------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 1 SORTED BY OXYGEN CAPACITY (OXY) Obs AGE WEIGHT OXY RUNTIME RSTPULSE RUNPULSE MAXPULSE LOXY LRUNTIME 1 45 87.66 37.388 14.03 56 186 192 3.62135 2.64120 2 54 91.63 39.203 12.88 44 168 172 3.66875 2.55568 3 57 73.37 39.407 12.63 58 174 176 3.67394 2.53607 4 44 81.42 39.442 13.08 63 174 176 3.67483 2.57108 5 51 69.63 40.836 10.95 57 168 172 3.70956 2.39334 6 44 89.47 44.609 11.37 62 178 182 3.79794 2.43098 7 45 66.45 44.754 11.12 51 176 176 3.80118 2.40875 8 47 77.45 44.811 11.63 58 176 176 3.80245 2.45359 9 51 67.25 45.118 11.08 48 172 172 3.80928 2.40514 10 40 75.07 45.313 10.07 62 185 185 3.81359 2.30956 11 52 76.32 45.441 9.63 48 164 166 3.81641 2.26488 12 40 75.98 45.681 11.95 70 176 180 3.82168 2.48073 13 51 73.71 45.790 10.47 59 186 188 3.82407 2.34851 14 54 79.38 46.080 11.17 62 156 165 3.83038 2.41323 15 51 77.91 46.672 10.00 48 162 168 3.84314 2.30259 16 48 91.63 46.774 10.25 48 162 164 3.84533 2.32728 17 47 79.15 47.273 10.60 47 162 164 3.85594 2.36085 18 52 82.78 47.467 10.50 53 170 172 3.86003 2.35138 19 48 61.24 47.920 11.50 52 170 176 3.86953 2.44235 20 49 76.32 48.673 9.40 56 186 188 3.88512 2.24071 21 43 81.19 49.091 10.85 64 162 170 3.89368 2.38417 22 49 81.42 49.156 8.95 44 180 185 3.89500 2.19165 23 38 89.02 49.874 9.22 55 178 180 3.90950 2.22138 24 49 73.37 50.388 10.08 67 168 168 3.91975 2.31055 25 44 73.03 50.541 10.13 45 168 168 3.92278 2.31550 26 57 59.08 50.545 9.93 49 148 155 3.92286 2.29556 27 54 83.12 51.855 10.33 50 166 170 3.94845 2.33505 28 44 85.84 54.297 8.65 45 156 168 3.99447 2.15756 29 50 70.87 54.625 8.92 48 146 155 4.00049 2.18830 30 42 68.15 59.571 8.17 40 166 172 4.08717 2.10047 31 38 81.87 60.055 8.63 48 170 186 4.09526 2.15524 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 2 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: AGE Moments N 31 Sum Weights 31 Mean 47.6774194 Sum Observations 1478 Std Deviation 5.21144316 Variance 27.1591398 Skewness -0.1345521 Kurtosis -0.676941 Uncorrected SS 71282 Corrected SS 814.774194 Coeff Variation 10.9306318 Std Error Mean 0.93600282 Basic Statistical Measures Location Variability Mean 47.67742 Std Deviation 5.21144 Median 48.00000 Variance 27.15914 Mode 44.00000 Range 19.00000 Interquartile Range 7.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 4. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 50.93726 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 3 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: AGE Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.970403 Pr < W 0.5302 Kolmogorov-Smirnov D 0.092957 Pr > D >0.1500 Cramer-von Mises W-Sq 0.043048 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.277467 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 57 99% 57 95% 57 90% 54 75% Q3 51 50% Median 48 25% Q1 44 10% 40 5% 38 1% 38 0% Min 38 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 38 31 54 2 38 23 54 14 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 4 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: AGE Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 40 12 54 27 40 10 57 3 42 30 57 26 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 38 2 6.5 6.5 44 4 12.9 32.3 49 3 9.7 61.3 52 2 6.5 83.9 40 2 6.5 12.9 45 2 6.5 38.7 50 1 3.2 64.5 54 3 9.7 93.5 42 1 3.2 16.1 47 2 6.5 45.2 51 4 12.9 77.4 57 2 6.5 100.0 43 1 3.2 19.4 48 2 6.5 51.6 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 5 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: AGE Stem Leaf # Boxplot Normal Probability Plot 56 00 2 | 57+ *+++ * 54 000 3 | | * *+*+ 52 00 2 | | **+++ 50 00000 5 +-----+ 51+ **+*++ 48 00000 5 *-----* | ****++ 46 00 2 | + | | +*++ 44 000000 6 +-----+ 45+ ***** 42 00 2 | | **+ 40 00 2 | | *+*+ 38 00 2 | 39+ * ++*+ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 6 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: WEIGHT Moments N 31 Sum Weights 31 Mean 77.4445161 Sum Observations 2400.78 Std Deviation 8.32856764 Variance 69.3650389 Skewness -0.2112754 Kurtosis -0.2698478 Uncorrected SS 188008.197 Corrected SS 2080.95117 Coeff Variation 10.7542381 Std Error Mean 1.49585491 Basic Statistical Measures Location Variability Mean 77.44452 Std Deviation 8.32857 Median 77.45000 Variance 69.36504 Mode 73.37000 Range 32.55000 Interquartile Range 9.75000 NOTE: The mode displayed is the smallest of 4 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 51.77275 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 7 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: WEIGHT Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.979926 Pr < W 0.8106 Kolmogorov-Smirnov D 0.072234 Pr > D >0.1500 Cramer-von Mises W-Sq 0.018724 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.158197 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 91.63 99% 91.63 95% 91.63 90% 89.02 75% Q3 82.78 50% Median 77.45 25% Q1 73.03 10% 67.25 5% 61.24 1% 59.08 0% Min 59.08 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs 59.08 26 87.66 1 61.24 19 89.02 23 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 8 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: WEIGHT Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs 66.45 7 89.47 6 67.25 9 91.63 2 68.15 30 91.63 16 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 59.08 1 3.2 3.2 73.03 1 3.2 25.8 77.91 1 3.2 54.8 83.12 1 3.2 80.6 61.24 1 3.2 6.5 73.37 2 6.5 32.3 79.15 1 3.2 58.1 85.84 1 3.2 83.9 66.45 1 3.2 9.7 73.71 1 3.2 35.5 79.38 1 3.2 61.3 87.66 1 3.2 87.1 67.25 1 3.2 12.9 75.07 1 3.2 38.7 81.19 1 3.2 64.5 89.02 1 3.2 90.3 68.15 1 3.2 16.1 75.98 1 3.2 41.9 81.42 2 6.5 71.0 89.47 1 3.2 93.5 69.63 1 3.2 19.4 76.32 2 6.5 48.4 81.87 1 3.2 74.2 91.63 2 6.5 100.0 70.87 1 3.2 22.6 77.45 1 3.2 51.6 82.78 1 3.2 77.4 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 9 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: WEIGHT Stem Leaf # Boxplot Normal Probability Plot 9 22 2 | 92.5+ *++++* 8 6899 4 | | **+*+*+ 8 111233 6 +-----+ | **+***+ 7 56667899 8 *--+--* | **+***+ 7 013334 6 +-----+ | ***+*+ 6 678 3 | | *+*+** 6 1 1 | | ++++*+ 5 9 1 | 57.5+++++* ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 10 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNTIME Moments N 31 Sum Weights 31 Mean 10.586129 Sum Observations 328.17 Std Deviation 1.38741409 Variance 1.92491785 Skewness 0.51465208 Kurtosis 0.13604218 Uncorrected SS 3531.7975 Corrected SS 57.7475355 Coeff Variation 13.1059624 Std Error Mean 0.24918693 Basic Statistical Measures Location Variability Mean 10.58613 Std Deviation 1.38741 Median 10.47000 Variance 1.92492 Mode . Range 5.86000 Interquartile Range 1.74000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 42.48268 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.973587 Pr < W 0.6223 Kolmogorov-Smirnov D 0.078874 Pr > D >0.1500 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 11 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNTIME Tests for Normality Test --Statistic--- -----p Value------ Cramer-von Mises W-Sq 0.037488 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.26425 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 14.03 99% 14.03 95% 13.08 90% 12.63 75% Q3 11.37 50% Median 10.47 25% Q1 9.63 10% 8.92 5% 8.63 1% 8.17 0% Min 8.17 Extreme Observations ----Lowest---- ----Highest---- Value Obs Value Obs 8.17 30 11.95 12 8.63 31 12.63 3 8.65 28 12.88 2 8.92 29 13.08 4 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 12 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNTIME Extreme Observations ----Lowest---- ----Highest---- Value Obs Value Obs 8.95 22 14.03 1 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 8.17 1 3.2 3.2 9.93 1 3.2 29.0 10.50 1 3.2 54.8 11.50 1 3.2 80.6 8.63 1 3.2 6.5 10.00 1 3.2 32.3 10.60 1 3.2 58.1 11.63 1 3.2 83.9 8.65 1 3.2 9.7 10.07 1 3.2 35.5 10.85 1 3.2 61.3 11.95 1 3.2 87.1 8.92 1 3.2 12.9 10.08 1 3.2 38.7 10.95 1 3.2 64.5 12.63 1 3.2 90.3 8.95 1 3.2 16.1 10.13 1 3.2 41.9 11.08 1 3.2 67.7 12.88 1 3.2 93.5 9.22 1 3.2 19.4 10.25 1 3.2 45.2 11.12 1 3.2 71.0 13.08 1 3.2 96.8 9.40 1 3.2 22.6 10.33 1 3.2 48.4 11.17 1 3.2 74.2 14.03 1 3.2 100.0 9.63 1 3.2 25.8 10.47 1 3.2 51.6 11.37 1 3.2 77.4 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 13 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNTIME Stem Leaf # Boxplot Normal Probability Plot 14 0 1 0 14.25+ * + 13 | +++ 13 1 1 | | * ++++ 12 69 2 | | * *+++ 12 0 1 | | +++ 11 56 2 | | +*** 11 01124 5 +-----+ 11.25+ +**** 10 5568 4 *--+--* | +*** 10 011123 6 | | | ****** 9 69 2 +-----+ | **+ 9 024 3 | | ++** 8 669 3 | | *+*+* * 8 2 1 | 8.25+ * +++ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 14 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RSTPULSE Moments N 31 Sum Weights 31 Mean 53.4516129 Sum Observations 1657 Std Deviation 7.61944315 Variance 58.055914 Skewness 0.37532513 Kurtosis -0.7399667 Uncorrected SS 90311 Corrected SS 1741.67742 Coeff Variation 14.2548424 Std Error Mean 1.36849239 Basic Statistical Measures Location Variability Mean 53.45161 Std Deviation 7.61944 Median 52.00000 Variance 58.05591 Mode 48.00000 Range 30.00000 Interquartile Range 11.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 39.05876 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.957676 Pr < W 0.2529 Kolmogorov-Smirnov D 0.149943 Pr > D 0.0755 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 15 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RSTPULSE Tests for Normality Test --Statistic--- -----p Value------ Cramer-von Mises W-Sq 0.100226 Pr > W-Sq 0.1083 Anderson-Darling A-Sq 0.566077 Pr > A-Sq 0.1356 Quantiles (Definition 5) Quantile Estimate 100% Max 70 99% 70 95% 67 90% 63 75% Q3 59 50% Median 52 25% Q1 48 10% 45 5% 44 1% 40 0% Min 40 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 40 30 62 14 44 22 63 4 44 2 64 21 45 28 67 24 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 16 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RSTPULSE Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 45 25 70 12 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 40 1 3.2 3.2 49 1 3.2 41.9 55 1 3.2 58.1 62 3 9.7 87.1 44 2 6.5 9.7 50 1 3.2 45.2 56 2 6.5 64.5 63 1 3.2 90.3 45 2 6.5 16.1 51 1 3.2 48.4 57 1 3.2 67.7 64 1 3.2 93.5 47 1 3.2 19.4 52 1 3.2 51.6 58 2 6.5 74.2 67 1 3.2 96.8 48 6 19.4 38.7 53 1 3.2 54.8 59 1 3.2 77.4 70 1 3.2 100.0 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 17 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RSTPULSE Stem Leaf # Boxplot Normal Probability Plot 7 0 1 | 72.5+ *++++ 6 7 1 | | *+++++ 6 22234 5 | | ***+*+*+ 5 5667889 7 +-----+ 57.5+ *+**+*+ 5 0123 4 *--+--* | ++****+ 4 5578888889 10 +-----+ | *+***+*+* * 4 044 3 | 42.5+ * +*++++ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 18 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNPULSE Moments N 31 Sum Weights 31 Mean 169.645161 Sum Observations 5259 Std Deviation 10.2519864 Variance 105.103226 Skewness -0.3490442 Kurtosis 0.04275973 Uncorrected SS 895317 Corrected SS 3153.09677 Coeff Variation 6.04319413 Std Error Mean 1.84131112 Basic Statistical Measures Location Variability Mean 169.6452 Std Deviation 10.25199 Median 170.0000 Variance 105.10323 Mode 162.0000 Range 40.00000 Interquartile Range 14.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 4. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 92.13281 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 19 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNPULSE Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.964206 Pr < W 0.3752 Kolmogorov-Smirnov D 0.098885 Pr > D >0.1500 Cramer-von Mises W-Sq 0.036268 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.29867 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 186 99% 186 95% 186 90% 185 75% Q3 176 50% Median 170 25% Q1 162 10% 156 5% 148 1% 146 0% Min 146 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 146 29 180 22 148 26 185 10 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 20 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNPULSE Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 156 28 186 1 156 14 186 13 162 21 186 20 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 146 1 3.2 3.2 164 1 3.2 29.0 172 1 3.2 61.3 180 1 3.2 87.1 148 1 3.2 6.5 166 2 6.5 35.5 174 2 6.5 67.7 185 1 3.2 90.3 156 2 6.5 12.9 168 4 12.9 48.4 176 3 9.7 77.4 186 3 9.7 100.0 162 4 12.9 25.8 170 3 9.7 58.1 178 2 6.5 83.9 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 21 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: RUNPULSE Stem Leaf # Boxplot Normal Probability Plot 18 5666 4 | 187.5+ * *+++++ * 18 0 1 | | *++++ 17 66688 5 +-----+ | ****++ 17 000244 6 *--+--* | ****++ 16 668888 6 | | 167.5+ ****++ 16 22224 5 +-----+ | *****+ 15 66 2 | | *+*++ 15 | | +++++ 14 68 2 | 147.5+ +++*+ * ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 22 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: MAXPULSE Moments N 31 Sum Weights 31 Mean 173.774194 Sum Observations 5387 Std Deviation 9.16409544 Variance 83.9806452 Skewness 0.01898547 Kurtosis -0.2344884 Uncorrected SS 938641 Corrected SS 2519.41935 Coeff Variation 5.27356522 Std Error Mean 1.64592013 Basic Statistical Measures Location Variability Mean 173.7742 Std Deviation 9.16410 Median 172.0000 Variance 83.98065 Mode 172.0000 Range 37.00000 Interquartile Range 12.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 5. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 105.5788 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 23 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: MAXPULSE Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.969825 Pr < W 0.5143 Kolmogorov-Smirnov D 0.125144 Pr > D >0.1500 Cramer-von Mises W-Sq 0.059937 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.370437 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 192 99% 192 95% 188 90% 186 75% Q3 180 50% Median 172 25% Q1 168 10% 164 5% 155 1% 155 0% Min 155 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 155 29 185 22 155 26 186 31 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 24 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: MAXPULSE Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 164 17 188 13 164 16 188 20 165 14 192 1 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 155 2 6.5 6.5 168 4 12.9 32.3 180 2 6.5 77.4 186 1 3.2 90.3 164 2 6.5 12.9 170 2 6.5 38.7 182 1 3.2 80.6 188 2 6.5 96.8 165 1 3.2 16.1 172 5 16.1 54.8 185 2 6.5 87.1 192 1 3.2 100.0 166 1 3.2 19.4 176 5 16.1 71.0 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 25 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: MAXPULSE Stem Leaf # Boxplot Normal Probability Plot 19 2 1 | 192.5+ +++*++ 18 55688 5 | | ** *+*+++ 18 002 3 +-----+ | ***++++ 17 66666 5 | | | ****+ 17 0022222 7 *--+--* | ***+*+ 16 568888 6 +-----+ | ***+*+ 16 44 2 | | +*+*++ 15 55 2 | 157.5+ *++++* ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 26 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: OXY Moments N 31 Sum Weights 31 Mean 47.3758065 Sum Observations 1468.65 Std Deviation 5.3272305 Variance 28.3793848 Skewness 0.43633214 Kurtosis 0.63025159 Uncorrected SS 70429.8597 Corrected SS 851.381545 Coeff Variation 11.2446223 Std Error Mean 0.95679884 Basic Statistical Measures Location Variability Mean 47.37581 Std Deviation 5.32723 Median 46.77400 Variance 28.37938 Mode . Range 22.66700 Interquartile Range 5.57700 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 49.51491 Pr > |t| <.0001 Sign M 15.5 Pr >= |M| <.0001 Signed Rank S 248 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.953656 Pr < W 0.1968 Kolmogorov-Smirnov D 0.140461 Pr > D 0.1192 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 27 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: OXY Tests for Normality Test --Statistic--- -----p Value------ Cramer-von Mises W-Sq 0.084738 Pr > W-Sq 0.1788 Anderson-Darling A-Sq 0.540539 Pr > A-Sq 0.1567 Quantiles (Definition 5) Quantile Estimate 100% Max 60.055 99% 60.055 95% 59.571 90% 54.297 75% Q3 50.388 50% Median 46.774 25% Q1 44.811 10% 39.442 5% 39.203 1% 37.388 0% Min 37.388 Extreme Observations -----Lowest----- -----Highest---- Value Obs Value Obs 37.388 1 51.855 27 39.203 2 54.297 28 39.407 3 54.625 29 39.442 4 59.571 30 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 28 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: OXY Extreme Observations -----Lowest----- -----Highest---- Value Obs Value Obs 40.836 5 60.055 31 Frequency Counts Percents Percents Percents Percents Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum Value Count Cell Cum 37.388 1 3.2 3.2 45.118 1 3.2 29.0 47.273 1 3.2 54.8 50.541 1 3.2 80.6 39.203 1 3.2 6.5 45.313 1 3.2 32.3 47.467 1 3.2 58.1 50.545 1 3.2 83.9 39.407 1 3.2 9.7 45.441 1 3.2 35.5 47.920 1 3.2 61.3 51.855 1 3.2 87.1 39.442 1 3.2 12.9 45.681 1 3.2 38.7 48.673 1 3.2 64.5 54.297 1 3.2 90.3 40.836 1 3.2 16.1 45.790 1 3.2 41.9 49.091 1 3.2 67.7 54.625 1 3.2 93.5 44.609 1 3.2 19.4 46.080 1 3.2 45.2 49.156 1 3.2 71.0 59.571 1 3.2 96.8 44.754 1 3.2 22.6 46.672 1 3.2 48.4 49.874 1 3.2 74.2 60.055 1 3.2 100.0 44.811 1 3.2 25.8 46.774 1 3.2 51.6 50.388 1 3.2 77.4 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 29 UNIVARIATE DISTRIBUTIONS The UNIVARIATE Procedure Variable: OXY Stem Leaf # Boxplot Normal Probability Plot 60 1 1 0 61+ * ++ 58 6 1 0 | * ++++ 56 | +++ 54 36 2 | | *+*++ 52 | | ++++ 50 4559 4 +-----+ | ++**** 48 7129 4 | | 49+ +**** 46 178359 6 *--+--* | ***** 44 68813478 8 +-----+ | ******** 42 | | ++++ 40 8 1 | | +++* 38 244 3 | | +*+* * 36 4 1 | 37+ *+++ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 30 BIVARIATE SIMPLE (Pearson) AND RANK (Spearman) CORRELATIONS The CORR Procedure 7 Variables: AGE WEIGHT RSTPULSE RUNPULSE MAXPULSE RUNTIME OXY Pearson Correlation Coefficients, N = 31 Prob > |r| under H0: Rho=0 AGE WEIGHT RSTPULSE RUNPULSE MAXPULSE RUNTIME OXY AGE 1.00000 -0.23354 -0.16410 -0.33787 -0.43292 0.18875 -0.30459 0.2061 0.3777 0.0630 0.0150 0.3092 0.0957 WEIGHT -0.23354 1.00000 0.04397 0.18152 0.24938 0.14351 -0.16275 0.2061 0.8143 0.3284 0.1761 0.4412 0.3817 RSTPULSE -0.16410 0.04397 1.00000 0.35246 0.30512 0.45038 -0.39936 0.3777 0.8143 0.0518 0.0951 0.0110 0.0260 RUNPULSE -0.33787 0.18152 0.35246 1.00000 0.92975 0.31365 -0.39797 0.0630 0.3284 0.0518 <.0001 0.0858 0.0266 MAXPULSE -0.43292 0.24938 0.30512 0.92975 1.00000 0.22610 -0.23674 0.0150 0.1761 0.0951 <.0001 0.2213 0.1997 RUNTIME 0.18875 0.14351 0.45038 0.31365 0.22610 1.00000 -0.86219 0.3092 0.4412 0.0110 0.0858 0.2213 <.0001 OXY -0.30459 -0.16275 -0.39936 -0.39797 -0.23674 -0.86219 1.00000 0.0957 0.3817 0.0260 0.0266 0.1997 <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 31 BIVARIATE SIMPLE (Pearson) AND RANK (Spearman) CORRELATIONS The CORR Procedure Spearman Correlation Coefficients, N = 31 Prob > |r| under H0: Rho=0 AGE WEIGHT RSTPULSE RUNPULSE MAXPULSE RUNTIME OXY AGE 1.00000 -0.16152 -0.11766 -0.29810 -0.38682 0.15883 -0.18351 0.3853 0.5285 0.1033 0.0316 0.3934 0.3231 WEIGHT -0.16152 1.00000 -0.02958 0.07541 0.14260 0.07483 -0.09318 0.3853 0.8745 0.6868 0.4441 0.6891 0.6181 RSTPULSE -0.11766 -0.02958 1.00000 0.36765 0.32634 0.48618 -0.38028 0.5285 0.8745 0.0419 0.0732 0.0056 0.0348 RUNPULSE -0.29810 0.07541 0.36765 1.00000 0.93152 0.28390 -0.43748 0.1033 0.6868 0.0419 <.0001 0.1217 0.0138 MAXPULSE -0.38682 0.14260 0.32634 0.93152 1.00000 0.20580 -0.32239 0.0316 0.4441 0.0732 <.0001 0.2667 0.0769 RUNTIME 0.15883 0.07483 0.48618 0.28390 0.20580 1.00000 -0.80806 0.3934 0.6891 0.0056 0.1217 0.2667 <.0001 OXY -0.18351 -0.09318 -0.38028 -0.43748 -0.32239 -0.80806 1.00000 0.3231 0.6181 0.0348 0.0138 0.0769 <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 32 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic AGE Minimum Value 38.00000 Maximum Value 57.00000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 33 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 The LOESS Procedure Smoothing Parameter: 0.3 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 14 kd Tree Bucket Size 1 Degree of Local Polynomials 1 Smoothing Parameter 0.30000 Points in Local Neighborhood 9 Residual Sum of Squares 589.91492 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 34 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 13 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 678.39396 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 35 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 The LOESS Procedure Smoothing Parameter: 0.7 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 9 kd Tree Bucket Size 4 Degree of Local Polynomials 1 Smoothing Parameter 0.70000 Points in Local Neighborhood 21 Residual Sum of Squares 725.15272 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 36 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 --------------------------------------------------- SmoothingParameter=0.3 --------------------------------------------------- Plot of DepVar*AGE. Symbol used is '*'. Plot of Pred*AGE. Symbol used is '+'. 60.00000 É * * 55.00000 É * * + + * + + * * 50.00000 É * * O * * X * + Y + * * * * * + * + * 45.00000 É * * * * * * + + * 40.00000 É * * * * 35.00000 É ˜ÉÉÉÉÉÉÉÉÉÉÉ 38.00000 40.00000 42.00000 44.00000 46.00000 48.00000 50.00000 52.00000 54.00000 56.00000 58.00000 AGE NOTE: 22 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 37 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*AGE. Symbol used is '*'. Plot of Pred*AGE. Symbol used is '+'. 60.00000 É * * 55.00000 É * * + * + * * 50.00000 É * * O + * * X + * + Y + * * + * * * + + * + * 45.00000 É * * * * * * + * 40.00000 É * * * * 35.00000 É ˜ÉÉÉÉÉÉÉÉÉÉÉ 38.00000 40.00000 42.00000 44.00000 46.00000 48.00000 50.00000 52.00000 54.00000 56.00000 58.00000 AGE NOTE: 21 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 38 smoothed plot of oxy versus age with smooth 0.3 0.5 0.7 --------------------------------------------------- SmoothingParameter=0.7 --------------------------------------------------- Plot of DepVar*AGE. Symbol used is '*'. Plot of Pred*AGE. Symbol used is '+'. 60.00000 É * * 55.00000 É * * + * + * * 50.00000 É * * O + * * X + * Y + + * * + + * * * * + * 45.00000 É * * * * * * + * 40.00000 É * * * * 35.00000 É ˜ÉÉÉÉÉÉÉÉÉÉÉ 38.00000 40.00000 42.00000 44.00000 46.00000 48.00000 50.00000 52.00000 54.00000 56.00000 58.00000 AGE NOTE: 22 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 39 smoothed plot of oxy versus weight with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic WEIGHT Minimum Value 59.08000 Maximum Value 91.63000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 40 smoothed plot of oxy versus weight with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 16 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 743.16828 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 41 smoothed plot of oxy versus weight with smooth 0.5 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*WEIGHT. Symbol used is '*'. Plot of Pred*WEIGHT. Symbol used is '+'. 60.00000 É * * 55.00000 É * * * * * 50.00000 É * + * O + + * **+ + X * + + + + + + Y +++ + * * * * * *+ + * + 45.00000 É * * * * * + * + * 40.00000 É * * * * 35.00000 É ˜ÉÉÉÉÉÉÉÉÉ 55.00000 60.00000 65.00000 70.00000 75.00000 80.00000 85.00000 90.00000 95.00000 WEIGHT NOTE: 11 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 42 smoothed plot of oxy versus rstpulse with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic RSTPULSE Minimum Value 40.00000 Maximum Value 70.00000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 43 smoothed plot of oxy versus rstpulse with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 14 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 593.04051 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 44 smoothed plot of oxy versus rstpulse with smooth 0.5 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*RSTPULSE. Symbol used is '*'. Plot of Pred*RSTPULSE. Symbol used is '+'. 60.00000 É * * 55.00000 É + * * * * * 50.00000 É + + * * O * + + + * * X + + * + Y * * * + * * + + * 45.00000 É * * + + * * + + + * 40.00000 É * * * * 35.00000 É ˜ÉÉÉÉÉÉÉ 40.00000 45.00000 50.00000 55.00000 60.00000 65.00000 70.00000 RSTPULSE NOTE: 17 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 45 smoothed plot of oxy versus runpulse with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic RUNPULSE Minimum Value 146.00000 Maximum Value 186.00000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 46 smoothed plot of oxy versus runpulse with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 12 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 676.40587 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 47 smoothed plot of oxy versus runpulse with smooth 0.5 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*RUNPULSE. Symbol used is '*'. Plot of Pred*RUNPULSE. Symbol used is '+'. 60.00000 É * * 55.00000 É * * + + * * * 50.00000 É + * * O * + + + * * X + * Y * * + * + * + * 45.00000 É * * + * * * + * 40.00000 É * * * 35.00000 É ˜ÉÉÉÉÉ 146.00000 156.00000 166.00000 176.00000 186.00000 RUNPULSE NOTE: 23 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 48 smoothed plot of oxy versus maxpulse with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic MAXPULSE Minimum Value 155.00000 Maximum Value 192.00000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 49 smoothed plot of oxy versus maxpulse with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 11 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 644.20377 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 50 smoothed plot of oxy versus maxpulse with smooth 0.5 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*MAXPULSE. Symbol used is '*'. Plot of Pred*MAXPULSE. Symbol used is '+'. 60.00000 É * * 55.00000 É* * + * * * 50.00000 É * * O * * * X + * Y * + * * + + + + + * + * * 45.00000 É * * * * * + + * 40.00000 É * * * 35.00000 É ˜ÉÉÉÉÉÉÉÉÉ 155.00000 160.00000 165.00000 170.00000 175.00000 180.00000 185.00000 190.00000 195.00000 MAXPULSE NOTE: 23 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 51 smoothed plot of oxy versus runtime with smooth 0.5 The LOESS Procedure Independent Variable Scaling Scaling applied: None Statistic RUNTIME Minimum Value 8.17000 Maximum Value 14.03000 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 52 smoothed plot of oxy versus runtime with smooth 0.5 The LOESS Procedure Smoothing Parameter: 0.5 Dependent Variable: OXY Fit Summary Fit Method kd Tree Blending Linear Number of Observations 31 Number of Fitting Points 16 kd Tree Bucket Size 3 Degree of Local Polynomials 1 Smoothing Parameter 0.50000 Points in Local Neighborhood 15 Residual Sum of Squares 147.92744 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 53 smoothed plot of oxy versus runtime with smooth 0.5 --------------------------------------------------- SmoothingParameter=0.5 --------------------------------------------------- Plot of DepVar*RUNTIME. Symbol used is '*'. Plot of Pred*RUNTIME. Symbol used is '+'. 60.00000 É * * + 55.00000 É * * + * + * * 50.00000 É * + * O * * + * X ++++ ++ + * Y * * ** * ++ +* + * 45.00000 É * * ** * + * + * + 40.00000 É + + * * * * + 35.00000 É ˜ÉÉÉÉÉÉÉÉ 8.00000 9.00000 10.00000 11.00000 12.00000 13.00000 14.00000 15.00000 RUNTIME NOTE: 9 obs hidden. ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 54 UNIVARIATE LINEAR REGRESSIONS WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 78.98823 78.98823 2.97 0.0957 Error 29 772.39332 26.63425 Corrected Total 30 851.38154 Root MSE 5.16084 R-Square 0.0928 Dependent Mean 47.37581 Adj R-Sq 0.0615 Coeff Var 10.89340 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 62.22064 8.66983 7.18 <.0001 AGE 1 -0.31136 0.18080 -1.72 0.0957 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 55 UNIVARIATE LINEAR REGRESSIONS WITH OXY The REG Procedure Model: MODEL2 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 22.55181 22.55181 0.79 0.3817 Error 29 828.82973 28.58034 Corrected Total 30 851.38154 Root MSE 5.34606 R-Square 0.0265 Dependent Mean 47.37581 Adj R-Sq -0.0071 Coeff Var 11.28436 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 55.43795 9.12663 6.07 <.0001 WEIGHT 1 -0.10410 0.11719 -0.89 0.3817 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 56 UNIVARIATE LINEAR REGRESSIONS WITH OXY The REG Procedure Model: MODEL3 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 135.78285 135.78285 5.50 0.0260 Error 29 715.59870 24.67582 Corrected Total 30 851.38154 Root MSE 4.96748 R-Square 0.1595 Dependent Mean 47.37581 Adj R-Sq 0.1305 Coeff Var 10.48526 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 62.30029 6.42453 9.70 <.0001 RSTPULSE 1 -0.27921 0.11903 -2.35 0.0260 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 57 UNIVARIATE LINEAR REGRESSIONS WITH OXY The REG Procedure Model: MODEL4 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 134.84474 134.84474 5.46 0.0266 Error 29 716.53681 24.70817 Corrected Total 30 851.38154 Root MSE 4.97073 R-Square 0.1584 Dependent Mean 47.37581 Adj R-Sq 0.1294 Coeff Var 10.49213 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 82.45825 15.04386 5.48 <.0001 RUNPULSE 1 -0.20680 0.08852 -2.34 0.0266 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 58 UNIVARIATE LINEAR REGRESSIONS WITH OXY The REG Procedure Model: MODEL5 Dependent Variable: OXY Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 47.71646 47.71646 1.72 0.1997 Error 29 803.66508 27.71259 Corrected Total 30 851.38154 Root MSE 5.26427 R-Square 0.0560 Dependent Mean 47.37581 Adj R-Sq 0.0235 Coeff Var 11.11174 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 71.29074 18.24976 3.91 0.0005 MAXPULSE 1 -0.13762 0.10488 -1.31 0.1997 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 59 AUGMENTED DATA SET WITH ADDITIONAL VALUES OF RUNTIME Obs RUNTIME LRUNTIME OXY 1 8.00 2.07944 . 2 8.10 2.09186 . 3 8.17 2.10047 59.571 4 8.20 2.10413 . 5 8.30 2.11626 . 6 8.40 2.12823 . 7 8.50 2.14007 . 8 8.60 2.15176 . 9 8.63 2.15524 60.055 10 8.65 2.15756 54.297 11 8.70 2.16332 . 12 8.80 2.17475 . 13 8.90 2.18605 . 14 8.92 2.18830 54.625 15 8.95 2.19165 49.156 16 9.00 2.19722 . 17 9.10 2.20827 . 18 9.20 2.21920 . 19 9.22 2.22138 49.874 20 9.30 2.23001 . 21 9.40 2.24071 . 22 9.40 2.24071 48.673 23 9.50 2.25129 . 24 9.60 2.26176 . 25 9.63 2.26488 45.441 26 9.70 2.27213 . 27 9.80 2.28238 . 28 9.90 2.29253 . 29 9.93 2.29556 50.545 30 10.00 2.30259 . 31 10.00 2.30259 46.672 32 10.07 2.30956 45.313 33 10.08 2.31055 50.388 34 10.10 2.31254 . 35 10.13 2.31550 50.541 36 10.20 2.32239 . ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 60 AUGMENTED DATA SET WITH ADDITIONAL VALUES OF RUNTIME Obs RUNTIME LRUNTIME OXY 37 10.25 2.32728 46.774 38 10.30 2.33214 . 39 10.33 2.33505 51.855 40 10.40 2.34181 . 41 10.47 2.34851 45.790 42 10.50 2.35138 . 43 10.50 2.35138 47.467 44 10.60 2.36085 . 45 10.60 2.36085 47.273 46 10.70 2.37024 . 47 10.80 2.37955 . 48 10.85 2.38417 49.091 49 10.90 2.38876 . 50 10.95 2.39334 40.836 51 11.00 2.39790 . 52 11.08 2.40514 45.118 53 11.10 2.40695 . 54 11.12 2.40875 44.754 55 11.17 2.41323 46.080 56 11.20 2.41591 . 57 11.30 2.42480 . 58 11.37 2.43098 44.609 59 11.40 2.43361 . 60 11.50 2.44235 . 61 11.50 2.44235 47.920 62 11.60 2.45101 . 63 11.63 2.45359 44.811 64 11.70 2.45959 . 65 11.80 2.46810 . 66 11.90 2.47654 . 67 11.95 2.48073 45.681 68 12.00 2.48491 . 69 12.10 2.49321 . 70 12.20 2.50144 . 71 12.30 2.50960 . 72 12.40 2.51770 . ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 61 AUGMENTED DATA SET WITH ADDITIONAL VALUES OF RUNTIME Obs RUNTIME LRUNTIME OXY 73 12.50 2.52573 . 74 12.60 2.53370 . 75 12.63 2.53607 39.407 76 12.70 2.54160 . 77 12.80 2.54945 . 78 12.88 2.55568 39.203 79 12.90 2.55723 . 80 13.00 2.56495 . 81 13.08 2.57108 39.442 82 13.10 2.57261 . 83 13.20 2.58022 . 84 13.30 2.58776 . 85 13.40 2.59525 . 86 13.50 2.60269 . 87 13.60 2.61007 . 88 13.70 2.61740 . 89 13.80 2.62467 . 90 13.90 2.63189 . 91 14.00 2.63906 . 92 14.03 2.64120 37.388 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 62 UNIVARIATE LINEAR REGRESSION OF RUNTIME WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY 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| Intercept 1 82.42177 3.85530 21.38 <.0001 RUNTIME 1 -3.31056 0.36119 -9.17 <.0001 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 63 UNIVARIATE LINEAR REGRESSION OF RUNTIME WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Test of First and Second Moment Specification DF Chi-Square Pr > ChiSq 2 4.38 0.1117 ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 64 UNIVARIATE LINEAR REGRESSION OF RUNTIME WITH OXY The REG Procedure Model: MODEL1 Dependent Variable: OXY Output Statistics Dep Var Predicted Std Error Std Error Student Obs OXY Value Mean Predict 95% CL Mean 95% CL Predict Residual Residual Residual -2-1 0 1 2 1 . 55.9373 1.0562 53.7772 58.0975 49.9223 61.9523 . . . 2 . 55.6063 1.0244 53.5111 57.7014 49.6143 61.5982 . . . 3 59.5710 55.3745 1.0023 53.3246 57.4245 49.3982 61.3508 4.1965 2.555 1.642 | |*** | 4 . 55.2752 0.9929 53.2445 57.3059 49.3055 61.2449 . . . 5 . 54.9442 0.9617 52.9773 56.9111 48.9958 60.8925 . . . 6 . 54.6131 0.9309 52.7093 56.5170 48.6853 60.5409 . . . 7 . 54.2821 0.9004 52.4405 56.1237 48.3740 60.1901 . . . 8 . 53.9510 0.8704 52.1708 55.7312 48.0618 59.8402 . . . 9 60.0550 53.8517 0.8615 52.0897 55.6137 47.9679 59.7354 6.2033 2.606 2.380 | |**** | 10 54.2970 53.7855 0.8556 52.0355 55.5354 47.9053 59.6656 0.5115 2.608 0.196 | | | 11 . 53.6199 0.8409 51.9001 55.3398 47.7487 59.4912 . . . 12 . 53.2889 0.8119 51.6283 54.9495 47.4347 59.1431 . . . 13 . 52.9578 0.7835 51.3553 54.5603 47.1199 58.7958 . . . 14 54.6250 52.8916 0.7779 51.3006 54.4827 47.0568 58.7265 1.7334 2.632 0.659 | |* | 15 49.1560 52.7923 0.7696 51.2183 54.3663 46.9621 58.6225 -3.6363 2.635 -1.380 | **| | 16 . 52.6268 0.7558 51.0810 54.1726 46.8041 58.4494 . . . 17 . 52.2957 0.7288 50.8051 53.7863 46.4875 58.1040 . . . 18 . 51.9647 0.7026 50.5276 53.4017 46.1699 57.7594 . . . 19 49.8740 51.8985 0.6975 50.4719 53.3250 46.1063 57.6906 -2.0245 2.655 -0.763 | *| | 20 . 51.6336 0.6774 50.2482 53.0190 45.8515 57.4157 . . . 21 . 51.3026 0.6531 49.9668 52.6383 45.5321 57.0730 . . . 22 48.6730 51.3026 0.6531 49.9668 52.6383 45.5321 57.0730 -2.6296 2.666 -0.986 | *| | 23 . 50.9715 0.6300 49.6830 52.2600 45.2118 56.7312 . . . 24 . 50.6404 0.6082 49.3966 51.8843 44.8906 56.3903 . . . 25 45.4410 50.5411 0.6019 49.3101 51.7722 44.7940 56.2882 -5.1001 2.678 -1.904 | ***| | 26 . 50.3094 0.5878 49.1073 51.5115 44.5684 56.0504 . . . 27 . 49.9783 0.5689 48.8148 51.1419 44.2453 55.7114 . . . 28 . 49.6473 0.5518 48.5188 50.7758 43.9213 55.3733 . . . 29 50.5450 49.5480 0.5470 48.4292 50.6667 43.8239 55.2721 0.9970 2.690 0.371 | | | ------------------------------------------------------------------------------------------------------------------------------ FITNESS DATA EXAMPLE FROM SAS MANUALS 11:49 Tuesday, February 17, 2004 65 UNIVARIATE LINEAR REGRESSION OF RUNTIME WITH OXY