| Variable Number | Variable Name | Variable Label | Coded Response |
|---|---|---|---|
| 1 | id | ID number | 3-digit number |
| 2 | sex | Sex | 1=male 2=female |
| 3 | race | Race or Ethnicity | 1=hispanic 2=asian 3=african-american 4=white |
| 4 | ses | Socioeconomic status | 1=low 2=medium 3=high |
| 5 | sctyp | School type | 1=public 2=private |
| 6 | hsp | High school program | 1=general 2=academic prepartory 3=vacational/technical |
| 7 | locus | Locus of control | (mean = 0 and sd = 1) |
| 8 | slfcpt | Self-concept | (mean = 0 and sd = 1) |
| 9 | mot | Motivation | (average of three motivational items) |
| 10 | car | Career choice | 1=clerical 2=craftsman 3=farmer 4=homemaker 5=labkorer 6=manager 7=military 8=operative 9=professional 1 10=professional 2 11=proprietor 12=protective 13=sales 14=school 15=service 16=technical 17=not working |
| 11 | read | Stdandardized reading score | (mean = 50 and sd = 10) |
| 12 | write | Stdandardized writing score | (mean = 50 and sd = 10) |
| 13 | math | Stdandardized math score | (mean = 50 and sd = 10) |
| 14 | sci | Stdandardized science score | (mean = 50 and sd = 10) |
| 15 | socst | Stdandardized soc st score | (mean = 50 and sd = 10) |
data hsb;
infile 'hsb.dat';
input id sex race ses sctyp hsp locus slfcpt mot
career read write math sci socst;
proc reg;
model locus = read write math/stb;
proc discrim manova canonical;
class ses;
var read write math;
proc cancorr;
var locus slfcpt mot;
with read write math;
proc factor method=prinit priors=smc heywood rotate=varimax;
var locus slfcpt mot read write math sci socst;
run;
---------------------------------------------------------------------------
[Regression Output]
Model: MODEL1
Dependent Variable: LOCUS
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 3 45.38359 15.12786 40.299 0.0001
Error 596 223.73220 0.37539
C Total 599 269.11579
Root MSE 0.61269 R-square 0.1686
Dep Mean 0.09653 Adj R-sq 0.1645
C.V. 634.69316
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.562191 0.15552897 -10.044 0.0001
READ 1 0.013507 0.00360415 3.748 0.0002
WRITE 1 0.012067 0.00354769 3.401 0.0007
MATH 1 0.006279 0.00388416 1.617 0.1065
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
READ 1 0.20358696
WRITE 1 0.17510731
MATH 1 0.08819281
[Discriminant Analysis Output]
Discriminant Analysis
600 Observations 599 DF Total
3 Variables 597 DF Within Classes
3 Classes 2 DF Between Classes
Class Level Information
Prior
SES Frequency Weight Proportion Probability
1 139 139.0000 0.231667 0.333333
2 299 299.0000 0.498333 0.333333
3 162 162.0000 0.270000 0.333333
Discriminant Analysis Pooled Covariance Matrix Information
Covariance Natural Log of the Determinant
Matrix Rank of the Covariance Matrix
3 12.2917218
Discriminant Analysis Pairwise Generalized Squared Distances Between Groups
2 _ _ -1 _ _
D (i|j) = (X - X )' COV (X - X )
i j i j
Generalized Squared Distance to SES
From SES 1 2 3
1 0 0.31342 0.98945
2 0.31342 0 0.19325
3 0.98945 0.19325 0
Discriminant Analysis
Multivariate Statistics and F Approximations
S=+1 M=0 N=+196.5
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.88906941 12.0096 6 1190 0.0001
Pillai's Trace 0.11099492 11.6733 6 1192 0.0001
Hotelling-Lawley Trace 0.12469921 12.3452 6 1188 0.0001
Roy's Greatest Root 0.12411623 24.6578 3 596 0.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Canonical Discriminant Analysis
Adjusted Approx Squared
Canonical Canonical Standard Canonical
Correlation Correlation Error Correlation
1 0.332283 0.325805 0.036348 0.110412
2 0.024138 -.010077 0.040835 0.000583
Eigenvalues of INV(E)*H
= CanRsq/(1-CanRsq)
Eigenvalue Difference Proportion Cumulative
1 0.1241 0.1235 0.9953 0.9953
2 0.0006 . 0.0047 1.0000
Test of H0: The canonical correlations in the
current row and all that follow are zero
Likelihood
Ratio Approx F Num DF Den DF Pr > F
1 0.88906941 12.0096 6 1190 0.0001
2 0.99941736 0.1737 2 596 0.8406
Total Canonical Structure
CAN1 CAN2
READ 0.888254 -0.295295
WRITE 0.752720 -0.443850
MATH 0.933310 0.324888
Between Canonical Structure
CAN1 CAN2
READ 0.999709 -0.024143
WRITE 0.999084 -0.042795
MATH 0.999680 0.025279
Pooled Within Canonical Structure
CAN1 CAN2
READ 0.876870 -0.308983
WRITE 0.733301 -0.458315
MATH 0.925962 0.341649
Total-Sample Standardized Canonical Coefficients
CAN1 CAN2
READ 0.448968815 -0.635268929
WRITE 0.137497524 -0.870695286
MATH 0.595918616 1.306821765
Pooled Within-Class Standardized Canonical Coefficients
CAN1 CAN2
READ 0.429673382 -0.607966834
WRITE 0.133341917 -0.844380139
MATH 0.567466508 1.244427616
Raw Canonical Coefficients
CAN1 CAN2
READ 0.0444392333 -.0628793431
WRITE 0.0141364479 -.0895182559
MATH 0.0632963677 0.1388059858
Class Means on Canonical Variables
SES CAN1 CAN2
1 -.5465768557 -.0228164669
2 0.0112924485 0.0241526513
3 0.4481342028 -.0250009496
Discriminant Analysis Linear Discriminant Function
_ -1 _ -1 _
Constant = -.5 X' COV X Coefficient Vector = COV X
j j j
SES
1 2 3
CONSTANT -17.65626 -21.00216 -23.90440
READ 0.16808 0.18992 0.21242
WRITE 0.27408 0.27776 0.28834
MATH 0.29651 0.33834 0.35917
Discriminant Analysis Classification Summary for Calibration Data: WORK.HSB
Resubstitution Summary using Linear Discriminant Function
Generalized Squared Distance Function:
2 _ -1 _
D (X) = (X-X )' COV (X-X )
j j j
Posterior Probability of Membership in each SES:
2 2
Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))
j k k
Number of Observations and Percent Classified into SES:
From SES 1 2 3 Total
1 95 16 28 139
68.35 11.51 20.14 100.00
2 122 51 126 299
40.80 17.06 42.14 100.00
3 39 27 96 162
24.07 16.67 59.26 100.00
Total 256 94 250 600
Percent 42.67 15.67 41.67 100.00
Priors 0.3333 0.3333 0.3333
Error Count Estimates for SES:
1 2 3 Total
Rate 0.3165 0.8294 0.4074 0.5178
Priors 0.3333 0.3333 0.3333
[Canonical Correlation Analysis]
Adjusted Approx Squared
Canonical Canonical Standard Canonical
Correlation Correlation Error Correlation
1 0.446310 0.440513 0.032720 0.199193
2 0.091170 . 0.040519 0.008312
3 0.002400 . 0.040859 0.000006
Eigenvalues of INV(E)*H
= CanRsq/(1-CanRsq)
Eigenvalue Difference Proportion Cumulative
1 0.2487 0.2404 0.9674 0.9674
2 0.0084 0.0084 0.0326 1.0000
3 0.0000 . 0.0000 1.0000
Test of H0: The canonical correlations in the
current row and all that follow are zero
Likelihood
Ratio Approx F Num DF Den DF Pr > F
1 0.79414650 15.9574 9 1445.791 0.0001
2 0.99168226 1.2450 4 1190 0.2900
3 0.99999424 0.0034 1 596 0.9533
Multivariate Statistics and F Approximations
S=3 M=-0.5 N=+196
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.79414650 15.9574 9 1445.791 0.0001
Pillai's Trace 0.20751038 14.7630 9 1788 0.0001
Hotelling-Lawley Trace 0.25712716 16.9323 9 1778 0.0001
Roy's Greatest Root 0.24873970 49.4163 3 596 0.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
Canonical Correlation Analysis
Raw Canonical Coefficients for the 'VAR' Variables
V1 V2 V3
LOCUS 1.2559521341 0.642735041 -0.636900954
SLFCPT -0.231449286 1.0673050885 1.012326503
MOT 1.2293420708 -2.373306414 1.6001728133
Raw Canonical Coefficients for the 'WITH' Variables
W1 W2 W3
READ 0.042654856 0.0805224686 -0.111464486
WRITE 0.0544447099 -0.130501783 -0.009401289
MATH 0.0183642562 0.0580981087 0.1426914796
Standardized Canonical Coefficients for the 'VAR' Variables
V1 V2 V3
LOCUS 0.8418 0.4308 -0.4269
SLFCPT -0.1633 0.7530 0.7142
MOT 0.4213 -0.8134 0.5484
Standardized Canonical Coefficients for the 'WITH' Variables
W1 W2 W3
READ 0.4309 0.8135 -1.1261
WRITE 0.5296 -1.2693 -0.0914
MATH 0.1729 0.5470 1.3434
Canonical Structure
Correlations Between the 'VAR' Variables and Their Canonical Variables
V1 V2 V3
LOCUS 0.9172 0.3603 -0.1702
SLFCPT 0.1024 0.5920 0.7994
MOT 0.5806 -0.4905 0.6499
Correlations Between the 'WITH' Variables and Their Canonical Variables
W1 W2 W3
READ 0.8813 0.3872 -0.2711
WRITE 0.9098 -0.4119 0.0506
MATH 0.8007 0.2965 0.5206
Correlations Between the 'VAR' Variables and the
Canonical Variables of the 'WITH' Variables
W1 W2 W3
LOCUS 0.4093 0.0329 -0.0004
SLFCPT 0.0457 0.0540 0.0019
MOT 0.2591 -0.0447 0.0016
Correlations Between the 'WITH' Variables and
the Canonical Variables of the 'VAR' Variables
V1 V2 V3
READ 0.3933 0.0353 -0.0007
WRITE 0.4061 -0.0376 0.0001
MATH 0.3573 0.0270 0.0012
[Factor Analysis Output]
Initial Factor Method: Iterated Principal Factor Analysis
Prior Communality Estimates: SMC
LOCUS SLFCPT MOT READ WRITE MATH SCI SOCST
0.205013 0.108939 0.173511 0.625200 0.538955 0.572827 0.556934 0.439018
Preliminary Eigenvalues: Total = 3.22039668 Average = 0.40254959
1 2 3 4
Eigenvalue 3.2643 0.4515 0.0714 -0.0529
Difference 2.8129 0.3800 0.1244 0.0092
Proportion 1.0136 0.1402 0.0222 -0.0164
Cumulative 1.0136 1.1538 1.1760 1.1596
5 6 7 8
Eigenvalue -0.0622 -0.1046 -0.1313 -0.2157
Difference 0.0425 0.0266 0.0845
Proportion -0.0193 -0.0325 -0.0408 -0.0670
Cumulative 1.1403 1.1078 1.0670 1.0000
1 factors will be retained by the PROPORTION criterion.
Iter Change Communalities
1 0.098014 0.20466 0.01092 0.08337 0.68936 0.59256 0.62595 0.58382 0.47367
2 0.018630 0.20151 0.00989 0.07749 0.70799 0.60450 0.63881 0.58696 0.47807
3 0.005926 0.20049 0.00982 0.07694 0.71392 0.60707 0.64198 0.58653 0.47801
4 0.002069 0.20023 0.00981 0.07686 0.71599 0.60759 0.64279 0.58602 0.47768
5 0.000772 0.20016 0.00980 0.07684 0.71676 0.60767 0.64299 0.58576 0.47752
Convergence criterion satisfied.
Eigenvalues of the Reduced Correlation Matrix:
Total = 3.31696379 Average = 0.41462047
1 2 3 4
Eigenvalue 3.3175 0.3783 0.1060 0.0145
Difference 2.9392 0.2722 0.0916 0.0639
Proportion 1.0002 0.1140 0.0320 0.0044
Cumulative 1.0002 1.1142 1.1462 1.1505
5 6 7 8
Eigenvalue -0.0494 -0.0539 -0.1027 -0.2933
Difference 0.0045 0.0488 0.1905
Proportion -0.0149 -0.0163 -0.0310 -0.0884
Cumulative 1.1356 1.1194 1.0884 1.0000
Factor Pattern
FACTOR1
LOCUS 0.44740
SLFCPT 0.09901
MOT 0.27720
READ 0.84662
WRITE 0.77953
MATH 0.80187
SCI 0.76535
SOCST 0.69103
Variance explained by each factor
FACTOR1
3.317508
Final Communality Estimates: Total = 3.317508
LOCUS SLFCPT MOT READ WRITE MATH SCI SOCST
0.200163 0.009803 0.076840 0.716759 0.607674 0.642991 0.585762 0.477516
Rotation Method: Varimax
Rotation not possible with 1 factor.