The SAS System d n b i u t t a s m o o t n t r p p r k a a q r O a i n c u a b c n c e a c s k g e s l e 1 ATLANTA MOTOR SPEEDWAY 24 1.54 62 197.478 163.633 2 BRISTOL MOTOR SPEEDWAY 36 0.53 62 126.370 101.074 3 CALIFORNIA SPEEDWAY 14 2.00 6 187.432 155.012 4 CHICAGOLAND SPEEDWAY 18 1.50 2 183.717 121.200 5 DARLINGTON RACEWAY 24 1.37 62 173.797 139.958 6 DAYTONA INTERNATIONAL SPEEDWAY 31 2.50 63 210.364 177.602 7 DOVER INTERNATIONAL SPEEDWAY 24 1.00 62 159.964 132.719 8 HOMESTEAD-MIAMI SPEEDWAY 6 1.50 4 156.440 140.335 9 INDIANAPOLIS MOTOR SPEEDWAY 12 2.50 9 181.072 155.912 10 KANSAS SPEEDWAY 15 1.50 2 176.449 110.576 11 LAS VEGAS MOTOR SPEEDWAY 12 1.50 5 172.563 146.530 12 LOWES MOTOR SPEEDWAY 24 1.50 62 186.034 160.306 13 MARTINSVILLE SPEEDWAY 12 0.53 62 95.371 82.223 14 MICHIGAN INTERNATIONAL SPEEDWAY 18 2.00 61 191.149 173.997 15 NEW HAMPSHIRE INTERNATIONAL SPEEDWAY 12 1.06 16 132.089 117.134 16 NORTH CAROLINA SPEEDWAY 23 1.02 63 158.035 131.103 17 PHOENIX INTERNATIONAL RACEWAY 10 1.00 15 134.718 118.132 18 POCONO RACEWAY 9 2.50 50 172.391 144.892 19 RICHMOND INTERNATIONAL RACEWAY 14 0.75 62 126.499 108.707 20 TALLADEGA SUPERSPEEDWAY 33 2.66 62 212.809 188.354 21 TEXAS MOTOR SPEEDWAY 24 1.50 6 192.137 144.276 The SAS System The GLM Procedure Number of observations 21 The SAS System The GLM Procedure Dependent Variable: topqual Sum of Source DF Squares Mean Square F Value Pr > F Model 6 18153.60724 3025.60121 129.42 <.0001 Error 14 327.29806 23.37843 Corrected Total 20 18480.90531 R-Square Coeff Var Root MSE topqual Mean 0.982290 2.878966 4.835125 167.9466 Source DF Type I SS Mean Square F Value Pr > F banking 1 2381.23302 2381.23302 101.86 <.0001 distance 1 11719.70494 11719.70494 501.30 <.0001 numraces 1 694.56967 694.56967 29.71 <.0001 banking*distance 1 28.98579 28.98579 1.24 0.2843 banking*banking 1 1815.64025 1815.64025 77.66 <.0001 distance*distance 1 1513.47357 1513.47357 64.74 <.0001 Source DF Type III SS Mean Square F Value Pr > F banking 1 202.552489 202.552489 8.66 0.0107 distance 1 2634.649063 2634.649063 112.70 <.0001 numraces 1 18.054793 18.054793 0.77 0.3943 banking*distance 1 17.490844 17.490844 0.75 0.4016 banking*banking 1 59.414574 59.414574 2.54 0.1332 distance*distance 1 1513.473572 1513.473572 64.74 <.0001 Standard Parameter Estimate Error t Value Pr > |t| Intercept 6.9424497 10.07665138 0.69 0.5021 banking 2.8052964 0.95305433 2.94 0.0107 distance 132.8460096 12.51396179 10.62 <.0001 numraces -0.0496646 0.05651431 -0.88 0.3943 banking*distance 0.1429537 0.16527142 0.86 0.4016 banking*banking -0.0329952 0.02069721 -1.59 0.1332 distance*distance -30.4069004 3.77913520 -8.05 <.0001 The SAS System The GLM Procedure Number of observations 21 The SAS System The GLM Procedure Dependent Variable: topqual Sum of Source DF Squares Mean Square F Value Pr > F Model 4 18119.01323 4529.75331 200.27 <.0001 Error 16 361.89208 22.61825 Corrected Total 20 18480.90531 R-Square Coeff Var Root MSE topqual Mean 0.980418 2.831773 4.755865 167.9466 Source DF Type I SS Mean Square F Value Pr > F banking 1 2381.23302 2381.23302 105.28 <.0001 distance 1 11719.70494 11719.70494 518.15 <.0001 banking*banking 1 1732.51371 1732.51371 76.60 <.0001 distance*distance 1 2285.56156 2285.56156 101.05 <.0001 Source DF Type III SS Mean Square F Value Pr > F banking 1 308.356042 308.356042 13.63 0.0020 distance 1 4242.116706 4242.116706 187.55 <.0001 banking*banking 1 57.056591 57.056591 2.52 0.1318 distance*distance 1 2285.561559 2285.561559 101.05 <.0001 Standard Parameter Estimate Error t Value Pr > |t| Intercept -0.2621893 7.74903773 -0.03 0.9734 banking 2.8150085 0.76240025 3.69 0.0020 distance 140.3490892 10.24820581 13.69 <.0001 banking*banking -0.0296964 0.01869734 -1.59 0.1318 distance*distance -31.7149346 3.15498213 -10.05 <.0001 The SAS System Plot of e*yhat. Legend: A = 1 obs, B = 2 obs, etc. e | | 7.5 + | | A | | A 5.0 + | | A A | A | A 2.5 + | A | A | A A | A A 0.0 +-------------------------------------------------------------------- | | A A A | A | -2.5 + | A | A A | | -5.0 + | | | | -7.5 + | | | A | -10.0 + | A | | | -12.5 + | ---+--------+--------+--------+--------+--------+--------+--------+-- 80 100 120 140 160 180 200 220 yhat The SAS System The UNIVARIATE Procedure Variable: e Moments N 21 Sum Weights 21 Mean 0 Sum Observations 0 Std Deviation 4.25377525 Variance 18.0946038 Skewness -0.939156 Kurtosis 1.03856017 Uncorrected SS 361.892077 Corrected SS 361.892077 Coeff Variation . Std Error Mean 0.92824986 Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation 4.25378 Median 0.653070 Variance 18.09460 Mode . Range 16.65040 Interquartile Range 4.47699 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 1.5 Pr >= |M| 0.6636 Signed Rank S 15.5 Pr >= |S| 0.6023 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.931307 Pr < W 0.1462 Kolmogorov-Smirnov D 0.130643 Pr > D >0.1500 Cramer-von Mises W-Sq 0.059546 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.46356 Pr > A-Sq 0.2363 Quantiles (Definition 5) Quantile Estimate 100% Max 6.36263 99% 6.36263 95% 5.74939 90% 4.15633 75% Q3 2.77905 50% Median 0.65307 25% Q1 -1.69793 The SAS System The UNIVARIATE Procedure Variable: e Quantiles (Definition 5) Quantile Estimate 10% -3.47578 5% -9.14841 1% -10.28777 0% Min -10.28777 Extreme Observations ------Lowest------ -----Highest----- Value Obs Value Obs -10.28777 15 3.58885 20 -9.14841 5 3.76562 4 -3.47578 14 4.15633 11 -3.32395 12 5.74939 19 -2.93086 18 6.36263 1 Stem Leaf # Boxplot 6 4 1 | 4 27 2 | 2 0868 4 +-----+ 0 37127 5 *--+--* -0 7988 4 +-----+ -2 539 3 | -4 -6 -8 1 1 0 -10 3 1 0 ----+----+----+----+ Normal Probability Plot 7+ ++++* | ++*+* | **+*+* 1+ ****+* | ***+*+ | * *+*+++ -5+ +++++ | ++++ | +++++ * -11+++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System Frequency 9 + ***** | ***** | ***** | ***** | ***** 8 + ***** | ***** | ***** | ***** | ***** 7 + ***** ***** | ***** ***** | ***** ***** | ***** ***** | ***** ***** 6 + ***** ***** | ***** ***** | ***** ***** | ***** ***** | ***** ***** 5 + ***** ***** | ***** ***** | ***** ***** | ***** ***** | ***** ***** 4 + ***** ***** | ***** ***** | ***** ***** | ***** ***** | ***** ***** 3 + ***** ***** ***** | ***** ***** ***** | ***** ***** ***** | ***** ***** ***** | ***** ***** ***** 2 + ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** 1 + ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** | ***** ***** ***** ***** -------------------------------------------------------------------- -10 -6 -2 2 6 e Midpoint