SAS Output

Chapter 9 : Speed and track conditions for Kentucky Derby

Raw data Listing

Obs	Winner	year	condition	speed
1	Ben Brush	1896	good	51.6634
2	Typhoon II	1897	slow	49.8113
3	Plaudit	1898	good	51.1628
4	Manuel	1899	fast	50.0000
5	Lieut. Gibson	1900	fast	52.2772
6	His Eminence	1901	fast	51.6634
7	Alan-a-Dale	1902	fast	51.2621
8	Judge Himes	1903	fast	51.1628
9	Elwood	1904	fast	51.3619
10	Agile	1905	slow	50.4780
11	Sir Huon	1906	fast	51.2422
12	Pink Star	1907	slow	49.7738
13	Stone Street	1908	slow	48.8166
14	Wintergreen	1909	slow	51.4821
15	Donau	1910	fast	52.2152
16	Meridian	1911	fast	52.8000
17	Worth	1912	slow	51.0046
18	Donerail	1913	fast	52.8846
19	Old Rosebud	1914	fast	53.4846
20	Regret	1915	fast	52.6316
21	George Smith	1916	fast	53.2258
22	*Omar Khayyam	1917	fast	52.9695
23	Exterminator	1918	slow	50.4587
24	Sir Barton	1919	slow	50.8475
25	Paul Jones	1920	slow	51.1628
26	Behave Yourself	1921	fast	53.1401
27	Morvich	1922	fast	52.9695
28	Zev	1923	fast	52.6316
29	Black Gold	1924	fast	52.7157
30	Flying Ebony	1925	slow	51.7241
31	Bubbling Over	1926	fast	53.3118
32	Whiskery	1927	slow	52.3810
33	Reigh Count	1928	slow	50.6135
34	Clyde Van Dusen	1929	slow	50.4587
35	Gallant Fox	1930	good	51.7241
36	Twenty Grand	1931	fast	54.1872
37	Burgoo King	1932	fast	52.7157
38	Brokers Tip	1933	good	52.0505
39	Cavalcade	1934	fast	53.2258
40	Omaha	1935	good	52.8000
41	Bold Venture	1936	fast	53.6585
42	War Admiral	1937	fast	53.5714
43	Lawrin	1938	fast	52.8846
44	Johnstown	1939	fast	53.4846
45	Gallahadion	1940	fast	52.8000
46	Whirlaway	1941	fast	54.3657
47	Shut Out	1942	fast	53.0547
48	Count Fleet	1943	fast	53.2258
49	Pensive	1944	good	53.1401
50	Hoop Jr.	1945	slow	51.9685
51	Assault	1946	slow	52.1327
52	Jet Pilot	1947	slow	52.0505
53	Citation	1948	slow	52.6316
54	Ponder	1949	fast	53.1401
55	Middleground	1950	fast	54.2763
56	Count Turf	1951	fast	53.8336
57	Hill Gail	1952	fast	54.2763
58	Dark Star	1953	fast	54.0984
59	Determine	1954	fast	53.6585
60	Swaps	1955	fast	54.1872
61	Needles	1956	fast	53.4846
62	Iron Liege	1957	fast	54.0098
63	Tim Tam	1958	slow	52.8000
64	*Tomy Lee	1959	fast	54.0098
65	Venetian Way	1960	good	53.9216
66	Carry Back	1961	good	53.2258
67	Decidedly	1962	fast	54.8173
68	Chateaugay	1963	fast	54.5455
69	Northern Dancer	1964	fast	55.0000
70	Lucky Debonair	1965	fast	54.4554
71	Kauai King	1966	fast	54.0984
72	Proud Clarion	1967	fast	54.7264
73	Forward Pass**	1968	fast	54.0098
74	Majestic Prince	1969	fast	54.1872
75	Dust Commander	1970	good	53.4846
76	Canonero II	1971	fast	53.5714
77	Riva Ridge	1972	fast	54.1872
78	Secretariat	1973	fast	55.2764
79	Cannonade	1974	fast	53.2258
80	Foolish Pleasure	1975	fast	54.0984
81	Bold Forbes	1976	fast	54.2763
82	Seattle Slew	1977	fast	54.0098
83	Affirmed	1978	fast	54.4554
84	Spectacular Bid	1979	fast	53.9216
85	Genuine Risk	1980	fast	54.0984
86	Pleasant Colony	1981	fast	54.0984
87	Gato Del Sol	1982	fast	53.9216
88	Sunny’s Halo	1983	fast	53.9216
89	Swale	1984	fast	53.9216
90	Spend a Buck	1985	fast	54.9085
91	Ferdinand	1986	fast	53.7459
92	Alysheba	1987	fast	53.4846
93	Winning Colors	1988	fast	54.0098
94	Sunday Silence	1989	slow	52.8000
95	Unbridled	1990	good	54.0984
96	Strike the Gold	1991	fast	53.6585
97	Lil E. Tee	1992	fast	53.6585
98	Sea Hero	1993	fast	53.9216
99	Go for Gin	1994	slow	53.3981
100	Thunder Gulch	1995	fast	54.4554
101	Grindstone	1996	fast	54.5455
102	Silver Charm	1997	fast	53.9216
103	Real Quiet	1998	fast	54.0098
104	Charismatic	1999	fast	53.6585
105	Fusaichi Pegasus	2000	fast	54.4900

Chapter 9 : Speed and track conditions for Kentucky Derby

Plot of the raw data

                                        Plot of speed*condition.  Symbol is value of Winner.                                        
                                                                                                                                    
                              speed |                                                                                               
                                    |                                                                                               
                                 56 +                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |  S                                                                                            
                                    |                                                                                               
                                 55 +  N                                                                                            
                                    |  D                                                                                            
                                    |  P                                                                                            
                                    |  C                                                                                            
                                    |  W                                                                                            
                                    |  T                             U                                                              
                                 54 +  I                             V                                                              
                                    |  C                                                                                            
                                    |  B                                                                                            
                                    |  O                             D                                                              
                                    |  B                                                           G                                
                                    |  G                             P                                                              
                                 53 +  *                                                                                            
                                    |  M                             O                             T                                
                                    |  R                                                           C                                
                                    |                                                                                               
                                    |  L                                                           W                                
                                    |  D                                                           A                                
                                 52 +                                B                             H                                
                                    |                                                                                               
                                    |  H                             B                             F                                
                                    |                                                              W                                
                                    |  A                                                                                            
                                    |  J                             P                             P                                
                                 51 +                                                              W                                
                                    |                                                              S                                
                                    |                                                              R                                
                                    |                                                              A                                
                                    |                                                                                               
                                    |                                                                                               
                                 50 +  M                                                                                            
                                    |                                                              T                                
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                 49 +                                                                                               
                                    |                                                              S                                
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                 48 +                                                                                               
                                    |                                                                                               
                                    ---+-----------------------------+-----------------------------+--                              
                                     fast                          good                          slow                               
                                                                                                                                    
                                                                 condition                                                          
                                                                                                                                    
NOTE: 60 obs hidden.

Chapter 9 : Speed and track conditions for Kentucky Derby

Plot of the raw data

                                          Plot of speed*year.  Symbol is value of Winner.                                           
                                                                                                                                    
     speed |                                                                                                                        
           |                                                                                                                        
        56 +                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                     S                                  
           |                                                                                                                        
        55 +                                                                            N                                           
           |                                                                          D                      S                      
           |                                                                               P                                        
           |                                                                           C L            A                TG   F       
           |                                                     W        M H                       B                               
           |                                           T                     D S          K  M  R  F    GP        U                 
        54 +                                                                     I *V       F        S S  GSS   W    S   SR         
           |                                                               C                                                        
           |                                                B                 D                               F    SL      C        
           |                          O                      W J                N             DC               A                    
           |                                      B                                                                   G             
           |                            G    B            C        CP    P           C            C                                 
        53 +                             *    M                   S                                                                 
           |                       M D                     O  L G                 T                              S                  
           |                           R       ZB       B               C                                                           
           |                                                                                                                        
           |            L                          W                                                                                
           |                      D                                   A                                                             
        52 +                                             B           H J                                                            
           |                                                                                                                        
           |        B    H                       F    G                                                                             
           |                     W                                                                                                  
           |              A E                                                                                                       
           |          P    J  S             P                                                                                       
        51 +                        W                                                                                               
           |                               S                                                                                        
           |                                        R                                                                               
           |                 A            E          C                                                                              
           |                                                                                                                        
           |                                                                                                                        
        50 +           M                                                                                                            
           |         T         P                                                                                                    
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
        49 +                                                                                                                        
           |                    S                                                                                                   
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
        48 +                                                                                                                        
           |                                                                                                                        
           ---+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--     
            1890      1900      1910      1920      1930      1940      1950      1960      1970      1980      1990      2000      
                                                                                                                                    
                                                                   year

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

The GLM Procedure

Class Level Information
Class	Levels	Values
condition	3	fast good slow

Number of Observations Read	105
Number of Observations Used	105

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

The GLM Procedure

Dependent Variable: speed

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	5	143.7858750	28.7571750	70.04	<.0001
Error	99	40.6500458	0.4106065
Corrected Total	104	184.4359208

R-Square	Coeff Var	Root MSE	speed Mean
0.779598	1.208063	0.640786	53.04243

Source	DF	Type I SS	Mean Square	F Value	Pr > F
year	1	103.5684162	103.5684162	252.23	<.0001
condition	2	38.1346829	19.0673414	46.44	<.0001
year*condition	2	2.0827760	1.0413880	2.54	0.0843

Source	DF	Type III SS	Mean Square	F Value	Pr > F
year	1	40.61645387	40.61645387	98.92	<.0001
condition	2	2.34155232	1.17077616	2.85	0.0625
year*condition	2	2.08277597	1.04138799	2.54	0.0843

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

Residual analysis

                                          Plot of resid*YHat.  Symbol is value of Winner.                                           
                                                                                                                                    
resid |                                                                                                                             
      |                                                                                                                             
  1.5 +                                                                                                                             
      |                                                                                                                             
      |                              W                                           T                  N    S                          
      |                                                                                W           D                                
  1.0 +              W                                                                                                              
      |                                                                O                    M         P                             
      |                                                                                      H      C                               
      |                            F                    C               G               V     DS     L          S                   
  0.5 +                                                          T                  B                                               
      |                 W               B                             D    BP B     W        C  I*          A                       
      |                        P                      A              M   *  M         J              K M R                          
      |          A                                   H J                           C          D        F   B                        
  0.0 +-----------------------S--------------------------------L--------R----------------------------------F-----------G------------
      |                                                                     ZB          CC      N           S GU      T  F          
      |   T                               P                          D            B  L S   P     G           S                      
      |                      E                                      B                 G                 C      GS W                 
 -0.5 +                                                                                                                             
      |            P                  R                        H  G                                              F   S SR           
      |                                C                                                     S                      S               
      |                                                                                                   C       A  L              
 -1.0 +                                                         AE                                                       C          
      |                                                          JS                                                                 
      |                                                                                                                             
      |                                                                                                                             
 -1.5 +                                                                                                                             
      |             S                                                                                                               
      |                                                                                                                             
      |                                                                                                                             
 -2.0 +                                                                                                                             
      |                                                                                                                             
      |                                                       M                                                                     
      |                                                                                                                             
 -2.5 +                                                                                                                             
      |                                                                                                                             
      ---+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+--
       50.0        50.5        51.0        51.5        52.0        52.5        53.0        53.5        54.0        54.5        55.0 
                                                                                                                                    
                                                                   YHat                                                             
                                                                                                                                    
NOTE: 4 obs hidden.

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

Residual analysis

                                          Plot of resid*year.  Symbol is value of Winner.                                           
                                                                                                                                    
     resid |                                                                                                                        
           |                                                                                                                        
       1.5 +                                                                                                                        
           |                                                                                                                        
           |                                       W   T                                N        S                                  
           |                                                     W                    D                                             
       1.0 +                     W                                                                                                  
           |                          O                                   M                P                                        
           |                                                                H          C                                            
           |                            G        F                      C    D S    V    L                   S                      
       0.5 +                                                B                     T                                                 
           |        B               WD       B    B          W      P      C     I *                  A                             
           |                       M     *  P M            O   J      A                   K  M  R                                   
           |                 A                            C          H J      D             F       B                               
       0.0 +------------L--------------R---S-------------------------------------------------------F--------------------G------     
           |                                   ZB                  C            N    C        D      S  GP        U    T    F       
           |         TP           D                     B     L   S      P                             S              G             
           |                              E              B      G                              C          GSS   W                   
      -0.5 +                                                                                                                        
           |             H     P                    R G                                                       F      S   SR         
           |                                         C                                                           S S                
           |                                                                                      C            A    L               
      -1.0 +              A E                                                                                              C        
           |               J  S                                                                                                     
           |                                                                                                                        
           |                                                                                                                        
      -1.5 +                                                                                                                        
           |                    S                                                                                                   
           |                                                                                                                        
           |                                                                                                                        
      -2.0 +                                                                                                                        
           |                                                                                                                        
           |           M                                                                                                            
           |                                                                                                                        
      -2.5 +                                                                                                                        
           |                                                                                                                        
           ---+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--     
            1890      1900      1910      1920      1930      1940      1950      1960      1970      1980      1990      2000      
                                                                                                                                    
                                                                   year

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

Residual analysis

                                        Plot of resid*condition.  Symbol is value of Winner.                                        
                                                                                                                                    
                              resid |                                                                                               
                                    |                                                                                               
                                1.5 +                                                                                               
                                    |                                                                                               
                                    |  T                                                           W                                
                                    |  W                                                                                            
                                1.0 +                                                              W                                
                                    |  O                                                                                            
                                    |  H                                                                                            
                                    |  G                             V                             F                                
                                0.5 +  B                                                           T                                
                                    |  D                             B                             W                                
                                    |  M                             O                             P                                
                                    |  C                                                           A                                
                                0.0 +--L-----------------------------------------------------------S--                              
                                    |  Z                             C                                                              
                                    |  D                             P                             T                                
                                    |  G                             B                             E                                
                               -0.5 +                                                                                               
                                    |  H                             G                             P                                
                                    |  S                                                           C                                
                                    |  C                                                                                            
                               -1.0 +  A                                                                                            
                                    |  J                                                                                            
                                    |                                                                                               
                                    |                                                                                               
                               -1.5 +                                                                                               
                                    |                                                              S                                
                                    |                                                                                               
                                    |                                                                                               
                               -2.0 +                                                                                               
                                    |                                                                                               
                                    |  M                                                                                            
                                    |                                                                                               
                               -2.5 +                                                                                               
                                    |                                                                                               
                                    ---+-----------------------------+-----------------------------+--                              
                                     fast                          good                          slow                               
                                                                                                                                    
                                                                 condition                                                          
                                                                                                                                    
NOTE: 66 obs hidden.

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - linear

Residual analysis

The UNIVARIATE Procedure

Variable: resid

Moments
N	105	Sum Weights	105
Mean	0	Sum Observations	0
Std Deviation	0.62519263	Variance	0.39086583
Skewness	-0.4247796	Kurtosis	0.80774296
Uncorrected SS	40.6500458	Corrected SS	40.6500458
Coeff Variation	.	Std Error Mean	0.06101255

Basic Statistical Measures
Location		Variability
Mean	0.000000	Std Deviation	0.62519
Median	0.022672	Variance	0.39087
Mode	.	Range	3.47678
		Interquartile Range	0.74486

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	91.5	Pr >= \|S\|	0.7715

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.982403	Pr < W	0.1784
Kolmogorov-Smirnov	D	0.05245	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.039921	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.276695	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	1.2569786
99%	1.2115248
95%	1.0653810
90%	0.7692421
75% Q3	0.3795203
50% Median	0.0226722
25% Q1	-0.3653388
10%	-0.7986058
5%	-0.9931567
1%	-1.6418310
0% Min	-2.2198062

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
-2.21981	4	1.12454	46
-1.64183	13	1.18918	36
-1.15429	8	1.19947	69
-1.14780	11	1.21152	32
-1.03063	7	1.25698	78

   Stem Leaf                     #  Boxplot                        Normal Probability Plot                                          
     12 016                      3     |         1.3+                                             ++*  *                            
     10 729                      3     |            |                                         ***+*                                 
      8 2509                     4     |            |                                      ***                                      
      6 01233877                 8     |            |                                   ****                                        
      4 0347479                  7     |            |                                +***                                           
      2 5567899112345789        16  +-----+         |                            *****                                              
      0 233013335899            12  *--+--*         |                         ****                                                  
     -0 997432211109632         15  |     |         |                     *****                                                     
     -2 7774210887441           13  +-----+         |                 *****                                                         
     -4 998200                   6     |        -0.5+                **+                                                            
     -6 9985421                  7     |            |            ****                                                               
     -8 988220                   6     |            |         ****                                                                  
    -10 553                      3     |            |     *+**+                                                                     
    -12                                             |   +++                                                                         
    -14                                             |+++                                                                            
    -16 4                        1     0            |   *                                                                           
    -18                                             |                                                                               
    -20                                             |                                                                               
    -22 2                        1     0        -2.3+*                                                                              
        ----+----+----+----+                         +----+----+----+----+----+----+----+----+----+----+                            
    Multiply Stem.Leaf by 10**-1                         -2        -1         0        +1        +2

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

*** ===> Best model <=== ***

The GLM Procedure

Class Level Information
Class	Levels	Values
condition	3	fast good slow

Number of Observations Read	105
Number of Observations Used	105

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

*** ===> Best model <=== ***

The GLM Procedure

Dependent Variable: speed

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	8	157.1190601	19.6398825	69.02	<.0001
Error	96	27.3168607	0.2845506
Corrected Total	104	184.4359208

R-Square	Coeff Var	Root MSE	speed Mean
0.851890	1.005672	0.533433	53.04243

Source	DF	Type I SS	Mean Square	F Value	Pr > F
year	1	103.5684162	103.5684162	363.97	<.0001
condition	2	38.1346829	19.0673414	67.01	<.0001
year*condition	2	2.0827760	1.0413880	3.66	0.0294
year*year	1	11.4570011	11.4570011	40.26	<.0001
yearyearcondition	2	1.8761840	0.9380920	3.30	0.0412

Source	DF	Type III SS	Mean Square	F Value	Pr > F
year	1	2.93641115	2.93641115	10.32	0.0018
condition	2	1.86621254	0.93310627	3.28	0.0419
year*condition	2	1.87218831	0.93609416	3.29	0.0415
year*year	1	2.75466449	2.75466449	9.68	0.0025
yearyearcondition	2	1.87618404	0.93809202	3.30	0.0412

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|
Intercept	-1176.386286	B	589.5339348	-2.00	0.0488
year	1.225935	B	0.6063550	2.02	0.0460
condition fast	-738.162017	B	658.2706525	-1.12	0.2649
condition good	1181.908988	B	934.0279139	1.27	0.2088
condition slow	0.000000	B	.	.	.
year*condition fast	0.769054	B	0.6767239	1.14	0.2586
year*condition good	-1.208707	B	0.9621921	-1.26	0.2121
year*condition slow	0.000000	B	.	.	.
year*year	-0.000306	B	0.0001559	-1.96	0.0529
yearyearcondition fast	-0.000200	B	0.0001739	-1.15	0.2534
yearyearcondition good	0.000309	B	0.0002478	1.25	0.2151
yearyearcondition slow	0.000000	B	.	.	.

The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

Residual analysis

                                          Plot of resid*YHat.  Symbol is value of Winner.                                           
                                                                                                                                    
resid |                                                                                                                             
      |                                                                                                                             
  1.5 +                                                                                                                             
      |                                                                                                                             
      |                                                                                                                             
      |                                                                                                                             
      |                                                                                                                             
      |                       W                      W                         O                                          S         
  1.0 +                                                                                                                             
      |                                                                                             T                               
      |                                                 L                                                                N          
      |                                                                                                                 S           
      |                                                                          G                           W   F      D           
      |                                                                   M  D                      V               G    P          
  0.5 +                           W                F                                                                T               
      |                                                                   C        *                                    C           
      |                 A                           B                                   B                          MH               
      |                                                                          OT           B                          LA         
      |     T                               P             H                     R                 G      B            S             
      |                                                                  D               M                W        R D    B         
  0.0 +-----------------------------------------------------------------A------------------------------------------S------M---------
      |                                    S                             J                           C     J        CSI* KF         
      |                                               P                H                               C    D            FSU        
      |                                                                                    ZB                     C      GS         
      |                                                     A                                    S                   D              
      |                                   E                    E                B                                     S F           
 -0.5 +                    P                                 J                                                C                     
      |                                                                                              B                N             
      |                                                           S           G                           L   S         A C         
      |                                               R                                                           P                 
      |                                                                                                     G                       
      |                                                                                                                             
 -1.0 +                                                C                                                                  C         
      |                                                                                                                             
      |                                                                                                                             
      |                                                                                                                             
      |                                                                                                                             
      |                                               M                                                                             
 -1.5 +                     S                                                                                                       
      |                                                                                                                             
      ---+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+--
       49.5        50.0        50.5        51.0        51.5        52.0        52.5        53.0        53.5        54.0        54.5 
                                                                                                                                    
                                                                   YHat                                                             
                                                                                                                                    
NOTE: 8 obs hidden.

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

Residual analysis

                                          Plot of resid*year.  Symbol is value of Winner.                                           
                                                                                                                                    
     resid |                                                                                                                        
           |                                                                                                                        
       1.5 +                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                     W    O            W                                             S                                  
       1.0 +                                                                                                                        
           |                                           T                                                                            
           |            L                                                               N                                           
           |                                                                                                 S                      
           |                            G                        W                    D                                     F       
           |                       M D                                              V      P                            G           
       0.5 +                        W            F                                                                     T            
           |                             *                              C              C                                            
           |        B        A               B                      P     M H                                                       
           |                                      B        O                      T      L            A                             
           |         T   H             R    P               B                  S                                      G             
           |                      D           M              W               D                      B                     R         
       0.0 +----------------------------------------------------------A----------------------M--R------------------------S-----     
           |                               S                   J       J   C     I * C    K        F    GP      W    S              
           |          P                                   C          H                      F D      S            U                 
           |                                   ZB                                                      S  GSS              C        
           |              A                                                   D                                  S                  
           |                E             E              B                                                    F    SL               
      -0.5 +               J   P                                   C                                                                
           |                                            B                       N                                                   
           |                  S                       G       L   S                            C               A                    
           |                                        R                    P                                                          
           |                                                    G                                                                   
           |                                                                                                                        
      -1.0 +                                         C                                            C                                 
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |                                                                                                                        
           |           M                                                                                                            
      -1.5 +                    S                                                                                                   
           |                                                                                                                        
           ---+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--     
            1890      1900      1910      1920      1930      1940      1950      1960      1970      1980      1990      2000      
                                                                                                                                    
                                                                   year

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

Residual analysis

                                        Plot of resid*condition.  Symbol is value of Winner.                                        
                                                                                                                                    
                              resid |                                                                                               
                                    |                                                                                               
                                1.5 +                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |  O                                                           W                                
                                1.0 +                                                                                               
                                    |  T                                                                                            
                                    |  L                                                                                            
                                    |  S                                                                                            
                                    |  G                                                                                            
                                    |  M                             V                                                              
                                0.5 +  T                                                           W                                
                                    |  *                                                           C                                
                                    |  B                             B                             A                                
                                    |  B                             O                             T                                
                                    |  H                                                           T                                
                                    |  D                                                                                            
                                0.0 +--M-----------------------------------------------------------A--                              
                                    |  J                             C                             S                                
                                    |  C                             P                             H                                
                                    |  Z                                                                                            
                                    |  A                                                           S                                
                                    |  E                             B                             E                                
                               -0.5 +  J                                                           P                                
                                    |  B                                                                                            
                                    |  S                             G                                                              
                                    |  P                                                           R                                
                                    |  G                                                                                            
                                    |                                                                                               
                               -1.0 +  C                                                           C                                
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |                                                                                               
                                    |  M                                                                                            
                               -1.5 +                                                              S                                
                                    |                                                                                               
                                    ---+-----------------------------+-----------------------------+--                              
                                     fast                          good                          slow                               
                                                                                                                                    
                                                                 condition                                                          
                                                                                                                                    
NOTE: 58 obs hidden.

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with GLM - quadratic

Residual analysis

The UNIVARIATE Procedure

Variable: resid

Moments
N	105	Sum Weights	105
Mean	0	Sum Observations	0
Std Deviation	0.51250573	Variance	0.26266212
Skewness	-0.1157465	Kurtosis	0.21748374
Uncorrected SS	27.3168607	Corrected SS	27.3168607
Coeff Variation	.	Std Error Mean	0.05001544

Basic Statistical Measures
Location		Variability
Mean	0.00000	Std Deviation	0.51251
Median	-0.07481	Variance	0.26266
Mode	.	Range	2.60589
		Interquartile Range	0.68680

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	0	Pr > \|t\|	1.0000
Sign	M	-5.5	Pr >= \|M\|	0.3291
Signed Rank	S	-5.5	Pr >= \|S\|	0.9861

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.990125	Pr < W	0.6419
Kolmogorov-Smirnov	D	0.062791	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.037907	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.236589	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	1.1207308
99%	1.0825225
95%	0.8444068
90%	0.6833044
75% Q3	0.3437084
50% Median	-0.0748126
25% Q1	-0.3430915
10%	-0.6332637
5%	-0.7640386
1%	-1.3832697
0% Min	-1.4851635

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
-1.485163	13	0.905388	36
-1.383270	4	1.051401	32
-0.977254	79	1.073519	78
-0.966192	34	1.082523	19
-0.829274	45	1.120731	14

   Stem Leaf                        #  Boxplot                        Normal Probability Plot                                       
     10 5782                        4     |         1.1+                                           * *+*+ *                         
      8 241                         3     |            |                                        ***++                               
      6 248017                      6     |            |                                     ****                                   
      4 027894589                   9     |            |                                 ****                                       
      2 01667991446679             14  +-----+         |                             *****                                          
      0 56811236779                11  |  +  |         |                         +****                                              
     -0 98853321110998888751100    23  *-----*         |                     ******                                                 
     -2 998855477544320            15  +-----+         |                *****+                                                      
     -4 610710                      6     |            |              ***+                                                          
     -6 657443331                   9     |            |         ******                                                             
     -8 873                         3     |            |     *+**+                                                                  
    -10                                                |  ++++                                                                      
    -12 8                           1     0            |++ *                                                                        
    -14 9                           1     0        -1.5+*                                                                           
        ----+----+----+----+---                         +----+----+----+----+----+----+----+----+----+----+                         
    Multiply Stem.Leaf by 10**-1                            -2        -1         0        +1        +2

Chapter 9 : Speed and track conditions for Kentucky Derby

Analysis of Covariance with REG

The REG Procedure

Model: MODEL1

Dependent Variable: speed

Number of Observations Read	105
Number of Observations Used	105

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	8	157.11906	19.63988	69.02	<.0001
Error	96	27.31686	0.28455
Corrected Total	104	184.43592

Root MSE	0.53343	R-Square	0.8519
Dependent Mean	53.04243	Adj R-Sq	0.8395
Coeff Var	1.00567

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	1	-1176.38627	589.53395	-2.00	0.0488
year	1	1.22594	0.60636	2.02	0.0460
Cond1	1	-738.16203	658.27068	-1.12	0.2649
Cond2	1	1181.90897	934.02793	1.27	0.2088
YC1	1	0.76905	0.67672	1.14	0.2586
YC2	1	-1.20871	0.96219	-1.26	0.2121
Year2	1	-0.00030556	0.00015589	-1.96	0.0529
YC12	1	-0.00019983	0.00017389	-1.15	0.2534
YC22	1	0.00030921	0.00024776	1.25	0.2151