2.75155 90 0.3646917 34 2.77741 78 0.4711688 35 3.07474 60 0.5422177 4 3.23435 65 Stem Leaf # Boxplot 32 3 1 | 30 7 1 | 28 | 26 91258 5 | 24 156790025 9 | 22 47889991228 11 +-----+ 20 0223461144 10 | | 18 33670123345668 14 *-----* 16 2557883588 10 | + | 14 57334466679 11 | | 12 015624779 9 +-----+ 10 007712 6 | 8 78944 5 | 6 1 1 | 4 74 2 | 2 56 2 | 0 3 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: x7 Normal Probability Plot 3.3+ ++* | +*+ | +++ | +***** | ***** | ***** | **** | **** 1.7+ ***+ | **** | **** | *** | *** | ++* | +++** |++++* * 0.1+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: x8 Moments N 98 Sum Weights 98 Mean 0.79242692 Sum Observations 77.6578378 Std Deviation 0.1578305 Variance 0.02491047 Skewness -0.0892121 Kurtosis -1.3480292 Uncorrected SS 63.9544762 Corrected SS 2.41631526 Coeff Variation 19.9173572 Std Error Mean 0.01594329 Basic Statistical Measures Location Variability Mean 0.792427 Std Deviation 0.15783 Median 0.780704 Variance 0.02491 Mode 1.000000 Range 0.53087 Interquartile Range 0.29403 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 49.70285 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.924455 Pr < W <0.0001 Kolmogorov-Smirnov D 0.113267 Pr > D <0.0100 Cramer-von Mises W-Sq 0.362327 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 2.35627 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 1.030873 99% 1.030873 95% 1.000000 90% 1.000000 75% Q3 0.948731 50% Median 0.780704 25% Q1 0.654700 10% 0.583907 5% 0.528295 1% 0.500000 The SAS System The UNIVARIATE Procedure Variable: x8 Quantiles (Definition 5) Quantile Estimate 0% Min 0.500000 Extreme Observations ------Lowest------ -----Highest----- Value Obs Value Obs 0.500000 78 1.00000 58 0.509185 71 1.00000 61 0.519875 72 1.00000 85 0.524431 29 1.00000 98 0.528295 89 1.03087 4 Stem Leaf # Boxplot 10 00000000000000003 17 | 9 555567777 9 +-----+ 9 0011244 7 | | 8 55577778899 11 | | 8 0333 4 | | 7 566779 6 *--+--* 7 01111111222223 14 | | 6 567788 6 +-----+ 6 00111222233344 14 | 5 56888 5 | 5 01223 5 | ----+----+----+----+ Multiply Stem.Leaf by 10**-1 Normal Probability Plot 1.025+ ********** * * | ***++++ | **+++ | ***++ | ***+ 0.775+ +** | ***** | ++*** | ****** | **** 0.525+* * ***+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2