SAS Output

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: resid (Studentized Residual without Current Obs)

Moments
N	34	Sum Weights	34
Mean	0.00322877	Sum Observations	0.10977821
Std Deviation	1.06223778	Variance	1.12834911
Skewness	-0.1945835	Kurtosis	0.85547767
Uncorrected SS	37.235875	Corrected SS	37.2355205
Coeff Variation	32899.1383	Std Error Mean	0.18217228

Basic Statistical Measures
Location		Variability
Mean	0.00323	Std Deviation	1.06224
Median	-0.14887	Variance	1.12835
Mode	.	Range	5.34371
		Interquartile Range	1.33709

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	0.017724	Pr > \|t\|	0.9860
Sign	M	-1	Pr >= \|M\|	0.8642
Signed Rank	S	-4.5	Pr >= \|S\|	0.9400

Quantiles (Definition 5)
Quantile	Estimate
100% Max	2.388392
99%	2.388392
95%	1.717966
90%	1.389806
75% Q3	0.870424
50% Median	-0.148870
25% Q1	-0.466665
10%	-1.284790
5%	-1.471129
1%	-2.955321
0% Min	-2.955321

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
-2.95532	1	1.08958	30
-1.47113	2	1.38981	31
-1.31782	3	1.49739	32
-1.28479	4	1.71797	33
-1.13006	5	2.38839	34

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: resid (Studentized Residual without Current Obs)

    Stem Leaf                     #             Boxplot                                   Normal Probability Plot               
       2 4                        1                |                   2.25+                                            ++*++   
       1 57                       2                |                       |                                        ++*+        
       1 0114                     4                |                       |                                  ****+*            
       0 5599                     4             +-----+                    |                              ****+                 
       0 11123                    5             |  +  |                    |                         +****                      
      -0 444333221                9             *-----*                    |                  ********                          
      -0 9875                     4             +-----+                    |               ***+++                               
      -1 331                      3                |                       |        *  *+**+                                    
      -1 5                        1                |                       |       ++++                                         
      -2                                                                   |  +++++                                             
      -2                                                                   |++  *                                               
      -3 0                        1                0                  -3.25+                                                    
         ----+----+----+----+                                               +----+----+----+----+----+----+----+----+----+----+ 
                                                                                -2        -1         0        +1        +2

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

Obs	resid	iat_mean	iat_n	BGmathDIFF03	countrycitzn
1	-2.95532	0.41825	104	-15	CY
2	-1.47113	0.25671	37	-27	JO
3	-1.31782	0.48889	106	-4	LT
4	-1.28479	0.51348	489	-4	RO
5	-1.13006	0.46123	58	-7	LV
6	-0.93648	0.44178	425	-7	TW
7	-0.81012	0.37852	822	-10	SG
8	-0.71557	0.49977	69	0	SK
9	-0.46667	0.36389	152	-9	IR
10	-0.43539	0.43354	317	-3	RU
11	-0.42133	0.44558	457	-2	HK
12	-0.38282	0.30604	541	-13	PH
13	-0.34145	0.39527	15471	-5	UK
14	-0.25794	0.36694	322	-7	MY
15	-0.25449	0.39784	55	-4	SI
16	-0.23661	0.44593	5649	0	SE
17	-0.18987	0.42329	1349	-2	NZ
18	-0.10787	0.39817	1502	-3	NO
19	0.07460	0.50838	3110	7	NL
20	0.09730	0.50682	2559	7	HU
21	0.12088	0.42598	210	1	BG
22	0.15771	0.28221	15	-10	MD
23	0.33642	0.29086	47	-8	MK
24	0.53613	0.39061	849	2	ZA
25	0.54454	0.35176	152	-1	ID
26	0.87042	0.44371	924	8	IL
27	0.91998	0.36790	2476	2	JP
28	1.02884	0.42425	1449	6	KR
29	1.05555	0.39549	1164	5	IT
30	1.08958	0.45299	1286	10	BE
31	1.38981	0.64834	17	24	TN
32	1.49739	0.37570	248306	5	US
33	1.71797	0.40781	8194	12	AU
34	2.38839	0.38852	163	15	CL

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: lever (Leverage)

Moments
N	34	Sum Weights	34
Mean	0.05882353	Sum Observations	2
Std Deviation	0.07159171	Variance	0.00512537
Skewness	5.05509621	Kurtosis	27.6901808
Uncorrected SS	0.28678436	Corrected SS	0.16913731
Coeff Variation	121.705907	Std Error Mean	0.01227788

Basic Statistical Measures
Location		Variability
Mean	0.058824	Std Deviation	0.07159
Median	0.041993	Variance	0.00513
Mode	.	Range	0.42444
		Interquartile Range	0.02901

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	4.791018	Pr > \|t\|	<.0001
Sign	M	17	Pr >= \|M\|	<.0001
Signed Rank	S	297.5	Pr >= \|S\|	<.0001

Quantiles (Definition 5)
Quantile	Estimate
100% Max	0.4455560
99%	0.4455560
95%	0.1078005
90%	0.0840637
75% Q3	0.0598733
50% Median	0.0419934
25% Q1	0.0308619
10%	0.0245581
5%	0.0221300
1%	0.0211158
0% Min	0.0211158

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
0.0211158	1	0.0750055	30
0.0221300	2	0.0840637	31
0.0238651	3	0.0967039	32
0.0245581	4	0.1078005	33
0.0266062	5	0.4455560	34

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: lever (Leverage)

    Stem Leaf                     #             Boxplot                                   Normal Probability Plot               
       4 5                        1                *                  0.475+                                                    
       4                                                                   |                                              *     
       3                                                                   |                                                    
       3                                                              0.325+                                                    
       2                                                                   |                                                    
       2                                                                   |                                             ++++++ 
       1                                                              0.175+                                      +++++++       
       1 01                       2                0                       |                               +++++++    *         
       0 555566667788            12             +--+--+                    |                        +++++********* *            
       0 2222333333444444444     19             *-----*               0.025+    *   *  * ****************                       
         ----+----+----+----+                                               +----+----+----+----+----+----+----+----+----+----+ 
     Multiply Stem.Leaf by 10**-1                                               -2        -1         0        +1        +2

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

Obs	lever	iat_mean	iat_n	BGmathDIFF03	countrycitzn
1	0.02112	0.42598	210	1	BG
2	0.02213	0.42329	1349	-2	NZ
3	0.02387	0.44178	425	-7	TW
4	0.02456	0.39061	849	2	ZA
5	0.02661	0.40781	8194	12	AU
6	0.02732	0.43354	317	-3	RU
7	0.02816	0.44558	457	-2	HK
8	0.02881	0.46123	58	-7	LV
9	0.03086	0.44371	924	8	IL
10	0.03105	0.38852	163	15	CL
11	0.03629	0.45299	1286	10	BE
12	0.03653	0.36694	322	-7	MY
13	0.03721	0.39549	1164	5	IT
14	0.03746	0.39527	15471	-5	UK
15	0.03846	0.36389	152	-9	IR
16	0.03913	0.35176	152	-1	ID
17	0.03982	0.37852	822	-10	SG
18	0.04417	0.39784	55	-4	SI
19	0.04490	0.42425	1449	6	KR
20	0.04565	0.39817	1502	-3	NO
21	0.04763	0.44593	5649	0	SE
22	0.04842	0.36790	2476	2	JP
23	0.05387	0.49977	69	0	SK
24	0.05648	0.41825	104	-15	CY
25	0.05657	0.51348	489	-4	RO
26	0.05987	0.37570	248306	5	US
27	0.06291	0.48889	106	-4	LT
28	0.06737	0.50838	3110	7	NL
29	0.07365	0.30604	541	-13	PH
30	0.07501	0.50682	2559	7	HU
31	0.08406	0.28221	15	-10	MD
32	0.09670	0.29086	47	-8	MK
33	0.10780	0.25671	37	-27	JO
34	0.44556	0.64834	17	24	TN

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: cookd (Cook's D Influence Statistic)

Moments
N	34	Sum Weights	34
Mean	0.04659849	Sum Observations	1.58434868
Std Deviation	0.13217431	Variance	0.01747005
Skewness	4.98448936	Kurtosis	26.6584793
Uncorrected SS	0.65033988	Corrected SS	0.57651162
Coeff Variation	283.645054	Std Error Mean	0.02266771

Basic Statistical Measures
Location		Variability
Mean	0.046598	Std Deviation	0.13217
Median	0.008496	Variance	0.01747
Mode	.	Range	0.75399
		Interquartile Range	0.02329

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	2.055721	Pr > \|t\|	0.0478
Sign	M	17	Pr >= \|M\|	<.0001
Signed Rank	S	297.5	Pr >= \|S\|	<.0001

Quantiles (Definition 5)
Quantile	Estimate
100% Max	0.754154572
99%	0.754154572
95%	0.210519388
90%	0.079688883
75% Q3	0.024835303
50% Median	0.008496469
25% Q1	0.001541358
10%	0.000396070
5%	0.000207454
1%	0.000162609
0% Min	0.000162609

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
0.000162609	1	0.0687300	30
0.000207454	2	0.0796889	31
0.000287180	3	0.1261569	32
0.000396070	4	0.2105194	33
0.000420599	5	0.7541546	34

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: cookd (Cook's D Influence Statistic)

   Stem Leaf                            #          Boxplot                                Normal Probability Plot               
      7 5                               1             *               0.775+                                              *     
      7                                                                    |                                                    
      6                                                                    |                                                    
      6                                                               0.625+                                                    
      5                                                                    |                                                    
      5                                                                    |                                                    
      4                                                               0.475+                                                    
      4                                                                    |                                                    
      3                                                                    |                                                +++ 
      3                                                               0.325+                                             +++    
      2                                                                    |                                         ++++       
      2 1                               1             *                    |                                     ++++ *         
      1                                                               0.175+                                 ++++               
      1 3                               1             *                    |                              +++      *            
      0 5678                            4             0                    |                          ++++     ***              
      0 000000000000001111111222224    27          +-----+            0.025+    *   *  * **********************                 
        ----+----+----+----+----+--                                         +----+----+----+----+----+----+----+----+----+----+ 
    Multiply Stem.Leaf by 10**-1                                                -2        -1         0        +1        +2

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

Obs	cookd	iat_mean	iat_n	BGmathDIFF03	countrycitzn
1	0.00016	0.42598	210	1	BG
2	0.00021	0.50838	3110	7	NL
3	0.00029	0.39817	1502	-3	NO
4	0.00040	0.50682	2559	7	HU
5	0.00042	0.42329	1349	-2	NZ
6	0.00118	0.28221	15	-10	MD
7	0.00130	0.36694	322	-7	MY
8	0.00144	0.44593	5649	0	SE
9	0.00154	0.39784	55	-4	SI
10	0.00233	0.39527	15471	-5	UK
11	0.00264	0.44558	457	-2	HK
12	0.00273	0.43354	317	-3	RU
13	0.00370	0.39061	849	2	ZA
14	0.00446	0.36389	152	-9	IR
15	0.00599	0.30604	541	-13	PH
16	0.00617	0.35176	152	-1	ID
17	0.00623	0.29086	47	-8	MK
18	0.01076	0.44178	425	-7	TW
19	0.01216	0.44371	924	8	IL
20	0.01376	0.37852	822	-10	SG
21	0.01480	0.49977	69	0	SK
22	0.01878	0.46123	58	-7	LV
23	0.02146	0.39549	1164	5	IT
24	0.02164	0.36790	2476	2	JP
25	0.02222	0.45299	1286	10	BE
26	0.02484	0.42425	1449	6	KR
27	0.03802	0.40781	8194	12	AU
28	0.04850	0.51348	489	-4	RO
29	0.05698	0.48889	106	-4	LT
30	0.06873	0.37570	248306	5	US
31	0.07969	0.38852	163	15	CL
32	0.12616	0.25671	37	-27	JO
33	0.21052	0.41825	104	-15	CY
34	0.75415	0.64834	17	24	TN

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: dffit (Standard Influence on Predicted Value)

Moments
N	34	Sum Weights	34
Mean	0.01670503	Sum Observations	0.56797114
Std Deviation	0.31859197	Variance	0.10150085
Skewness	1.35431853	Kurtosis	6.41406488
Uncorrected SS	3.35901589	Corrected SS	3.34952791
Coeff Variation	1907.16153	Std Error Mean	0.05463807

Basic Statistical Measures
Location		Variability
Mean	0.01671	Std Deviation	0.31859
Median	-0.02608	Variance	0.10150
Mode	.	Range	1.96893
		Interquartile Range	0.26327

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	0.30574	Pr > \|t\|	0.7617
Sign	M	-1	Pr >= \|M\|	0.8642
Signed Rank	S	0.5	Pr >= \|S\|	0.9933

Quantiles (Definition 5)
Quantile	Estimate
100% Max	1.245880
99%	1.245880
95%	0.427561
90%	0.284029
75% Q3	0.155328
50% Median	-0.026078
25% Q1	-0.107943
10%	-0.314598
5%	-0.511364
1%	-0.723047
0% Min	-0.723047

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
-0.723047	1	0.223073	30
-0.511364	2	0.284029	31
-0.341455	3	0.377884	32
-0.314598	4	0.427561	33
-0.194631	5	1.245880	34

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

The UNIVARIATE Procedure

Variable: dffit (Standard Influence on Predicted Value)

    Stem Leaf                     #             Boxplot                                   Normal Probability Plot               
      12 5                        1                *                    1.3+                                              *     
      10                                                                   |                                                    
       8                                                                   |                                                  + 
       6                                                                   |                                            ++++++  
       4 3                        1                |                       |                                      ++++*+        
       2 111288                   6                |                    0.3+                               ++***** *            
       0 22359116                 8             +--+--+                    |                         +*******                   
      -0 97651977755532          14             *-----*                    |              ************                          
      -2 41                       2                |                       |           *+*+++++                                 
      -4 1                        1                0                       |      ++*+++                                        
      -6 2                        1                0                   -0.7+++++*+                                              
         ----+----+----+----+                                               +----+----+----+----+----+----+----+----+----+----+ 
     Multiply Stem.Leaf by 10**-1                                               -2        -1         0        +1        +2

TIMSS Regression Diagnostics

Weighted

2003 math difference ON IAT

Obs	dffit	iat_mean	iat_n	BGmathDIFF03	countrycitzn
1	-0.72305	0.41825	104	-15	CY
2	-0.51136	0.25671	37	-27	JO
3	-0.34145	0.48889	106	-4	LT
4	-0.31460	0.51348	489	-4	RO
5	-0.19463	0.46123	58	-7	LV
6	-0.17075	0.49977	69	0	SK
7	-0.16498	0.37852	822	-10	SG
8	-0.14643	0.44178	425	-7	TW
9	-0.10794	0.30604	541	-13	PH
10	-0.09333	0.36389	152	-9	IR
11	-0.07297	0.43354	317	-3	RU
12	-0.07172	0.44558	457	-2	HK
13	-0.06736	0.39527	15471	-5	UK
14	-0.05470	0.39784	55	-4	SI
15	-0.05292	0.44593	5649	0	SE
16	-0.05022	0.36694	322	-7	MY
17	-0.02856	0.42329	1349	-2	NZ
18	-0.02359	0.39817	1502	-3	NO
19	0.01775	0.42598	210	1	BG
20	0.02005	0.50838	3110	7	NL
21	0.02771	0.50682	2559	7	HU
22	0.04778	0.28221	15	-10	MD
23	0.08507	0.39061	849	2	ZA
24	0.10989	0.35176	152	-1	ID
25	0.11007	0.29086	47	-8	MK
26	0.15533	0.44371	924	8	IL
27	0.20752	0.36790	2476	2	JP
28	0.20752	0.39549	1164	5	IT
29	0.21143	0.45299	1286	10	BE
30	0.22307	0.42425	1449	6	KR
31	0.28403	0.40781	8194	12	AU
32	0.37788	0.37570	248306	5	US
33	0.42756	0.38852	163	15	CL
34	1.24588	0.64834	17	24	TN