Results: MathReg3.sas

Gender, Ethnicity and Math performance

Replication and Prediction

Try to replicate HS Engl neg, mtongue neg, totscore pos

with a Bonferroni correction (check p < 0.05/3 = 0.01666667)

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

The Reg Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 288
Number of Observations with Missing Values 291

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 36155 7230.94549 36.45 <.0001
Error 282 55948 198.39605    
Corrected Total 287 92102      

Fit Statistics

Root MSE 14.08531 R-Square 0.3925
Dependent Mean 57.73264 Adj R-Sq 0.3818
Coeff Var 24.39749    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -57.59065 12.01535 -4.79 <.0001
hsgpa High School GPA 1 1.15692 0.25532 4.53 <.0001
hscalc HS Calculus 1 0.17755 0.10404 1.71 0.0890
hsengl HS English 1 -0.04691 0.13560 -0.35 0.7297
totscore Total # right on diagnostic test 1 1.58048 0.26400 5.99 <.0001
mtongue English vs. Other 1 -1.34224 1.96918 -0.68 0.4960

Gender, Ethnicity and Math performance

Replication and Prediction

Re-running Model I to generate y-hat and prediction intervals

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

The Reg Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 575
Number of Observations Used 287
Number of Observations with Missing Values 288

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 44881 8976.29511 48.56 <.0001
Error 281 51948 184.86704    
Corrected Total 286 96829      

Fit Statistics

Root MSE 13.59658 R-Square 0.4635
Dependent Mean 60.59582 Adj R-Sq 0.4540
Coeff Var 22.43815    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -66.75516 11.25053 -5.93 <.0001
hsgpa High School GPA 1 1.58918 0.22087 7.20 <.0001
hscalc HS Calculus 1 0.21759 0.10208 2.13 0.0339
hsengl HS English 1 -0.30024 0.12270 -2.45 0.0150
totscore Total # right on diagnostic test 1 0.97213 0.25185 3.86 0.0001
mtongue English vs. Other 1 -4.69657 2.12640 -2.21 0.0280

Gender, Ethnicity and Math performance

Replication and Prediction

Does 95 Percent Prediction Interval Work?

The FREQ Procedure

The Freq Procedure

Table sample * ininterval

Cross-Tabular Freq Table

Frequency
Row Pct
Table of sample by ininterval
sample ininterval
No Yes Total
1
15
5.23
272
94.77
287
 
2
16
5.56
272
94.44
288
 
Total
31
544
575

Gender, Ethnicity and Math performance

Replication and Prediction

Look at predictions for the replication sample

The Print Procedure

Data Set WORK.PREDATAI

Obs id sample grade2 Yhat lowpred hipred
288 1 2 56 56.9902 29.7434 84.237
289 5 2 50 67.2468 40.3676 94.126
290 7 2 70 75.2607 48.0535 102.468
291 8 2 50 64.4434 37.5368 91.350
292 9 2 8 40.1746 13.2310 67.118
293 10 2 44 63.7024 36.7248 90.680
294 11 2 60 64.1388 37.1040 91.174
295 14 2 45 52.5751 25.6372 79.513
296 16 2 66 58.2555 31.1480 85.363
297 22 2 67 75.9451 48.8433 103.047
298 24 2 53 47.9072 20.7438 75.071
299 26 2 57 61.5182 34.0401 88.996
300 27 2 63 59.6520 32.6718 86.632
301 28 2 85 72.8493 45.5924 100.106
302 31 2 74 68.0087 41.1374 94.880
303 33 2 42 55.6494 28.8043 82.494
304 37 2 82 55.7751 28.7476 82.803
305 39 2 52 40.9542 13.9559 67.953
306 41 2 57 62.3288 35.1769 89.481
307 42 2 45 48.9517 21.8819 76.022
308 43 2 54 70.4219 43.3316 97.512
309 44 2 55 61.9839 34.9214 89.046
310 46 2 87 55.6769 28.6793 82.674
311 47 2 72 62.9110 35.7286 90.093
312 49 2 70 55.7603 28.9262 82.594
313 54 2 37 54.7851 27.4779 82.092
314 56 2 76 66.4962 39.4922 93.500
315 59 2 61 57.5443 30.5529 84.536
316 61 2 50 48.4294 21.5140 75.345
317 63 2 93 73.5729 46.5924 100.553
318 64 2 50 55.3756 28.2983 82.453
319 66 2 50 60.5584 33.4505 87.666
320 67 2 50 43.3720 16.1305 70.613
321 68 2 4 40.2249 13.2433 67.206
322 69 2 60 73.9939 47.0298 100.958
323 71 2 81 73.5426 46.4751 100.610
324 73 2 60 55.8579 28.9218 82.794
325 75 2 33 63.9896 36.8912 91.088
326 76 2 54 65.2833 38.2166 92.350
327 80 2 42 45.8056 18.9235 72.688
328 82 2 43 51.8896 24.9855 78.794
329 83 2 61 56.5618 29.7032 83.420
330 84 2 66 55.8077 28.9278 82.688
331 85 2 60 63.2927 36.2579 90.327
332 86 2 78 66.8285 39.9120 93.745
333 87 2 57 64.8301 37.6616 91.999
334 89 2 57 67.1128 40.1009 94.125
335 90 2 25 53.8689 27.0056 80.732
336 91 2 80 73.1003 45.7481 100.453
337 92 2 42 53.9935 26.9847 81.002
338 94 2 48 36.7874 9.6845 63.890
339 96 2 80 76.9438 49.9986 103.889
340 97 2 44 65.6277 38.7294 92.526
341 100 2 53 51.7145 24.6643 78.765
342 101 2 58 55.7925 28.8873 82.698
343 103 2 62 44.2805 17.2349 71.326
344 105 2 93 78.2754 51.3036 105.247
345 107 2 63 87.0741 59.8816 114.267
346 108 2 58 63.5372 36.5865 90.488
347 111 2 63 43.9793 16.8732 71.086
348 124 2 58 71.0778 44.0415 98.114
349 125 2 58 60.9046 33.9284 87.881
350 127 2 36 42.8923 15.7702 70.014
351 128 2 77 58.6096 31.7044 85.515
352 129 2 50 57.2283 30.3446 84.112
353 132 2 84 74.3925 47.4166 101.368
354 133 2 31 54.1500 27.2293 81.071
355 134 2 43 62.8897 36.0048 89.775
356 135 2 60 44.0270 16.9823 71.072
357 138 2 68 63.9213 36.8311 91.012
358 139 2 51 62.2665 35.4018 89.131
359 140 2 77 75.6305 48.5170 102.744
360 141 2 64 72.3565 45.2470 99.466
361 144 2 71 51.6855 24.8209 78.550
362 146 2 61 59.3762 32.4564 86.296
363 148 2 55 63.4643 36.4633 90.465
364 153 2 55 62.2291 35.2080 89.250
365 154 2 52 41.7263 14.6916 68.761
366 155 2 57 65.6139 38.5882 92.640
367 156 2 4 46.6328 19.3561 73.910
368 157 2 43 56.3267 29.3411 83.312
369 159 2 15 55.0560 28.1016 82.010
370 160 2 60 76.0953 49.0052 103.185
371 161 2 68 65.5591 38.5091 92.609
372 164 2 91 97.2248 69.6937 124.756
373 167 2 77 62.1101 35.2829 88.937
374 170 2 71 52.4450 25.6000 79.290
375 173 2 42 38.1380 11.1086 65.167
376 175 2 56 55.7365 28.7376 82.735
377 176 2 58 70.0805 43.1800 96.981
378 178 2 58 63.8665 36.8311 90.902
379 179 2 66 52.9265 25.9389 79.914
380 180 2 44 60.2376 32.6649 87.810
381 181 2 21 45.1646 18.2388 72.090
382 182 2 61 55.2858 28.3444 82.227
383 184 2 63 70.2468 43.1040 97.390
384 186 2 55 52.7068 25.3760 80.038
385 191 2 55 62.8759 36.0325 89.719
386 192 2 78 89.2524 62.0573 116.448
387 194 2 60 36.6150 9.5869 63.643
388 195 2 81 69.6431 42.3268 96.959
389 199 2 54 56.1344 28.9400 83.329
390 201 2 65 60.1072 33.2383 86.976
391 206 2 80 75.6613 48.5017 102.821
392 209 2 60 45.9427 19.0134 72.872
393 210 2 71 65.9256 38.6296 93.222
394 216 2 50 46.2291 19.3406 73.118
395 218 2 52 51.5790 24.7299 78.428
396 219 2 60 70.9177 44.0184 97.817
397 220 2 38 41.1173 14.0189 68.216
398 221 2 75 65.0089 38.1425 91.875
399 222 2 55 49.2378 22.3233 76.152
400 224 2 56 62.2703 35.3284 89.212
401 226 2 61 68.5606 41.5609 95.560
402 228 2 80 64.5115 37.1559 91.867
403 230 2 29 41.6651 14.4773 68.853
404 232 2 60 65.5810 38.4421 92.720
405 233 2 67 61.1151 34.2790 87.951
406 234 2 64 61.5946 34.6453 88.544
407 235 2 70 54.8784 27.9466 81.810
408 236 2 38 45.5461 18.4480 72.644
409 238 2 76 62.9265 35.8081 90.045
410 239 2 19 44.8212 17.4067 72.236
411 240 2 46 55.0875 28.2006 81.974
412 247 2 72 70.2599 43.2020 97.318
413 251 2 16 64.6552 37.5302 91.780
414 253 2 56 65.3529 37.9915 92.714
415 255 2 74 70.4566 43.4401 97.473
416 256 2 55 45.0406 17.9679 72.113
417 257 2 81 71.6277 44.6932 98.562
418 258 2 37 56.5092 29.3891 83.629
419 259 2 39 58.0499 31.0901 85.010
420 264 2 56 60.1029 33.2680 86.938
421 265 2 51 54.6896 27.7174 81.662
422 267 2 50 67.7636 40.8460 94.681
423 268 2 46 75.3850 47.8373 102.933
424 269 2 60 57.0764 29.9148 84.238
425 270 2 55 52.8761 25.8440 79.908
426 273 2 70 69.7053 42.7597 96.651
427 274 2 84 72.9354 45.7860 100.085
428 275 2 61 51.9778 24.6805 79.275
429 276 2 94 73.5118 46.5482 100.475
430 280 2 50 47.6063 20.6149 74.598
431 281 2 67 43.4564 16.4328 70.480
432 283 2 51 42.6219 15.6986 69.545
433 285 2 50 50.9778 23.5548 78.401
434 286 2 63 68.2644 41.1682 95.361
435 287 2 58 54.3852 27.4279 81.342
436 291 2 66 66.4074 39.4810 93.334
437 292 2 41 47.7598 20.5258 74.994
438 293 2 81 74.3910 47.4480 101.334
439 294 2 72 64.3708 37.5001 91.241
440 303 2 70 47.8009 20.7779 74.824
441 304 2 76 86.9881 59.7725 114.204
442 305 2 73 66.3434 39.3870 93.300
443 306 2 67 64.3708 37.4683 91.273
444 307 2 70 65.8247 38.7842 92.865
445 310 2 75 67.6506 40.6919 94.609
446 312 2 50 64.5146 37.6487 91.381
447 313 2 62 52.0285 24.8963 79.161
448 315 2 60 64.0997 37.0121 91.187
449 318 2 50 60.2186 33.3597 87.078
450 320 2 68 62.8668 35.9286 89.805
451 321 2 71 55.5262 28.6768 82.376
452 322 2 53 46.9134 19.8654 73.961
453 323 2 66 49.8586 22.9468 76.770
454 326 2 61 62.1336 35.1031 89.164
455 327 2 3 50.8036 23.7588 77.849
456 329 2 60 52.5166 25.5248 79.508
457 331 2 56 56.9565 30.0466 83.866
458 333 2 46 61.2660 34.3612 88.171
459 334 2 60 69.8367 42.8310 96.842
460 335 2 88 89.2460 62.0720 116.420
461 338 2 87 70.8360 43.5028 98.169
462 339 2 53 55.9812 29.1236 82.839
463 342 2 58 51.4919 24.6341 78.350
464 343 2 70 54.7616 27.8142 81.709
465 344 2 43 38.9744 11.9455 66.003
466 345 2 53 43.5778 16.4175 70.738
467 346 2 41 52.4185 25.2746 79.562
468 347 2 50 49.9536 23.0331 76.874
469 350 2 70 47.8280 20.8804 74.776
470 352 2 53 54.0918 27.2202 80.963
471 355 2 65 72.0911 45.0654 99.117
472 357 2 58 48.5795 21.3063 75.853
473 358 2 50 52.9378 26.0149 79.861
474 360 2 35 44.9407 17.7273 72.154
475 361 2 70 57.6158 30.4009 84.831
476 367 2 60 48.5642 21.6414 75.487
477 368 2 4 54.7222 27.5461 81.898
478 371 2 63 50.4874 23.1981 77.777
479 374 2 41 49.5384 21.9662 77.111
480 377 2 63 60.1563 33.2221 87.090
481 378 2 93 91.8757 64.3487 119.403
482 380 2 43 47.7648 20.7287 74.801
483 381 2 65 57.8418 30.9000 84.784
484 382 2 75 81.0683 54.0680 108.069
485 383 2 52 50.6872 23.8294 77.545
486 384 2 72 59.8749 32.9292 86.821
487 385 2 50 43.0837 15.8418 70.326
488 394 2 50 50.0319 23.0808 76.983
489 395 2 33 39.5837 12.1597 67.008
490 398 2 55 54.6913 27.7664 81.616
491 401 2 60 39.4367 12.4824 66.391
492 404 2 33 41.1591 14.0960 68.222
493 406 2 67 65.2214 38.3454 92.097
494 407 2 90 84.4530 57.3725 111.533
495 410 2 36 39.0211 11.9876 66.055
496 412 2 80 89.3037 62.1650 116.442
497 416 2 1 65.1159 38.1365 92.095
498 417 2 58 60.6217 33.7866 87.457
499 422 2 60 48.7166 21.7392 75.694
500 424 2 60 55.0818 28.0986 82.065
501 425 2 55 37.9871 10.5391 65.435
502 426 2 62 46.5147 19.5153 73.514
503 427 2 93 88.5608 61.4007 115.721
504 428 2 38 57.6213 30.3645 84.878
505 434 2 41 62.8100 35.3864 90.234
506 437 2 67 72.1267 44.9326 99.321
507 439 2 13 37.1692 10.1163 64.222
508 440 2 86 68.8400 41.8993 95.781
509 441 2 63 62.8961 35.7614 90.031
510 442 2 50 50.3250 23.1177 77.532
511 444 2 76 68.1240 41.2287 95.019
512 445 2 50 67.1645 40.2459 94.083
513 446 2 50 60.7460 33.8568 87.635
514 447 2 54 62.5014 35.6200 89.383
515 449 2 70 59.0328 32.0743 85.991
516 450 2 71 63.2743 36.4101 90.139
517 454 2 72 77.8400 50.5477 105.132
518 457 2 88 80.4267 53.4094 107.444
519 460 2 54 53.8689 27.0056 80.732
520 461 2 35 45.2744 18.2724 72.276
521 462 2 47 50.6437 23.5576 77.730
522 463 2 60 61.0873 34.2345 87.940
523 465 2 55 72.0292 45.0685 98.990
524 472 2 86 85.0496 57.9497 112.150
525 475 2 40 47.5823 20.2846 74.880
526 478 2 42 51.5466 24.3650 78.728
527 481 2 50 66.4766 39.4348 93.518
528 482 2 60 57.1727 30.1630 84.182
529 483 2 77 71.5300 44.5785 98.482
530 487 2 28 54.8090 27.7930 81.825
531 488 2 44 47.1229 20.2273 74.019
532 490 2 60 63.9738 36.8414 91.106
533 492 2 64 67.9059 40.8812 94.931
534 493 2 51 74.2808 46.8748 101.687
535 495 2 61 67.5010 40.5395 94.463
536 498 2 15 36.9568 9.8969 64.017
537 503 2 38 65.5548 38.4067 92.703
538 505 2 37 46.9437 19.9813 73.906
539 508 2 30 40.9037 13.8995 67.908
540 509 2 50 46.4487 19.5327 73.365
541 510 2 42 64.5543 37.1753 91.933
542 512 2 68 69.5511 42.4872 96.615
543 513 2 16 53.1265 25.9463 80.307
544 515 2 73 61.9000 35.0321 88.768
545 516 2 73 74.8620 47.8114 101.913
546 518 2 66 53.8698 26.9830 80.757
547 519 2 60 49.5451 22.2766 76.814
548 521 2 55 61.4058 34.4909 88.321
549 522 2 88 71.0578 44.0437 98.072
550 526 2 93 83.3378 56.2880 110.388
551 530 2 93 89.8946 62.4987 117.290
552 531 2 55 49.2952 22.1256 76.465
553 532 2 50 49.3409 22.3137 76.368
554 537 2 60 54.2313 27.2352 81.227
555 540 2 83 76.5183 49.5426 103.494
556 541 2 65 62.1249 35.0183 89.231
557 542 2 44 48.0874 21.1196 75.055
558 543 2 13 58.9297 32.0762 85.783
559 548 2 72 69.8951 42.9850 96.805
560 549 2 70 52.5434 24.9969 80.090
561 551 2 77 62.2388 35.1980 89.280
562 552 2 36 68.3782 41.1567 95.600
563 553 2 65 57.3101 29.8683 84.752
564 554 2 63 68.4601 41.1721 95.748
565 558 2 62 52.9834 25.7185 80.248
566 559 2 71 56.7651 29.9234 83.607
567 560 2 26 46.1175 18.5835 73.651
568 564 2 51 39.1308 11.9984 66.263
569 568 2 33 51.4009 24.5191 78.283
570 570 2 76 66.5817 39.6657 93.498
571 571 2 84 68.9431 42.0576 95.829
572 572 2 86 69.7688 42.5831 96.954
573 574 2 75 73.9960 46.9713 101.021
574 575 2 60 61.3668 34.3274 88.406
575 576 2 62 61.0100 34.1332 87.887

Gender, Ethnicity and Math performance

Replication and Prediction

Accuracy of predicting Letter Grades From Model I

The FREQ Procedure

The Freq Procedure

Table 1 of prelgrade * lgrade

Cross-Tabular Freq Table

Frequency
Row Pct
Table 1 of prelgrade by lgrade
Controlling for sample=1
prelgrade(Predicted Letter Grade) lgrade(Letter Grade)
A B C D F Total
A
23
92.00
2
8.00
0
0.00
0
0.00
0
0.00
25
 
B
10
26.32
15
39.47
9
23.68
1
2.63
3
7.89
38
 
C
8
10.26
24
30.77
26
33.33
18
23.08
2
2.56
78
 
D
4
4.30
11
11.83
23
24.73
30
32.26
25
26.88
93
 
F
0
0.00
0
0.00
10
18.87
16
30.19
27
50.94
53
 
Total
45
52
68
65
57
287

Table 2 of prelgrade * lgrade

Cross-Tabular Freq Table

Frequency
Row Pct
Table 2 of prelgrade by lgrade
Controlling for sample=2
prelgrade(Predicted Letter Grade) lgrade(Letter Grade)
A B C D F Total
A
10
71.43
3
21.43
1
7.14
0
0.00
0
0.00
14
 
B
17
39.53
10
23.26
10
23.26
5
11.63
1
2.33
43
 
C
3
3.37
18
20.22
27
30.34
29
32.58
12
13.48
89
 
D
2
2.44
11
13.41
22
26.83
24
29.27
23
28.05
82
 
F
0
0.00
2
3.33
10
16.67
19
31.67
29
48.33
60
 
Total
32
44
70
77
65
288

Gender, Ethnicity and Math performance

Replication and Prediction

Accuracy of predicting Letter Grades From Model I

The GLM Procedure

The GLM Procedure

Data

Number of Observations

Number of Observations Read 579
Number of Observations Used 287

Gender, Ethnicity and Math performance

Replication and Prediction

Accuracy of predicting Letter Grades From Model I

The GLM Procedure

 

Dependent Variable: grade Final mark

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 44881.47557 8976.29511 48.56 <.0001
Error 281 51947.63942 184.86704    
Corrected Total 286 96829.11498      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.463512 22.43815 13.59658 60.59582

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
hsgpa 1 34656.39945 34656.39945 187.47 <.0001
hscalc 1 4583.78372 4583.78372 24.80 <.0001
hsengl 1 1868.10929 1868.10929 10.11 0.0016
mtongue 1 1018.76587 1018.76587 5.51 0.0196
totscore 1 2754.41724 2754.41724 14.90 0.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
hsgpa 1 9570.776191 9570.776191 51.77 <.0001
hscalc 1 839.979800 839.979800 4.54 0.0339
hsengl 1 1106.961987 1106.961987 5.99 0.0150
mtongue 1 901.842716 901.842716 4.88 0.0280
totscore 1 2754.417244 2754.417244 14.90 0.0001

Estimates

Parameter Estimate Standard
Error		 t Value Pr > |t|
New Student 1 68.8304749 2.03472531 33.83 <.0001
New Student 2 89.8475792 9.20203932 9.76 <.0001

Solution

Parameter Estimate Standard
Error		 t Value Pr > |t|
Intercept -66.75515730 11.25053168 -5.93 <.0001
hsgpa 1.58917946 0.22086613 7.20 <.0001
hscalc 0.21758848 0.10207778 2.13 0.0339
hsengl -0.30024435 0.12269821 -2.45 0.0150
mtongue -4.69657329 2.12640239 -2.21 0.0280
totscore 0.97213267 0.25184911 3.86 0.0001

Gender, Ethnicity and Math performance

Replication and Prediction

Accuracy of predicting Letter Grades From Model I

The Print Procedure

Data Set WORK.STUDENT

Obs hsgpa hscalc hsengl mtongue totscore id
1 80 90 70 1 15 -1
2 80 90 0 1 15 -2

Gender, Ethnicity and Math performance

Replication and Prediction

Prediction intervals for new students

The Print Procedure

Data Set WORK.NEWGUESS

Obs id hsgpa hscalc hsengl totscore PredictedY LowerLimit UpperLimit
1 -1 80 90 70 15 68.8305 41.7684 95.893
2 -2 80 90 0 15 89.8476 57.5301 122.165